Quantum Dit Processing Method

Abstract

A method for performing quantum computations in a qudit processor. The qudit processor includes a plurality of tracks, each including a first, second, and third location. The method includes receiving qudits at a manipulation device in each track, manipulating a state of the qudit, transferring each qudit from the manipulation device to a first location in each track, enabling an interaction between the first and second qudits, transferring each qudit from the first to the second location, enabling an interaction between the first and third qudits, transferring each qudit from the second to the third location, and enabling an interaction between the first and fourth qudits. The method further includes either transferring each qudit from the third to the first location and enabling an interaction between the first and second qudits or transferring each qudit from the third location to a manipulation device in the respective track and manipulating a state of each qudit.

Description

[Technical field]

[0001] The present invention relates to a qud processor and a qud processing method. [Background technology]

[0002] Quantum computing involves the manipulation and processing of quantum bits. A quantum bit or qubit is the quantum equivalent of a classical "bit" used in classical computing, and contains information. There are several quantum computing schemes that can be used to process quantum bits. A quantum bit is generally understood to be a two-state quantum system. More generally, quantum computing can be performed using quantum dits or "qudits", whose number of states is an integer greater than or equal to two. A qutrit is another example of a qudit, whose number of states is three.

[0003] Qubits are typically arranged in arrays in qubit processors. Examples of qubits include silicon spin qubits and trapped ion qubits. In these examples, the native entanglement operation is short-range. Therefore, for two qubits in an array to interact, they must be in close proximity. To enable interactions between qubits, the array of qubits may be close-packed. However, addressing qubits in a close-packed array can lead to crosstalk, i.e., unwanted interactions between qubits.

[0004] In the near future era of intermediate-scale quantum computing (or NISQ), the number and density of qubits on each device is set to increase: for example, it is possible to create a dense two-dimensional grid of electron spin qubits using silicon metal oxide semiconductor (SiMOS) devices.

[0005] In a typical design, the number of classical control lines required to address the qubits in the array scales with the area of ​​the array, i.e., the number of qubits in the array, while the space available for positioning the classical control lines scales with the perimeter of the array. Increasing the number and density of qubits poses challenges for the classical wiring of the processor and problems with thermal dissipation.

[0006] To reduce crosstalk, qubits in the array can be spaced apart, in which case interactions between qubits can be enabled by bringing related qubits closer together, and qubit movement can be enabled, for example, by shuttling.

[0007] However, spacing qubits in this way reduces the qubit density of a qubit processor, and therefore reduces the number of qubits that can be packed onto a single integrated platform such as a silicon chip. Summary of the Invention [Problem to be solved by the invention]

[0008] It is desirable to create improved quantum bit processors and processing methods. [Means for solving the problem]

[0009] One aspect of the invention provides a method for performing quantum computations in a qudit processor, the method comprising receiving a plurality of qudits at a manipulation device in each of the separate predefined tracks, the receiving a plurality of qudits at a manipulation device in each of the separate predefined tracks comprising receiving a first qudit at a manipulation device in a first predefined track, receiving a second qudit at a manipulation device in a second predefined track at least a portion of which is within a quantum interaction distance from the first track, receiving a third qudit at a manipulation device in a third predefined track at least a portion of which is within a quantum interaction distance from the first track, and receiving a fourth qudit at a manipulation device in a fourth predefined track at least a portion of which is within a quantum interaction distance from the first track.The method further includes manipulating states of the plurality of qudits in the manipulation device within their respective tracks; transferring the plurality of qudits from the manipulation device to a first location within their respective tracks; enabling an interaction between the first qudit and the second qudit when the first qudit is at the first location within the first track and the second qudit is at the first location within the second track by positioning the first location within the first track and the first location within the second track within a quantum interaction distance; transferring the plurality of qudits from the first location to a second location within their respective tracks; and positioning the second location within the first track and the third location within the third track within a quantum interaction distance. enabling an interaction between the first qudit and the third qudit when the first qudit is at the second location in the first track and the third qudit is at the second location in the third track by positioning two locations within a quantum interaction distance of each of the first and fourth tracks; transferring the plurality of qudits from the second location to a third location in their respective tracks; and enabling an interaction between the first qudit and the fourth qudit when the first qudit is at the third location in the first track and the fourth qudit is at the third location in the fourth track by positioning the third location in the first track and the third location in the fourth track within a quantum interaction distance of each of the first and fourth tracks. The method further includes either transferring the plurality of qudits from the third location to a first location in their respective tracks and enabling an interaction between the first qudit and the second qudit when the first qudit is at the first location in the first track and the second qudit is at the first location in the second track, or transferring the plurality of qudits from the third location to the manipulation devices in their respective tracks and manipulating states of the plurality of qudits at the manipulation devices in their respective tracks.

[0010] Advantageously, the method provides synchronized periodic shuttling for a plurality of qudits, where each qudit in the plurality of qudits is transferred from one location to a next location in a defined track, the relative positioning of the tracks periodically enabling interactions between qudit pairs in the plurality of qudits.

[0011] According to this method, the first qudit is transferred around the first defined track from the manipulation device to the first location within the first track, then to the second location, and then to the third location. The first qudit is either transferred from the third location within the first track back to the manipulation device or directly to the first location. The transfer of the first qudit can then continue around the first track from one location to the next location within the track.

[0012] The manipulation devices may include initialization devices, readout devices, and / or gate devices. The manipulation devices in each track need not be the same. Typically, when the manipulation devices include initialization devices, the manipulation of the state of the qudits includes initializing the state of the qudits. Typically, when the manipulation devices include readout devices, the manipulation of the state of the qudits includes reading, i.e., measuring, the state of the qudits. Typically, when the manipulation devices include gate devices, the manipulation of the state of the qudits includes performing a gate operation on the state of the qudits. The gate operation may include an X, Y, or Z rotation, a Hadamard gate, a phase shift, or any other well-known quantum operation.

[0013] Optionally, the manipulation device in a track is configurable to initialize, read, and operate on the state of the qudits. Optionally, the manipulation device in a track can include multiple manipulation elements, each configured to initialize, read, or operate on the state of the qudits. Optionally, the manipulation device can have multiple functions, but manipulation of the state of the qudits in the manipulation device can only include performing a subset of the possible functions of the manipulation device.

[0014] The second, third and fourth qudits progress in a similar manner within their respective tracks. Optionally there may be more than four qudits and more than four tracks, typically with one qudit within each track, and each qudit may progress in a similar manner within its respective track. In other words, a nth qudit may be transferred around a nth defined track from a manipulation device in the nth track to a first location, then to a second location, and then to a third location. The nth qudit may be transferred from the third location in the nth track to either the manipulation device or the first location. The nth qudit may then continue to be transferred around the nth track from one location to the next within the track. Typically there are at least 50 tracks, and optionally there may be up to several thousand tracks. In an ideal system there is no upper limit to the number of tracks that may exist.

[0015] The second, third and fourth defined tracks are typically positioned within the qudit processor such that at least a portion of each of the second, third and fourth defined tracks is within a quantum interaction distance from the first track. The quantum interaction distance is the spacing between two qudits that enables interaction between the two qudits. The interaction can be enabled directly or indirectly. Typically, for silicon spin qudits, the quantum interaction distance required for direct interaction is between 1 nanometer and 100 nanometers, preferably between 5 nanometers and 50 nanometers. For electron spin qudits stored in quantum wells, the spacing is preferably defined as the spacing between the centers of the quantum wells in which the electrons are located. The quantum interaction distance is typically roughly equal to the size of each quantum well. Optionally, the interaction can be enabled indirectly using an intermediary dot that is preferably positioned between the two interacting qudits. In this example, the quantum interaction distance can be greater than 100 nanometers. For direct interaction, in one example, there is an overlap between the wave functions of the qudits in the pair of interacting qudits. For a mediated interaction, in one example case, it is mediated by a mediator dot, and for every qudit in the qudit pair there is wavefunction overlap with the mediator dot.

[0016] At least a portion of the second track is within a quantum interaction distance from the first track. Preferably, the portion of the second track includes a first location within the second track. Typically, the second location and the third location within the second track are not within a quantum interaction distance from the first track.

[0017] At least a portion of the third track is within a quantum interaction distance from the first track. Preferably, the portion of the third track includes a second location within the third track. Typically, the first location and the third location within the third track are not within a quantum interaction distance from the first track.

[0018] At least a portion of the fourth track is within a quantum interaction distance from the first track. Preferably, the portion of the fourth track includes a third location within the fourth track. Typically, the first location and the second location within the fourth track are not within a quantum interaction distance from the first track.

[0019] Typically, the first location of the first track is closest to the first location of the second defined track, typically, the second location of the first track is closest to the second location of the third defined track, and typically, the third location of the first track is closest to the third location of the fourth defined track.

[0020] The relative positioning of the defined tracks enables interactions between the first qudit and the second, third and fourth qudits at the first, second and third locations within the tracks, respectively. Interactions between pairs of qudits are typically enabled by positioning the locations of those qudits within a quantum interaction distance.

[0021] Additional defined tracks may be provided for additional qudits. Preferably, at least a portion of each additional track is within quantum interaction distance of another track. The other track may be the first, second, third or fourth track. For example, at least a portion of a fifth track may be within quantum interaction distance from the second track. Optionally, at least another portion of the fifth track may be within quantum interaction distance from the third track.

[0022] In each defined track, the third location is preferably the last location in each track. Typically, there are multiple intermediate locations between the first and second locations and / or between the second and third locations in each track. Optionally, the number of intermediate locations in the first track, and therefore the number of total locations, may be different from the number of intermediate locations (and the total) in the second track. Alternatively, the number of locations in each track may be the same.

[0023] Advantageously, the method provides synchronized periodic shuttling for a qudit array, the qudit array including the first, second, third, and fourth qudits in the plurality of qudits. Each qudit in the array is transferred from one location to the next in a defined track, the relative placement of the tracks periodically enabling interactions between qudit pairs in the array. In this manner, crosstalk is also advantageously reduced due to the separation of non-interacting qudits.

[0024] Preferably, the plurality of qudits is a first plurality of qudits, and the method further comprises, after the step of transferring the first plurality of qudits from the first location to a second location within their respective tracks, receiving a second plurality of qudits at a first location within each defined track, such that each track contains two qudits, each qudit of the second plurality of qudits following a corresponding qudit of the first plurality of qudits within their respective tracks.

[0025] Advantageously, this reduces the space required for processing of qudits. When there are two qudits in a defined track, the qudit density in the qudit processor is doubled. Transferring the qudits around the track reduces crosstalk since non-interacting qudits are positioned with spacing greater than the quantum interaction distance. Furthermore, processing two qudits consecutively and simultaneously in the same qudit processor advantageously improves efficiency.

[0026] Optionally, receiving a second plurality of qudits at the first locations within the respective tracks comprises receiving the second plurality of qudits at the manipulation devices within the respective defined tracks, manipulating states of the second plurality of qudits at the manipulation devices within their respective tracks, and transferring the second plurality of qudits from the manipulation devices to the first locations within their respective tracks.

[0027] Typically, the second plurality of qudits includes the same number of qudits as the first plurality of qudits. In this example, each defined track typically hosts two qudits, one from the first plurality of qudits and one from the second plurality of qudits.

[0028] Optionally, the second plurality of qudits can include a different number of qudits than the first plurality of qudits. In this example, some defined tracks can host two qudits, one qudit from the first plurality of qudits and one qudit from the second plurality of qudits, and other defined tracks can host one qudit from either the first plurality of qudits or the second plurality of qudits.

[0029] Each qudit of the second plurality of qudits follows a corresponding qudit of the first plurality of qudits in their respective tracks, and preferably, the second plurality of qudits are transferred from the first location to the second location in their respective tracks after the first plurality of qudits are transferred from the second location to the third location in their respective tracks.

[0030] Thus, at a particular point in time, the first qudit of the first plurality of qudits may be at the third location within the first track, while the first qudit of the second plurality of qudits is at the second location within the first track.

[0031] Typically, when the first qudit of the first plurality of qudits is at the third location in the first track, the fourth qudit of the first plurality of qudits is at the third location in the fourth track, and by positioning the third location in the first track and the third location in the fourth track within a quantum interaction distance, an interaction between the first and fourth qudits of the first plurality of qudits is enabled.

[0032] Typically, when the first qudit of the second plurality of qudits is at the second location in the first track, the third qudit of the second plurality of qudits is at the second location in the third track, and by positioning the second location in the first track and the second location in the third track within a quantum interaction distance, an interaction between the first and third qudits of the second plurality of qudits is enabled.

[0033] Optionally, the first qudit of the first plurality of qudits may be at the third location in the first track, while the first qudit of the second plurality of qudits is at the first location in the first track.

[0034] Typically, when the first qudit of the first plurality of qudits is at the third location in the first track, the fourth qudit of the first plurality of qudits is at the third location in the fourth track, and by positioning the third location in the first track and the third location in the fourth track within a quantum interaction distance, an interaction between the first and fourth qudits of the first plurality of qudits is enabled.

[0035] Typically, when the first qudit of the second plurality of qudits is at the first location in the first track, the second qudit of the second plurality of qudits is at the first location in the second track, and by positioning the first location in the first track and the first location in the second track within a quantum interaction distance, an interaction between the first and second qudits of the second plurality of qudits is enabled.

[0036] In this manner, interactions between qudit pairs in the first plurality of qudits and qudit pairs in the second plurality of qudits are enabled. These interactions may be enabled simultaneously or sequentially. Preferably, as the first and second plurality of qudits are transferred around a plurality of defined tracks, each qudit in the first and second plurality of qudits interacts with another corresponding qudit in an adjacent track when adjacent tracks are set within a quantum interaction distance.

[0037] Advantageously, this allows for an increased density of qudits within a qudit processor while still maintaining sufficient spacing of non-interacting qudits, thereby increasing the storage capacity of the processor without requiring additional space to process qudits. This enables scalability of the qudit processor architecture. Advantageously, the first and second pluralities of qudits are processed sequentially and simultaneously within the same qudit processor. Furthermore, the first and second pluralities of qudits may be processed independently of each other.

[0038] Optionally, the method may further include receiving a third plurality of qudits at the first locations within the respective defined tracks after the step of transferring the second plurality of qudits from the first locations to the second locations within their respective tracks, such that each track contains three qudits, each qudit of the third plurality of qudits following a corresponding qudit of the second plurality of qudits within their respective tracks.

[0039] Typically, the method may include receiving an i-th plurality of qudits at the first location within each defined track, such that each track includes i qudits, where i>3. Typically, a first qudit of the i-th plurality of qudits follows a first qudit of the third plurality of qudits (optionally with intermediate qudits), which in turn follows the first qudit of the third plurality of qudits, which in turn follows the first qudit of the second plurality of qudits, which in turn follows the first qudit of the second plurality of qudits. Typically, a first qudit of the i-th plurality of qudits follows directly after a first qudit of the (i-1)-th plurality of qudits.

[0040] Furthermore, the first qudit of the first plurality of qudits typically follows the first qudit of the i-th plurality of qudits as the first qudit of their respective plurality of qudits progresses around the first track, and the second, third, fourth, or n-th qudits of each of the second, third, fourth, or n-th tracks typically progress within their respective tracks in a similar manner.

[0041] Advantageously, this allows for a further increase in the density of qudits within a qudit processor while still maintaining sufficient spacing of non-interacting qudits, thereby further increasing the storage capacity of the processor without requiring additional space to process the qudits. Advantageously, each of the plurality of qudits is processed sequentially and simultaneously within the same qudit processor. Furthermore, each of the plurality of qudits may be processed independently of each other.

[0042] Optionally, each of the qudits in a track may be transferred simultaneously, or alternatively, one qudit in the track may be transferred separately from another qudit in the same track.

[0043] Optionally, each of the qudits in the first plurality of qudits may be transferred simultaneously, and each of the qudits in the second plurality of qudits may be transferred simultaneously. Optionally, the transfer of all of the qudits in the first plurality of qudits may occur at the same time as the transfer of all of the qudits in the second plurality of qudits, or may occur at different times. Alternatively, one or more qudits in the first and / or second plurality of qudits may be transferred separately from other qudits in the same plurality of qudits.

[0044] Typically, each qudit of the first plurality of qudits interacts only with other qudits in the first plurality of qudits, and each qudit of the second plurality of qudits interacts only with other qudits in the second plurality of qudits. In other words, the first plurality of qudits are processed independently of the second plurality of qudits. Typically, each qudit of the plurality is processed independently of each of the other plurality of qudits.

[0045] However, preferably, the method may further include enabling an interaction between the first qudit of the first plurality of qudits and the first qudit of the second plurality of qudits by positioning the first qudit of the first plurality of qudits and the first qudit of the second plurality of qudits within a quantum interaction distance along the first track.

[0046] Preferably, the positioning of the first qudit from a distinct plurality of qudits is temporary to effect an interaction therebetween, the first qudit from the distinct plurality of qudits being positionable within a quantum interaction distance for a period of time required to effect a required interaction.

[0047] Thus, the method typically further includes separating the first qudit of the first and second pluralities of qudits following the interaction between the first qudit of the first plurality of qudits and the first qudit of the second plurality of qudits such that a spacing between the first qudits of the first and second pluralities of qudits is greater than a quantum interaction distance.

[0048] Optionally, the method may further include enabling interaction between any two adjacent qudits in the same track. Generally speaking, the n qudit of the i plurality of qudits and the n qudit of the i+1 plurality of qudits may be positioned within a quantum interaction distance along the nth track, thereby enabling interaction between the n qudit of the i plurality of qudits and the n qudit of the i+1 plurality of qudits. Interaction may be enabled at a defined location, such as the first, second or third location, in the nth track. Typically, interaction is enabled at an intermediate location between the defined locations. Optionally, the intermediate location is not within a quantum interaction distance of another track. Advantageously, crosstalk is prevented as interacting qudits are separated from qudits in other tracks.

[0049] Advantageously, enabling interactions between qudits from different qudits provides a pseudo-3D architecture using a 2D architecture. Each of the tracks is arranged on a two-dimensional (2D) surface, and each of the qudits can only be transferred within the surface. However, in this manner, a normal qudit processor using a 2D architecture can be used to enable interactions between adjacent qudits in a qudit array, while in addition advantageously enabling interactions between corresponding qudits in different arrays. This therefore allows complex and efficient qudit processing using a simple architecture that is relatively easy to implement. Fewer classical control lines are required to implement the qudit processing method, and therefore the architecture is easily scalable. This architecture advantageously allows high qudit density within the qudit processor using shuttling to separate non-interacting qudits. The resulting pseudo-3D architecture includes additional connectivity that advantageously enhances the computational power of the device, for example, by enabling the implementation of transverse controlled-NOT (CNOT) gates within the 2D topology code to reduce the time of logic operations.

[0050] Optionally, interactions between qudits from different qudits may be enabled within one or more tracks within the qudit processor, or for all tracks of the qudit processor.

[0051] Following interaction between the first and fourth qudits at the third locations within their respective tracks, the qudits are transferred from the third locations within their respective tracks to either the first location or the manipulation device, this applies to each of the plurality of qudits being processed, if there is one or more of the plurality of qudits.

[0052] Optionally, transferring the plurality of qudits from the third location to the first location within their respective tracks can include transferring the plurality of qudits from the third location within their respective tracks to the manipulation device, and transferring the plurality of qudits from the manipulation device to the first location within the first track.

[0053] Optionally, the state of each qudit is manipulated, i.e. initialized, read out, or calculated (e.g. rotated) in the manipulation device. Alternatively, the qudits can be held in the manipulation device without manipulation of their state.

[0054] Optionally, qudits may be transferred from the manipulation device to a reservoir, e.g., an electronic reservoir. Optionally, qudits may be transferred from the reservoir to the first location. Optionally, one or more predefined tracks may have a corresponding reservoir.

[0055] Optionally, the state of each of the plurality of qudits may be manipulated in a manipulation device before the plurality of qudits are transferred from the manipulation device to the first location in the first track.

[0056] Advantageously, the state of each qudit in the plurality of qudits can be manipulated after each qudit has been transported around its respective track and interacted with other qudits at various locations. For example, the state of one or more qudits can be read out and the effect of the interactions on the state of the qudit can be inferred. Alternatively or additionally, a single gate operation, such as a rotation or phase shift, can be used to perform an operation on the state of one or more qudits.

[0057] Optionally, a manipulation device may be configured to manipulate the state of the qudits multiple times, for example by initially reading out the state of one or more of the plurality of qudits at the manipulation device and subsequently initializing the state of the one or more of the plurality of qudits at the manipulation device prior to transfer from the manipulation device to the first location in the first track.

[0058] Advantageously, the state of a qudit may be read, initialized, and / or operated on in preparation for a subsequent interaction. Initializing the state of a qudit typically involves providing a zero reference point against which the effects of the interaction can be measured. Alternatively, initializing the state of a qudit may involve setting a particular qudit state. Reading the state of a qudit may be used to measure the effects of a previous interaction on other qudits with which the qudit or the qudit for which the measurement is made has interacted. Operations on the state of a qudit may extend the depth of a quantum circuit.

[0059] Optionally, one or more of the qudits may be transferred from the third location (i.e. the last location in the defined track) directly to the first location without being transferred to the manipulation device. Advantageously, this may allow a longer series of quantum interactions to occur within the array prior to further manipulation. This type of configuration is only possible with a looped track, which allows the qudits to follow a circuitous path. Preferably, the qudits follow a circuitous path from the manipulation device to the manipulation device all the way around.

[0060] The steps of transferring qudits between locations typically depend on the type of qudit selected. Typically, each of the transferring steps involves shuttling. Shuttling is a process that allows qudits to be "shuttle" by modifying the local potential energy and transferring charge. A charged particle, such as an electron or ion, can be shuttled forward by raising the potential energy of its current location and lowering the potential energy of its intended shuttled location, while maintaining a high potential barrier elsewhere to guide the charged particle. This process is advantageous because it is reliable and tolerant to failures. In addition, transfer using shuttling allows global control of the movement of multiple qudit groups through the processor.

[0061] Preferably, when the transferring step involves shuttling, the qudit is an electron spin qudit or a trapped ion qudit. Conveniently, this type of qudit is easily transferred using shuttling. Typically, when the qudit is an electron spin qudit, the shuttling is electron shuttling. Typically, when the qudit is a trapped ion qudit, the shuttling is ion shuttling. Typically, the qudit is an electron spin qudit in silicon.

[0062] Optionally, the qudits in one or more tracks are shuttled along their respective tracks while the qudits in other tracks are kept stationary, advantageously enabling additional interactions between qudits within the qudit processor.

[0063] Preferably, each of said tracks forms a substantially polygonal loop. The polygonal loop is defined such that it is possible to provide a looped route from said first location to said second location, from there to said third location and then back to said first location. Optionally, in the case of tracks including intermediate locations between said first and second locations and / or between said second and third locations, said polygonal loop is defined such that it is possible to provide a looped route from said first location to any intermediate location between said first and second locations, from there to said second location and then to any intermediate location between said second and third locations and then back to said first location. Alternatively, tracks of more complex shapes can be defined, such as a figure eight where the tracks cross in the middle. Regardless of the shape, preferably said tracks form a detour loop.

[0064] As described herein, qudits may be transferred from the third location to the manipulation device and from there to the first location, or may be transferred directly from the third location to the first location, bypassing the manipulation device. Alternatively, qudits may be transferred from the third location to the manipulation device, but from there to the first location, without manipulation in the manipulation device. Each track is typically predefined within a qudit processor and includes a set of locations from which qudits can be received and transferred.

[0065] Advantageously, the looped track enables the qudits to be transferred multiple times around the loop in a circular manner, such that although there is a limited number of interactions that the qudits can undergo each time they pass the track, multiple transfers of the qudits around the track are possible due to the looped nature of the track, such that any number of interactions in the qudit processing method can be performed.

[0066] Preferably, the loop forms a closed path. Conveniently, this allows a direct transfer from the third location in the track to the first location in the track. Typically, qudits passing through the loop can be transferred out of the loop, for example to a manipulation device, and subsequently transferred from the manipulation device back to the loop after one or more steps of manipulating the state of the qudits.

[0067] Optionally, one or more locations on each track may be corners or vertices of the polygonal loop. Optionally, each of the locations on each track may be a corner of the polygonal loop. For example, the tracks may form a substantial triangle, i.e., a polygonal loop having three corners or vertices connected by three sides. The first location of the track may be positioned at a first corner, the second location of the track may be positioned at a second corner, and the third location of the track may be positioned at a third corner. A location positioned at a corner is typically positioned substantially at a corner of the polygonal loop. Typically, a location positioned at a corner is positioned at or near a curved or angled portion of the loop.

[0068] Advantageously, when the location is at a corner, the interactions between qudits in adjacent tracks associated with the corner location are well defined, and interactions at corners advantageously have high fidelity since the qudits are stationary during the interaction.

[0069] Alternatively or additionally, one or more locations on each track may be set along an edge of the polygonal loop. Optionally, each location on each track may be set along an edge of the polygonal loop. For example, the tracks may be substantially triangular. The first location of the track may be positioned along a first edge, the second location of the track may be positioned along a second edge, and the third location of the track may be positioned along a third edge. The locations positioned along an edge may be positioned within an area that is less than the length of the edge. Alternatively, the locations positioned along an edge may be positioned along an area that extends along the edge and occupies substantially the entire edge.

[0070] Advantageously, when the location is located along an edge, interaction between qudits in adjacent tracks associated with the edge location can occur over long periods of time.

[0071] Locating one or more locations along the edge advantageously reduces the effective processing time of an interaction around the loop. This is particularly beneficial when the rate limiting step is one or more interactions. The effective processing time of an interaction is preferably reduced by extending the gate operation over a portion of the edge of the loop and performing the interaction in parallel with the transfer of the qudits along the track. The effective processing time can be further reduced by extending the gate operation over the entire edge of the loop and performing the interaction in parallel with the transfer of the qudits.

[0072] Another aspect of the invention provides a qudit processor for performing a method according to the first aspect, the qudit processor including a plurality of predefined distinct tracks, each track configured to receive one or more qudits, each track configured to transfer its one or more qudits along its track, at least a portion of each track being positioned within a quantum interaction distance from one or more other tracks such that interactions between qudits in different tracks are effective.

[0073] Advantageously, the qudit processor provides a platform for processing one or more qudit arrays simultaneously. Interaction between qudits in adjacent tracks (i.e., inter-track interaction) is enabled by positioning one location in one track within a quantum interaction distance from another location in the other track. When two qudits are positioned at the one and the other locations, respectively, they are close enough to interact, enabling interaction between the two qudits.

[0074] A further aspect of the invention provides a qudit processor including a first predefined track, the track forming a loop. The qudit processor also includes second through k predefined tracks, k>3, each of the second through k tracks forming a loop. Each track (i.e., each of the first and second through k tracks) is configured to receive one or more qudits and forward the one or more qudits along the track. Each of the second through k predefined tracks is distinct from the first predefined track. At least a portion of each of the second through k tracks is located within a quantum interaction distance from the first track such that interaction between qudits in the first track and the second through k tracks is effective.

[0075] Conveniently, the qudit processor enables simultaneous processing of one or more qudits. An interaction is enabled between a qudit in the first track and a qudit in the second to kth tracks. An inter-track interaction is enabled by positioning each of the portions of the second to kth tracks within a quantum interaction distance from a portion of the first track. An interaction is enabled between two qudits when they are positioned on the portions of the tracks that are within a quantum interaction distance of each other such that they are sufficiently close to interact.

[0076] The qudit processor is typically implemented in a silicon device, and preferably the tracks are gate-defined using a plurality of electrodes. Typically the tracks are formed as a result of an electric field created by a pattern of electrodes. This is called electrostatic confinement. Optionally, the qudits can be confined within a first two-dimensional plane within the qudit processor, and the electrodes can be provided in a second two-dimensional plane separate from the first two-dimensional plane. Preferably, the vertical spacing between the first and second two-dimensional planes is small enough that application of a bias potential to an electrode in the second two-dimensional plane can be used to manipulate the state of the qudits in the first two-dimensional plane.

[0077] Typically, each track is defined by applying a potential to a corresponding electrode, the magnitude of which can be modified to enhance the confinement of the qudits within said track.

[0078] Alternatively, a track may be defined by a structural deformation in the first two-dimensional plane that contains the qudits.

[0079] The transfer of one or more qudits typically involves shuttling. Preferably, the shuttling is effected by modifying one or more potentials applied to the electrodes. Typically, switching the potentials moves the qudit along a track. Conveniently, this can be performed globally such that multiple qudits within a qudit processor can be shuttled simultaneously.

[0080] In a qudit processor, k>3. Thus, a qudit processor includes at least a first defined track, a second defined track, a third defined track, and a fourth defined track. A qudit processor optionally includes more defined tracks. Typically, a qudit processor has at least 50 tracks, and optionally there may be thousands of tracks, although there is no upper limit to the number of tracks.

[0081] Typically the loop is closed. In other words it is possible to provide an endless loop that allows the qudits to circulate indefinitely. Preferably the loop is substantially polygonal. The loop geometry of the track enables the qudits in the processor to circulate around the track multiple times, advantageously removing the limit on the number of processing steps that can be performed within a single quantum circuit. Preferably the loop extends from a manipulation device back to the same manipulation device.

[0082] A qudit processor may include additional manipulation devices that are not directly connected to any of the defined tracks. A qudit may be transferred from a track to one of these manipulation devices in order to manipulate the state of the qudit. Following manipulation, the qudit may be transferred to a reservoir and another qudit may be transferred around the track, or the qudit may be transferred back to the same track or another track.

[0083] Interaction between qudits in the same track (i.e., intra-track interaction) can be enabled by positioning two qudits within a quantum interaction distance in a track. The combination of inter-track and intra-track interactions advantageously provides a pseudo-3D architecture using a 2D qudit processor architecture. This therefore enables complex and efficient qudit processing using a simple architecture that is relatively easy to implement. The use of inter-track and intra-track interactions provides additional connectivity and advantageously enhances the computational power of the qudit processor. Quantitative processing methods that typically require complex and costly to create 3D qudit arrays can advantageously instead be performed using the qudit processing methods and qudit processors of the present invention.

[0084] Typically, each of the first and second through kth tracks includes one or more locations. For example, each track can include a first location, a second location, and a third location. Qudits within a track can be received at each location and typically transferred from the first location to the second location, from there to the third location, and then back to the first location.

[0085] Typically, each track (i.e., the first and second through k-th tracks) further includes a manipulation device configured to initialize and / or read and / or operate on the state of the qudits on that track. For example, a manipulation device in a track may have an initialization function, a manipulation device in a track may have a read function, and a manipulation device in a track may have a gate operation function. Furthermore, a manipulation device may have two of these functions, such as initialization and read, read and gate operation, or initialization and gate operation. Furthermore, a manipulation device may have all three of the above functions, i.e. initialization, read, and gate operation. A manipulation device having an initialization function may be referred to as an initialization device. A manipulation device having a read function may be referred to as a read device. A manipulation device having a gate operation function may be referred to as a gate device.

[0086] A manipulation device having an initialization function is typically used to initialize the state of one or more qudits on the track, for example, qudits may be received at the initialization device or optionally from the third location of the track, and after initializing the state of the qudits, the qudits may be transferred to the first location of the track.

[0087] A manipulation device having a read function is typically used to read out the state of one or more qudits on the track. For example, the qudit may be transferred from the third location of the track to the manipulation device, and then the qudit may be transferred to the first location of the track after reading out the state of the qudit. Optionally, the manipulation device may be used to further manipulate the state of the qudit and transfer it from the initialization device to the first location of the track.

[0088] A manipulation device having a gate operation function is typically used to perform a gate operation on the state of one or more qudits on its track. The gate operation can be, for example, a rotation or a phase shift. For example, the rotation can be an X rotation, a Y rotation, a Z rotation, or a Hadamard operation.

[0089] Optionally, the manipulation device for one or more tracks includes multiple manipulation elements, each configured to manipulate the state of the qudits on that track. For a manipulation device having multiple manipulation elements, the functionality of each manipulation element can be the same, or optionally, one or more of the manipulation elements can have different functionality.

[0090] Advantageously, the inclusion of multiple operational elements allows operations on multiple qudits to be performed in parallel, and thus where the rate-limiting step is an operational step such as reading or initialising the state of the qudit, or performing a gate operation on the state of the qudit, throughput can be increased, in other words the spacing between qudits in the track can be reduced, allowing more qudits to occupy the track at any one time.

[0091] Typically, the addition of multiple manipulation elements does not impact the processing time in the qudit processing method, however, the architecture described herein advantageously allows the inclusion of multiple manipulation elements to be used to reduce the effective processing time and therefore the overall processing time of multiple qudits in the processor.

[0092] The rate-limiting step typically depends on the quantum circuit implemented in the qudit processor. The rate-limiting step can be initialization, readout, gate operations and / or interactions, or transfer. Since the transfer of qudits is relatively fast compared to other processes, it is usually not the rate-limiting step.

[0093] A further aspect of the invention provides a method of performing quantum computation in a qudit processor, the method including the steps of manipulating a state of a first qudit at a manipulation device within a defined track, transferring the first qudit from the manipulation device to a first location within the track, and transferring the first qudit from the first location within the track to a second location within the track. The method further includes the steps of manipulating a state of a second qudit at the manipulation device within the track, transferring the second qudit from the manipulation device to the first location within the track, transferring the first qudit from the second location within the track to a third location within the track, and transferring the second qudit from the first location within the track to the second location within the track. The method further includes either transferring the first qudit from the third location in the track to the first location in the track, or transferring the first qudit from the third location in the track to the manipulation device in the track and manipulating a state of the first qudit at the manipulation device. The method further includes transferring the second qudit from the second location in the track to the third location in the track. One or more qudit operations and / or interactions are enabled for the first and second qudits on the track.

[0094] Advantageously, the method enables serial, simultaneous and optionally independent processing of multiple qudits, where the first qudit and the second qudit follow the same path through the qudit processor and thus the space occupied by these qudits is smaller than if the two qudits were processed at separate locations within the processor.

[0095] The second qudit follows the first qudit around the defined track, moving from one location to the next, preferably such that the transfer of the first qudit from an nth location in the track enables the transfer of the second qudit to the nth location.

[0096] The states of the first and second qudits are manipulated in an operating device. The operating can include one or more of initialization, readout, and calculation. Optionally, the operating device includes a group of operating elements. For example, the first qudit can be manipulated in a first operating element and the second qudit can be manipulated in a second operating element. Alternatively, the first and second qudits can be manipulated in the same operating element.

[0097] The first and second qudits each travel from the manipulation device to the first location, from there to the second location, to the third location, and from there back to the first location. Optionally, the first and / or second qudits can be transferred from the third location to a manipulation device capable of manipulating the state of the qudits. Typically, the state of the first and / or second qudits can be manipulated multiple times before being transferred from the manipulation device to the first location. Alternatively, the state of the first and / or second qudits can be transferred directly from the manipulation device to the first location following a manipulation step. Alternatively, the state of the first and / or second qudits can be unmanipulated while in the manipulation device. As a further alternative, the first and / or second qudits can be transferred directly from the third location to the first location.

[0098] The track may optionally include one or more intermediate locations between the first and second locations, and one or more intermediate locations between the second and third locations.

[0099] One or more qudit operations and / or interactions are enabled for the first and second qudits on the track. Typically, operations and / or interactions are enabled at at least one of the first, second, and third locations, but operations and / or interactions may be enabled at one or more intermediate locations in addition to or instead of the first, second, and third locations. Typically, the operations are single-qudit operations. Typically, the interactions are two-qudit operations occurring between the first qudit and another qudit in another track, or between the second qudit and another qudit in another track.

[0100] The method advantageously provides periodic interaction for a plurality of qudits: the first and / or second qudits can be transferred around the loop indefinitely, thereby advantageously allowing the implementation of quantum circuits of arbitrary depth using the method.

[0101] More than two qudits can be processed simultaneously within the track, with each qudit being spatially separated from adjacent qudits and following the same path as the preceding qudit. Optionally, j qudits can be processed within the track according to this method. Typically, after the j-1 qudit has been transferred from the m location within the track, the j qudit can be transferred to the m location within the track.

[0102] Preferably, the predefined track is a first predefined track, and the method further comprises: manipulating a state of another first qudit in a manipulation device in a second predefined track distinct from the first predefined track; transferring the another first qudit from the manipulation device in the second track to a first location in the second track; and transferring the another first qudit from the first location in the second track to a second location in the second track. Further, the method preferably comprises manipulating a state of another second qudit in the manipulation device in the second track; transferring the another second qudit from the manipulation device in the second track to the first location in the second track; transferring the another first qudit from the second location in the second track to a third location in the second track; and transferring the another second qudit from the first location in the second track to the second location in the second track. Further, the method preferably includes either transferring the other first qudit from the third location in the second track to the first location in the second track, or transferring the other first qudit from the third location in the second track to the manipulation device in the second track and manipulating a state of the other first qudit at the manipulation device in the second track. Further, the method preferably includes transferring the other second qudit from the second location in the second track to the third location in the second track. Preferably, one or more qudit operations and / or interactions are enabled for the other first qudit and the other second qudit on the second track.

[0103] Advantageously, the method further allows for serial, simultaneous and optionally independent processing of a plurality of qudits. Optionally, the first and further first qudits form part of a first qudit array and the second and further second qudits form part of a second qudit array. Preferably, the first and second qudit arrays can be processed simultaneously within the same qudit processor.

[0104] The first qudit array and the second qudit array can each contain more than two qudits. Advantageously, using this method, multiple qudits can be processed in a small space, which in turn increases the qudit density, while reducing crosstalk between non-interacting qudits.

[0105] Preferably, the first location in the first track and the first location in the second track are within a quantum interaction distance, and further the method includes enabling an interaction between the first qudit and the another first qudit when the first qudit is at the first location in the first track and the another first qudit is at the first location in the second track, and enabling an interaction between the second qudit and the another second qudit when the second qudit is at the first location in the first track and the another second qudit is at the first location in the second track.

[0106] Advantageously, the method enables interactions between qudits in the first track and qudits in the second track, which advantageously increases options for circuit design and enables two-qudit interactions between qudits in different tracks. Using the method, two-qudit interactions between qudit pairs in the same array are enabled.

[0107] Optionally, the first qudit and the second qudit may be positioned within a quantum interaction distance along the first track. The first qudit is in the first array and the second qudit is in the second array, and thus the method advantageously enables interaction between qudits in the first array and qudits in the second array. The method advantageously provides a pseudo-3D architecture using a 2D qudit processor architecture. This therefore enables complex and efficient qudit processing using a simple architecture that is relatively easy to implement.

[0108] In another aspect of the invention, a qudit processor is provided that includes a manipulation device and a defined track that forms a loop from the manipulation device to the manipulation device. There are at least first, second and third gate devices that are configured to perform quantum operations provided at first, second and third locations along the track, respectively. The track is configured to receive a plurality of qudits and transfer the plurality of qudits continuously around the track in the loop in a first direction from the manipulation device to a first location, a second location and a third location, enabling one or more qudit operations at the first, second and third gate devices and / or enabling one or more quantum interactions for one or more of the plurality of qudits. Advantageously, the processor enables continuous and simultaneous processing of a plurality of qudits within the defined track. Providing a processor with this advantage further enables a higher qudit density within the processor, since the same number of qudits occupies less space.

[0109] The first direction is from the first location to the second location, from the second location to the third location, and from the third location to the first location. Preferably, the track is an infinite loop from the manipulation device back to the same manipulation device. In this way, qudits can circulate around the loop moving continuously between the first, second, and third locations and from the third location back to the first location indefinitely.

[0110] Preferably, the interaction between the two qudits is effected by positioning the two qudits within a quantum interaction distance.

[0111] Another aspect of the invention provides a method for performing quantum computations in a qudit processor, the method comprising receiving a plurality of qudits at a manipulation device in a respective predefined track, where receiving the plurality of qudits at a manipulation device in a respective predefined track comprises receiving a first qudit at a manipulation device in a first predefined track, receiving a second qudit at a manipulation device in a second predefined track, at least a portion of which is within a quantum interaction distance from the first track, receiving a third qudit at a manipulation device in a third predefined track, at least a portion of which is within a quantum interaction distance from the first track, and receiving a fourth qudit at a manipulation device in a fourth predefined track, at least a portion of which is within a quantum interaction distance from the first track.The method further includes manipulating states of the plurality of qudits in the manipulation device within their respective tracks; transferring the plurality of qudits from the manipulation device to a first location within their respective tracks; enabling an interaction between the first qudit and the second qudit when the first qudit is at the first location within the first track and the second qudit is at the first location within the second track by positioning the first location within the first track and the first location within the second track within a quantum interaction distance; transferring the plurality of qudits from the first location to a second location within their respective tracks; and positioning the second location within the first track and the second location within the third track within a quantum interaction distance. enabling an interaction between the first qudit and the third qudit when the first qudit is at the second location in the first track and the third qudit is at the second location in the third track by positioning the locations within a quantum interaction distance; transferring the plurality of qudits from the second location to a third location in their respective tracks; and enabling an interaction between the first qudit and the fourth qudit when the first qudit is at the third location in the first track and the fourth qudit is at the third location in the fourth track by positioning the third location in the first track and the third location in the fourth track within a quantum interaction distance.The method further includes either transferring the plurality of qudits from the third location to the first location within their respective tracks and enabling an interaction between the first qudit and the second qudit when the first qudit is at the first location within the first track and the second qudit is at the first location within the second track, or transferring the plurality of qudits from the third location to the manipulation devices within their respective tracks and manipulating states of the plurality of qudits at the manipulation devices within their respective tracks.

[0112] A further aspect of the invention provides a qudit processor for performing a method according to the first aspect, the qudit processor comprising a plurality of defined tracks, each track configured to receive one or more qudits, each track configured to forward its one or more qudits along its track, at least a portion of each track being positioned within a quantum interaction distance from one or more other tracks such that interactions between qudits in different tracks are effective.

[0113] An aspect of the invention provides a qudit processor including a first predefined track, the track forming a loop. The qudit processor also includes second through k predefined tracks, k>3, each of the second through k tracks forming a loop. Each track (i.e., each of the first and second through k tracks) is configured to receive one or more qudits and to forward the one or more qudits along its track. At least a portion of each of the second through k tracks is positioned within a quantum interaction distance from the first track such that interactions between qudits in the first track and the second through k tracks are effective.

[0114] In many instances, the qudits may be qubits, which correspond to a two-state quantum system, although those skilled in the art will appreciate that in other applications, more quantum states may be used.

[0115] It will be apparent that method features may be provided as apparatus features and vice versa. In addition, preferred features of one aspect of the invention may be provided in combination with other features of the invention.

[0116] The present invention will now be described in detail with reference to the accompanying drawings, in which: FIG. [Brief description of the drawings]

[0117] [Figure 1] FIG. 2 is a schematic plan view of a qubit processor. [Diagram 2] FIG. 2 is a schematic plan view of a qubit processor. [Figure 3A] A logical schematic of a qubit processor. [Figure 3B] FIG. 3B is a schematic plan view of the qubit processor logically illustrated in FIG. 3A. [Figure 4A] A logical schematic of a qubit processor. [Figure 4B] FIG. 4B is a schematic plan view of the qubit processor logically illustrated in FIG. 4A. [Figure 5A] A logical schematic of a qubit processor. [Figure 5B] FIG. 5B is a schematic plan view of the qubit processor logically illustrated in FIG. 5A. [Figure 6] FIG. 2 is a schematic plan view of a qubit processor. [Figure 7A] A logical schematic of a qubit processor. [Figure 7B] FIG. 7B is a schematic plan view of the qubit processor logically illustrated in FIG. 7A. [Figure 8A] A logical schematic of a qubit processor. [Figure 8B] FIG. 8B is a schematic plan view of the qubit processor logically illustrated in FIG. 8A. [Figure 9A] A schematic diagram of a qubit processor. [Figure 9B] FIG. 9B is a schematic diagram of the qubit processor of FIG. [Figure 10] 1 is a flow chart of a quantum bit processing method. [Figure 11] 1 is a flow chart of a quantum bit processing method. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0118] FIG. 1 is a schematic plan view of a qubit processor at time t. The qubit processor includes a defined track 101. In this example, the track 101 is a substantially square loop. In this example, the manipulation devices 131, 132 have an initialization function and a readout function. The manipulation device having the initialization function is called the initialization device 131, and the manipulation device having the readout function is called the readout device 132. The initialization device 131 and the readout device 132 form part of the manipulation devices 131, 132 connected to the track 101. In alternative examples, only the initialization device or only the readout device may be present. In further examples, the manipulation devices may include gate devices in addition to or instead of the initialization device and / or the readout device.

[0119] Within the track 101 there are four conceptual locations 111, 112, 113, 114, namely a first location 111 at a first corner of the track 101, a second location 112 at a second corner of the track 101, a third location 113 at a third corner of the track 101, and a fourth location 114 at a fourth corner of the track 101. The fourth location in this example is the last location in the track. Any conceivable labeling convention can be used for these locations, depending on the number of locations there are and the shape of the associated track. Each location is provided with a gate device 115, 116, 117, 118. It is possible to enable qubit operations and / or interactions at one or more of the gate devices 115-118.

[0120] In FIG. 1, there are six qubits 121, 122, 123, 124, 125, and 126. At time t, qubits 121-126 are approximately equally spaced around track 101. During at least a portion of the operation, the qubits are in motion and are transferred in a clockwise direction around the loop as indicated by the arrows in track 101. At time t, the first qubit 121 is at the last location, i.e., the fourth location 114, in this clockwise orbit starting from initialization device 131. The first qubit 121 undergoes a quantum operation at the fourth location 114. The particular quantum operation performed on the first qubit 121 is determined by a gate device 118 present at the fourth location 114. Each of gate devices 115-118 in this example enables a single qubit operation such as an X, Y, or Z rotation, a Hadamard gate, a phase shift, or any other well-known quantum operation. In another example, a gate device can enable two-qubit interaction.

[0121] 1 illustrates a single track 101. However, typically multiple tracks are arranged in an array throughout a qubit processor, with a portion of each track within quantum interaction distance of at least one adjacent track, enabling interactions between qubits in different tracks.

[0122] At time t, the second qubit 122 is between the third location 113 and the fourth location 114. Prior to time t, the second qubit 122 was at the third location 113 and underwent a quantum operation at the third location 113 in accordance with the gate device 117. Following the operation at the third location 113, the second qubit 122 is transferred from the third location 113 in the track 101 to the fourth location 114 in the track 101. In this example, the transfer from the third location 113 to the fourth location 114 includes a transfer of the second qubit 122 from the third location 113 to a location intermediate between the third location 113 and the fourth location 114, and then a transfer of the second qubit 122 from the location intermediate between the third location 113 and the fourth location 114 to the fourth location 114. The second qubit 122 is at a location intermediate between the third location 113 and the fourth location 114 at time t.

[0123] At time t, the third qubit 123 is at a location midway between the second location 112 and the third location 113. Before time t, the third qubit 123 is at the second location 112, and after time t, the third qubit 123 will be transferred to the third location 113. In this example, the transfer from the second location 112 to the third location 113 includes transferring the third qubit 123 from the second location 112 to a location midway between the second location 112 and the third location 113, and then transferring the third qubit 123 from the location midway between the second location 112 and the third location 113 to the third location 113. The third qubit 123 is at a location midway between the second location 112 and the third location 113 at time t.

[0124] At time t, a fourth qubit 124 is at the second location 112. The fourth qubit 124 is undergoing a quantum operation at the second location 112. The particular quantum operation performed on the fourth qubit 124 at time t is determined by a gating device 116 at the second location 112. The gating device 116 at the second location 112 may be the same as or different from the gating device 118 at the fourth location 114.

[0125] At time t, the fifth qubit 125 is at a location midway between the first location 111 and the second location 112. Before time t, the fifth qubit 125 is at the first location 111, and after time t, the fifth qubit 125 will be transferred to the second location 112. In this example, the transfer from the first location 111 to the second location 112 includes transferring the fifth qubit 125 from the first location 111 to a location midway between the first location 111 and the second location 112 within the track 101, and then transferring the fifth qubit 125 from the location midway between the first location 111 and the second location 112 to the second location 112. The fifth qubit 125 is at a location midway between the first location 111 and the second location 112 at time t.

[0126] At time t, the sixth qubit 126 is between the initialization device 131 and the first location 111. In this example, prior to time t, the sixth qubit 126 was in the initialization device 131. The state of the sixth qubit 126 was initialized while the sixth qubit 126 was in the initialization device 131. After initialization, the sixth qubit 126 was transferred from the initialization device 131 towards the first location 111 in the track 101. In this example, transferring the sixth qubit 126 from the initialization device 131 to the first location 111 includes transferring the sixth qubit 126 from the initialization device 131 to a location intermediate between the initialization device 131 and the first location 111, and then transferring the sixth qubit 126 from the intermediate location to the first location 111. The sixth qubit 126 is in a location intermediate between the initialization device 131 and the first location 111 at time t.

[0127] In another example, before time t, the sixth quantum bit 126 is transferred from the fourth location 114 to the first location 111 without being transferred to the initialization device 131 or the readout device 132.

[0128] In this example, the sixth qubit 126 follows the fifth qubit 125, which follows the fourth qubit 124, which follows the third qubit 123, which follows the second qubit 122, which follows the first qubit 121, which follows the sixth qubit 126. In another example, there can be n qubits, where n>6, and the first qubit 121 follows the nth qubit. In this example, each qubit follows the preceding qubit in a clockwise direction around the track 101, as shown by the arrows in the track 101, with each qubit separated by a distance greater than the quantum interaction distance. In another example, the qubits can proceed in a counterclockwise direction around the track 101.

[0129] In a further example, two adjacent qubits (i.e., first and second qubits 111, 112; second and third qubits 112, 113; third and fourth qubits 113, 114; fourth and fifth qubits 114, 115; fifth and sixth qubits 115, 116; or sixth and first qubits 116, 111) can be positioned within a quantum interaction distance to enable a two-qubit interaction between the qubit pair. The positioning can occur by holding the preceding qubit stationary and transferring the subsequent qubit towards the preceding qubit. Alternatively, the positioning can occur by holding the subsequent qubit stationary and transferring the preceding qubit backwards along the track towards the subsequent qubit. As a further alternative, this positioning can occur by transferring both the leading qubit and the trailing qubit towards each other (i.e., transferring the trailing qubit along track 101 in the normal transfer direction and the leading qubit in the opposite direction). Positioning that places adjacent qubits within the quantum interaction distance is temporary, but allows sufficient time for the qubits to interact. Following the interaction, they are separated by transferring the leading qubit forward along track 101 such that they are separated by a distance greater than the quantum interaction distance.

[0130] 1 illustrates a qubit processor at time t. The number of qubits on track may vary over time. For example, one or more qubits may be transferred from the fourth location 114 to the readout device 132, and the state of the one or more qubits may be read out. Alternatively, one or more initialized qubits may be transferred from the initialization device 131 to the first location 111. After being read out, the qubits may be transferred from the readout device 132 to the initialization device 131.

[0131] As shown in FIG. 1, at time t, the first location 111 and the third location 113 are empty, and the second location 112 and the fourth location 114 are occupied. In this example, each location 111-114 corresponds to a particular quantum operation, so that each qubit 121-126 undergoes a first quantum operation when it is at the first location 111. Each qubit 121-126 undergoes a second quantum operation when it is at the second location 112. Each qubit 121-126 undergoes a third quantum operation when it is at the third location 113. Each qubit 121-126 undergoes a fourth quantum operation when it is at the fourth location 114. In examples with more than four locations, this may be true for each location on the track. In this way, all qubits 121-126 in the track can be processed in parallel.

[0132] Alternatively, one or more locations can be reconfigured during a qubit processing sequence to perform different quantum operations, which may be employed to implement quantum circuits of arbitrary depth on tracks of finite size.

[0133] The time it takes each qubit to go around the loop is T loop This can also be called the cycling period, which is the sum of each processing step performed around the loop. A processing step includes transferring a qubit from one location to the next around the loop, performing a quantum operation and / or interaction involving one or two qubits, initializing the state of the qubit if performed, and reading out the state of the qubit if performed. The time it takes to perform each of the m processing steps in the track is τ m and T loop Let m be the number of τ in the track. m It is equal to the sum of all τ m typically varies for each processing step and for different quantum circuits.

[0134] The number of qubits that can be processed in the track 101 is T loopand the time required to execute the longest processing step, i.e., the rate-limiting step time τ max However, as we will see later, the time it takes to execute the rate limiting step depends on τ max can be shortened. In this example, the qubits are processed in a steady state, in other words undergoing processing steps continuously, as defined above. Thus, the number of qubits that can be processed simultaneously in the track 101 is K loop =T loop / τ max This avoids collisions between adjacent qubits.

[0135] In another example, the number of qubits that can be processed at any one time in a track is increased by including a buffering step between processing steps. The buffering step involves leaving qubits stationary on the track for a period of time. The buffering step can be employed when the preceding qubits are undergoing a lengthy processing step. This avoids the need for long rate-limiting steps, i.e. large τ max The effect of the buffering step is reduced.

[0136] T loop may vary as a qubit moves around the track. This may be because some processing steps are omitted or modified as a qubit or qubits move around the track. Optionally, a buffering step can be included to ensure that qubits in a track do not collide if a processing step is omitted.

[0137] Figure 2 diagrammatically illustrates a qubit processor at a time t. The qubit processor illustrated in Figure 2 shares similar features with the qubit processor shown in Figure 1, and similar reference numbers are used to refer to similar features.

[0138] The qubit processor of Figure 2 includes a substantially rectangular defined track 201, with four locations 211, 212, 213, 214 located at the four corners of the track 201, and six qubits 221, 222, 223, 224, 225, 226 progressing clockwise around the track 201 in that order. There are four gate devices 215, 216, 217, 218, one positioned at each location 211-214 in the track 201. For simplicity, the qubits 221-226 are shown in the same positions within the track 201 as in Figure 1. However, it will be understood that the qubits 221-226 progress clockwise around the track 201, as indicated by the arrows.

[0139] In FIG. 2, the qubit processor includes multiple operation elements 231, 232, 233, 234. In this example, the qubit processor includes a first initialization element 231, a second initialization element 232, a first readout element 233, and a second readout element 234. In another example, each element 231-234 may have the same function (i.e., one of readout, initialization, or operation), or the first element 231 may have a first function and the remaining elements 232-234 may have a second function, or the first element 231 may have a first function and the second element 232 may have a second function, and the third and fourth elements 233, 234 may have a third function. In a further example, one or more of the elements 231-234 may have multiple functions. Any combination of operation elements is possible.

[0140] 2 illustrates a single track 201. However, multiple tracks are typically arranged in an array throughout a qubit processor, with a portion of each track within quantum interaction distance of at least one adjacent track to enable interactions between qubits in different tracks. One or more tracks may include multiple operational elements, and tracks may contain different operational elements and / or different operational elements having different functions.

[0141] Each of the multiple operation elements 231 to 234 shortens the effective processing time required for the operation. This shortens the overall processing time without using the empty processing step such as the buffering described above. Each operation element can operate the state of one quantum bit at any time. Therefore, when there are multiple initialization elements as shown here, it is possible to initialize the respective states of multiple quantum bits in parallel. Similarly, when there are multiple read elements as shown here, it is possible to read the respective states of multiple quantum bits in parallel. Furthermore, when there are multiple gate operation elements, parallel operation of the respective states of multiple quantum bits is possible. When there are multiple gate operation elements, the quantum operation performed in each gate operation element does not need to be the same.

[0142] In general, increasing the manipulation elements by a factor of m reduces the effective manipulation time by a factor of m, as long as there are more than m qubits in the track.

[0143] The time required to initialize, read, and / or compute the state of a qubit may be longer than the time required to perform any of the other processing steps. This means that the manipulation step may be the rate-limiting step, i.e., the time required to perform any of the initialization, read, or computation processing steps is longer than τ max Therefore, when m is multiple, if m operation elements are included to reduce the effective operation time, the rate limiting step time τ max is τ max / m, the number of qubits that can be processed simultaneously in track 101, K loop increases.

[0144] When an initialization, or readout, or gating operation is a rate-limiting step, by using elements of multiple initialization, readout, and / or gating operations, it is possible to reduce the effective processing time such that a particular operational step is no longer the rate-limiting step.

[0145] 2 , first qubit 221 is at fourth location 214 in track 201. In this example, first qubit 221 is transferred to first readout element 233 after time t. After transfer of first qubit 221 to first readout element 233, second qubit 222 is transferred to second readout element 234. While second qubit 222 is received by second readout element 234, the state of first qubit 221 is read out at first readout element 233. Thus, the states of first qubit 221 and second qubit 222 are read out in parallel.

[0146] In this example, the first qubit 221 is transferred to the first initialization element 231 after the state of the first qubit 221 is read out at the first readout element 233. Once the first qubit 221 is no longer at the first readout element 233, the third qubit 223 is received by the first readout element 233 to read out the state of the third qubit 223. At the first initialization element 231, the state of the first qubit 221 is initialized while the states of the second and / or third qubits 222, 223 are read out at the first and second readout elements 233, 234. The first qubit 221 is transferred to the first location 211 in the track 201 once the state of the first qubit 221 has been initialized.

[0147] In another example, one or more of the first, second, and third quantum bits 221-223 are transferred directly from the fourth location 214 to the first location 211 without being transferred to the readout elements 233, 234 or the initialization elements 231, 232.

[0148] Subsequent qubits in the track follow the path of the qubits described above. Each qubit 221-226 is transferred from the fourth location 214 in the track 201 to either an operating element 231-234 or the first location 211 in the track 201.

[0149] 3A diagrammatically illustrates a qubit processor having an array of qubits, where there are five qubits, 321, 341, 351, 361, 371. A first qubit, 321, can interact with a second, third, fourth, and fifth qubit, 341, 351, 361, 371, using first, second, third, and fourth gate devices, 315, 316, 317, 318, respectively.

[0150] FIG. 3B diagrammatically illustrates the qubit processor of FIG. 3A at time t1. The qubit processor includes five defined tracks 301, 302, 303, 304, 305. The second, third, fourth, and fifth tracks 302-305 are arranged around the first track 301 such that the corners of the second through fifth tracks 302-305 are within quantum interaction distance of the corners of the first track 301. This enables interaction between qubits in adjacent tracks. Crosstalk between qubits in tracks 301-305 is avoided because the qubits are spaced apart. This spacing also provides additional space for classical control wiring.

[0151] In this example, the nearest portions of adjacent tracks 301-305 enable direct interaction between the qubits in the adjacent tracks. In another example, the nearest portions of adjacent tracks are separated using a mediator dot that mediates, or enables, two-qubit interaction in the form of an elongated quantum dot positioned between the adjacent tracks. In either case, the nearest portions of at least some of the adjacent tracks are within a quantum interaction distance from each other. The use of a mediator dot to mediate interaction between qubit pairs can be implemented in any of the qubit processors described herein.

[0152] Each track includes a manipulation device 331, 332, 333, 334, 335. Each manipulation device 331-335 can include one or more manipulation elements, as described in more detail in connection with FIG. 2. In one example based on FIG. 3B, one or more of the manipulation devices 331-335 can be composed of one or more gate operation elements. Each gate operation element can be configured to perform the same gate operation, a different gate operation, or a variation of the same gate operation. For example, each gate operation element can be configured to perform a rotation, but the rotations can be different for different gate operation elements.

[0153] 3B, each qubit 321, 341, 351, 361, 371 is in a separate track 301-305, i.e., first qubit 321 is in first track 301, second qubit 341 is in second track 302, third qubit 351 is in third track 303, fourth qubit 361 is in fourth track 304, and fifth qubit 371 is in fifth track 305. In this example, each qubit 321, 341, 351, 361, 371 is transferred from one location to the next in a clockwise manner around its respective track 301-305.

[0154] Each track 301-305 is substantially square and includes four locations, one at each corner. The first track 301 includes a first location 322, a second location 323, a third location 324, and a fourth location 325. The second track 302 includes a first location 342, a second location 343, a third location 344, and a fourth location 345. The third track 303 includes a first location 352, a second location 353, a third location 354, and a fourth location 355. The fourth track 304 includes a first location 362, a second location 363, a third location 364, and a fourth location 365. The fifth track 305 includes a first location 372, a second location 373, a third location 374, and a fourth location 375.

[0155] Within each track 301-305, a respective quantum bit 321, 341, 351, 361, 371 is received by a manipulation device 331-335, manipulated, and transferred from the manipulation device 331-335 to a first location 322, 342, 352, 362, 372, from the first location 322, 342, 352, 362, 372 to a second location 323, 343, 353, 363, 373, from the second location 323, 343, 353, 363, 373 to a third location 324, 344, 354, 364, 374, and from the third location 324, 344, 354, 364, 374 to a fourth location 325, 345, 355, 365, 375.

[0156] In one example, each qubit 321, 341, 351, 361, 371 is transferred from a fourth location 325, 345, 355, 365, 375 in a respective track 301-305 to a manipulation device 331-335 where one or more manipulation steps are performed on the state of the qubit, and then transferred from the manipulation device 331-335 to the first location 322, 342, 352, 362, 372. In another example, each qubit 321, 341, 351, 361, 371 is transferred directly from the fourth location 325, 345, 355, 365, 375 to the first location 322, 342, 352, 362, 372 without being transferred to a manipulation device 331-335. In a further example, each quantum bit 321, 341, 351, 361, 371 is transferred to a manipulation device 331-335, but no manipulation steps are performed in the manipulation device.

[0157] In the first gate device 315, the first location 322 of the first track 301 and the first location 342 of the second track 302 are positioned within the quantum interaction distance. In the second gate device 316, the second location 323 of the first track 301 and the second location 353 of the third track 303 are positioned within the quantum interaction distance. In the third gate device 317, the third location 324 of the first track 301 and the third location 364 of the fourth track 304 are positioned within the quantum interaction distance. In the fourth gate device 318, the fourth location 325 of the first track 301 and the fourth location 375 of the fifth track 305 are positioned within the quantum interaction distance.

[0158] A snapshot is shown in FIG. 3B, where at time t1, the first qubit 321 is at the first location 322 of the first track 301, and the second qubit 341 is at the first location 342 of the second track 302. Thus, due to the close position of the first qubit 321 and the second qubit 341 at time t1, an interaction between the first qubit 321 and the second qubit 341 is valid. Specifically, the physical separation between the first and second qubits 341, 321 is shorter than the short distance required for the exchange interaction between the qubit pair. This two-qubit interaction will proceed according to the first gate device 315. This two-qubit interaction is not instantaneous, but takes a finite time. The time taken depends on the details of the interaction, and may consist of multiple partial interactions, each performed successively. Typically, each partial interaction may take 1 to 50 nanoseconds. Typically, each interaction takes 20-2000 nanoseconds (for silicon electron spin qubits). Each interaction occurring in the first through fourth gate devices 315-318 described in this specification falls within this interaction time range. The time typically depends on the implementation method, i.e., the hardware used to implement the interaction between the qubits.

[0159] Following the interaction between the first and second quantum bits 321, 341, each quantum bit 321, 341, 351, 361, 371 will be transferred within their respective tracks 301-305 from a first location 322, 342, 352, 362, 372 to a second location 323, 343, 353, 363, 373, as indicated by arrows in FIG. 3B.

[0160] First qubit 321 will be shuttled from first location 322 to second location 323 in first track 301. Second qubit 341 will be shuttled from first location 342 to second location 343 in second track 302. Third qubit 351 will be shuttled from first location 352 to second location 353 in third track 303. Fourth qubit 361 will be shuttled from first location 362 to second location 363 in fourth track 304. Fifth qubit 371 will be shuttled from first location 372 to second location 373 in fifth track 305.

[0161] In this example, the shuttling of qubits 321, 341, 351, 361, 371 is performed simultaneously. The shuttling step takes a finite time. At time t2, where t2>t1, qubits 321, 341, 351, 361, 371 are positioned at second locations 323, 343, 353, 363, 373. Thus, at time t2, the first and third qubits 321, 351 are within quantum interaction distance. At time t2, the close positioning of the first and third qubits 321, 351 enables an interaction between the first and third qubits 321, 351. This two-qubit interaction will proceed according to the second gate device 316.

[0162] Following interaction between the first and third qubits 321, 351, each qubit 321, 341, 351, 361, 371 will be transferred within their respective tracks 301-305, as indicated by the arrows in FIG. 3B, from the second location 323, 343, 353, 363, 373 to the third location 324, 344, 354, 364, 374. The transfer of the qubits involves electron shuttling, as previously described for the transfer from the first location to the second location. Again, the electron shuttling is performed synchronously.

[0163] At time t3, where t3>t2, qubits 321, 341, 351, 361, 371 are positioned at third locations 324, 344, 354, 364, 374 within their respective tracks 301-305. Thus, at time t3, the first and fourth qubits 321, 361 are within quantum interaction distance. At time t3, the close location of the first and fourth qubits 321, 361 enables an interaction between the first and fourth qubits 321, 361. This two-qubit interaction will proceed according to the third gate device 317.

[0164] Following interaction between the first and fourth qubits 321, 361, each qubit 321, 341, 351, 361, 371 will be transferred within their respective tracks 301-305, as indicated by the arrows in FIG. 3B, from the third location 324, 344, 354, 364, 374 to the fourth location 325, 345, 355, 365, 375. The transfer of the qubits involves electron shuttling, as previously described for the transfer from the first location to the second location, which again is performed synchronously.

[0165] At time t4, where t4>t3, qubits 321, 341, 351, 361, 371 are positioned at fourth locations 325, 345, 355, 365, 375. Thus, at time t4, the first and fifth qubits 321, 371 are within quantum interaction distance. At time t4, the close location of the first and fifth qubits 321, 371 enables an interaction between the first and fifth qubits 321, 371. This two-qubit interaction will proceed according to the fourth gate device 318.

[0166] Following the interaction between the first and fifth qubits 321, 371, each qubit 321, 341, 351, 361, 371 will be transferred from the fourth location 325, 345, 355, 365, 375 in their respective tracks 301-305. Each qubit 321, 341, 351, 361, 371 is transferred to the manipulators 331-335 or to the first location 322, 342, 352, 362, 372 in their respective tracks 301-305. The transfer of the qubits involves electronic shuttling as described above for the transfer from the first location to the second location. Again, electronic shuttling is performed synchronously. In this example, the state of the first qubit 321 is read out at the first manipulator 331. In the second through fifth manipulation devices 332-335, the states of the second through fifth qubits 341, 351, 361, 371 are rotated according to a Hadamard gate. In other examples, the states of the qubits can be initialized, read, or computed by any of the manipulation devices.

[0167] At time t5, where t5>t4, the qubits 321, 341, 351, 361, 371 are positioned at first locations 322, 342, 352, 362, 372. Thus, at time t5, the first and second qubits 321, 341 are within quantum interaction distance. The positioning of the qubits 321, 341, 351, 361, 371 at time t5 is the same as the positioning of the qubits 321, 341, 351, 361, 371 at time t1. Thus, at time t5, an interaction between the first and second qubits 321, 341 is effective as described for time t1. The transition of the qubits through the qubit processor as described above and the interaction effective at each location is repeated in a periodic manner. In one or more further examples, there may be additional tracks, tracks of different shapes, and / or additional qubits within each track.

[0168] The qubit processor of Figures 3A and 3B can be used to process an array of qubits. Interactions between a qubit in the array (here, a first qubit 321) and its neighbors in the array (here, second, third, fourth, and fifth qubits 341, 351, 361, 371) are enabled periodically according to the positioning of the qubits 321, 341, 351, 361, 371 in the processor. The positions of the qubits 321, 341, 351, 361, 371 are set according to predefined tracks 301-305. In this example, there are five qubits in the array, although typically many more qubits are present in an array.

[0169] In this example, each qubit pair positioned at a location that enables the interaction undergoes a two-qubit interaction according to the gate device. In another example, qubit pairs positioned at a location that enables the interaction may not interact, or one or both qubits may undergo a single-qubit operation. This is typically achieved by introducing an electrostatic barrier between the first track and the second, third, fourth, or fifth track as required. The electrostatic barrier has the effect that the quantum interaction distance between qubit pairs positioned on either side of the electrostatic barrier is reduced. Thus, qubit pairs may be physically separated by, for example, 50 nanometers, but no interaction is effective due to the barrier. Such a barrier can be implemented in any qubit processor described herein. The electrostatic barrier effectively prevents wave function overlap even for qubits that are positioned relatively close to each other such that the qubits would interact without the barrier. The barrier is typically temporary so as to enable or prevent the two qubits according to the desired circuit design. The use of an electrostatic barrier can be implemented in any qubit processor described herein.

[0170] In this example, the qubits are shuttled synchronously around their respective tracks, however, in other examples, the qubits are shuttled asynchronously, either by holding the qubits in one or more tracks stationary while shuttling the qubits in other tracks around those tracks, or by shuttling the qubits around the tracks at different rates.

[0171] Figure 4A diagrammatically illustrates a qubit processor having multiple arrays of qubits. Each array of qubits 420, 430, 440, 450 is diagrammatically represented by a plane 406, 407, 408, 409. Each array 420, 430, 440, 450 is similar to the arrays described in connection with Figures 3A and 3B. In Figure 4A, qubit interactions can occur within arrays 420, 430, 440, 450 as described in connection with Figures 3A and 3B, or between arrays 420, 430, 440, 450 as diagrammatically represented as interactions between planes 406-409.

[0172] In the first plane 406, first, second, third, and fourth gate devices 415, 416, 417, 418 can be used to create two-qubit interactions between a first qubit 421 and second, third, fourth, and fifth qubits 422, 423, 424, 425. Corresponding interactions can occur in the second, third, and fourth planes 407, 408, 409. Gate devices 415-418 enable interactions between qubit pairs within the array for all arrays.

[0173] Two-qubit interactions 491 between corresponding qubits can occur between adjacent planes, i.e., between the first plane 406 and the second plane 407, between the second plane 407 and the third plane 408, between the third plane 408 and the fourth plane 409, and between the fourth plane 409 and the first plane 406. Most of the two-qubit interactions 491 are illustrated in Figure 4A. However, the two-qubit interaction between the fourth plane 409 and the first plane 406 is not shown in the figure.

[0174] For example, a two-qubit interaction 491 is possible between a second qubit 422 in a first plurality of qubits 420 illustrated in a first plane 406 and a second qubit 432 in a second plurality of qubits 430 illustrated in a second plane 407. This is possible because the second qubits 422, 432 of the first and second plurality of qubits 420, 430 are positioned within the same track within the qubit processor (see FIG. 4B).

[0175] Furthermore, two-qubit interactions can occur between any qubits in adjacent planes, not just corresponding qubits. For simplicity, these interactions are not illustrated in Figure 4A.

[0176] Figure 4B diagrammatically illustrates the qubit processor of Figure 4A at time t1. The qubit processor includes five defined tracks 401, 402, 403, 404, 405. Each track includes a manipulation device 410, 411, 412, 413, 414. Each manipulation device 410-414 includes one or more manipulation elements as described in relation to Figure 2.

[0177] The arrangement of tracks 401-405 is similar to that of FIG. 3B. The second, third, fourth, and fifth tracks 402-405 are arranged around the first track 401 such that the corners of the second through fifth tracks 402-405 are within quantum interaction distance of the corners of the first track 401. This enables interactions between qubits in adjacent tracks. The interactions are defined using first, second, third, and fourth gate devices 415, 416, 417, 418. In FIG. 4B, the number of qubits in each track 401-405 exceeds one. Compared to FIG. 3B, the qubit processor of FIG. 4B has four times the number of qubits occupying the same space, resulting in a four times higher qubit density.

[0178] In another example, the second through fifth tracks 402-405 are separated from the first track 401 by a mediator dot, i.e., an elongated quantum dot. In that example, the first mediator dot is positioned between the nearest corners of the first and second tracks, the nearest corners of the first and third tracks, the nearest corners of the first and fourth tracks, and the nearest corners of the first and fifth tracks. This further spaces the qubits in the qubit processor to avoid crosstalk, while enabling interaction between qubits in adjacent tracks by increasing the quantum interaction distance.

[0179] Each qubit in tracks 401-405 forms a separate portion of the plurality of qubits. The qubit processor of FIG. 4B illustrates four portions of the plurality of qubits 420, 430, 440, 450. First plurality of qubits 420 includes five qubits 421, 422, 423, 424, 425. Second plurality of qubits 430 includes five qubits 431, 432, 433, 434, 435. Third plurality of qubits 440 includes five qubits 441, 442, 443, 444, 445. Fourth plurality of qubits 450 includes five qubits 451, 452, 453, 454, 455.

[0180] The first defined track 401 includes a first qubit 421, 431, 441, 451 from each of the plurality of qubits. The second defined track 402 includes a second qubit 422, 432, 442, 452 from each of the plurality of qubits. The third defined track 403 includes a third qubit 423, 433, 443, 453 from each of the plurality of qubits. The fourth defined track 404 includes a fourth qubit 424, 434, 444, 454 from each of the plurality of qubits. The fifth defined track 405 includes a fifth qubit 425, 435, 445, 455 from each of the plurality of qubits.

[0181] Each track 401-405 includes four locations, each located at a corner of the substantially rectangular track 401-405. The first track 401 includes a first, second, third, and fourth location 461, 462, 463, 464. The second track 402 includes a first, second, third, and fourth location 466, 467, 468, 469. The third track 403 includes a first, second, third, and fourth location 471, 472, 473, 474. The fourth track 404 includes a first, second, third, and fourth location 476, 477, 478, 479. The fifth track 405 includes a first, second, third, and fourth location 481, 482, 483, 484.

[0182] 4B diagrammatically illustrates a qubit processor at time t1, where first plurality of qubits 420 are in first locations 461, 466, 471, 476, 481, second plurality of qubits 430 are in second locations 462, 467, 472, 477, 482, third plurality of qubits 440 are in third locations 463, 468, 473, 478, 483, and fourth plurality of qubits 450 are in fourth locations 464, 469, 474, 479, 484.

[0183] Thus, at time t1, the first and second qubits 421, 422 of the first plurality of qubits 420 are positioned within a quantum interaction distance such that at this time an interaction between the first and second qubits 421, 422 of the first plurality of qubits 420 is valid. At time t1, the first qubit 421 of the first plurality of qubits 420 is at a first location 461 in the first track 401. At time t1, the second qubit 422 of the first plurality of qubits 420 is at a first location 466 in the second track 402. This two-qubit interaction will proceed according to the first gate device 415.

[0184] At the same time, at time t1, the first and third qubits 431, 433 of the second plurality of qubits 430 are positioned within a quantum interaction distance such that at this time an interaction between the first and third qubits 431, 433 of the second plurality of qubits 430 is effective. At time t1, the first qubit 431 of the second plurality of qubits 430 is at a second location 462 in the first track 401. At time t1, the third qubit 433 of the second plurality of qubits 430 is at a second location 472 in the third track 403. This two-qubit interaction will proceed according to the second gate device 416.

[0185] Also at time t1, the first and fourth qubits 441, 444 of the third plurality of qubits 440 are positioned within the quantum interaction distance, such that at this time an interaction between the first and fourth qubits 441, 444 of the third plurality of qubits 440 is also valid. At time t1, the first qubit 441 of the third plurality of qubits 440 is at a third location 463 in the first track 401. At time t1, the fourth qubit 444 of the third plurality of qubits 440 is at a third location 478 in the fourth track 404. This two-qubit interaction will proceed according to the third gate device 417.

[0186] Furthermore, at time t1, the first and fifth qubits 451, 455 of the fourth plurality of qubits 450 are positioned within a quantum interaction distance such that at this time an interaction between the fifth qubits 451, 455 of the fourth plurality of qubits 450 is valid. At time t1, the first qubit 451 of the fourth plurality of qubits 450 is at a fourth location 464 in the first track 401. At time t1, the fifth qubit 455 of the fourth plurality of qubits 450 is at a fourth location 484 in the fifth track 405. This two-qubit interaction will proceed according to the fourth gate device 418.

[0187] Following the above two-qubit interaction, each of the plurality of qubits 420, 430, 440, 450 is shuttled clockwise along the tracks 401-405 from its respective location at time t1 to the next location along the tracks 401-405. In this example, the shuttle is clockwise for all tracks 401-405. In another example, the shuttle can be counterclockwise for all tracks. In an alternative example, the shuttle can be in one direction, e.g., clockwise, for the first track 401 and in another direction, e.g., counterclockwise, for the tracks 402-405 adjacent to the first track 401. The direction of movement of the qubits along the tracks in this example is indicated by the arrows in FIG. 4B.

[0188] Shuttling is as described in relation to Figure 3B. In this example, shuttling of all qubits 421-425, 431-435, 441-445, 451-455 is performed simultaneously. In another example, shuttling of some qubits can be performed after shuttling of other qubits, for example if the interaction times at gate devices 415-418 are different. In this example, the interaction times at each of gate devices 415-418 are equal.

[0189] At time t2, where t2>t1, the shuttling process is completed and the qubit is received at the next location in the track as described for a single qubit in relation to FIG. 3B.

[0190] Thus, at time t2, the following interactions become effective: Each of the described interactions between qubit pairs becomes effective due to the qubit pairs being in close proximity such that an exchange interaction is possible, i.e., the qubit pairs are positioned within a quantum interaction distance.

[0191] First, at time t2, an interaction becomes effective between the first and third qubits 421, 423 of the first plurality of qubits 420. At time t2, the first qubit 421 of the first plurality of qubits 420 is at the second location 462 in the first track 401. The third qubit 423 of the first plurality of qubits 420 is at the second location 472 in the third track 403.

[0192] Second, at time t2, an interaction between the first and fourth qubits 431, 434 of the second plurality of qubits 430 becomes effective. At time t2, the first qubit 431 of the second plurality of qubits 430 is at a third location 463 in the first track 401. The fourth qubit 434 of the second plurality of qubits 430 is at a third location 478 in the fourth track 404.

[0193] Third, at time t2, an interaction becomes effective between the first and fifth qubits 441, 445 of the third plurality of qubits 440. At time t2, the first qubit 441 of the third plurality of qubits 440 is at a fourth location 464 in the first track 401. The fifth qubit 445 of the third plurality of qubits 440 is at a fourth location 484 in the fifth track 405.

[0194] Fourth, at time t2, an interaction between the first and second qubits 451, 452 of the fourth plurality of qubits 450 becomes effective. At time t2, the first qubit 451 of the fourth plurality of qubits 450 is at a first location 461 in the first track 401. The second qubit 452 of the fourth plurality of qubits 450 is at a first location 466 in the second track 402.

[0195] The terms "first," "second," "third," and "fourth" are used to distinguish between four different two-qubit interactions that occur within the qubit processor. In this example, the interactions occur simultaneously. In other examples, the interactions may not begin and / or end simultaneously, but nevertheless, the terms "first," "second," "third," and "fourth" do not imply a temporal relationship between the interactions.

[0196] Following the above two-qubit interaction, each of the plurality of qubits 420, 430, 440, 450 is shuttled clockwise along tracks 401-405 from the location at time t2 to the next location along tracks 401-405.

[0197] At time t3, where t3>t2, the shuttling step is completed and the qubits are received at the next locations within their respective tracks, as described for a single qubit in relation to FIG. 3B.

[0198] Thus, at time t3, the following interactions become effective: Each of the described interactions between qubit pairs becomes effective due to the qubit pairs being in close proximity such that an exchange interaction is possible, i.e., the qubit pairs are positioned within a quantum interaction distance.

[0199] At time t3, an interaction between the first and fourth qubits 421, 424 of the first plurality of qubits 420 becomes effective. At time t3, the first qubit 421 of the first plurality of qubits 420 is at a third location 463 in the first track 401. The fourth qubit 424 of the first plurality of qubits 420 is at a third location 478 in the fourth track 404.

[0200] At time t3, another interaction becomes effective between the first and fifth qubits 431, 435 of the second plurality of qubits 430. At time t3, the first qubit 431 of the second plurality of qubits 430 is at a fourth location 464 in the first track 401. The fifth qubit 435 of the second plurality of qubits 430 is at a fourth location 484 in the fifth track 405.

[0201] At time t3, another interaction becomes effective between the first and second qubits 441, 442 of the third plurality of qubits 440. At time t3, the first qubit 441 of the third plurality of qubits 440 is at a first location 461 in the first track 401. The second qubit 442 of the third plurality of qubits 440 is at a first location 466 in the second track 402.

[0202] At time t3, another interaction becomes effective between the first and third qubits 451, 453 of the fourth plurality of qubits 450. At time t3, the first qubit 451 of the fourth plurality of qubits 450 is at a second location 462 in the first track 401. The third qubit 453 of the fourth plurality of qubits 450 is at a second location 472 in the third track 403.

[0203] Following the above two-qubit interaction, each of the plurality of qubits 420, 430, 440, 450 is shuttled clockwise along tracks 401-405 from a location at time t3 to a next location along tracks 401-405. At time t4, where t4>t3, the shuttling step is completed and the qubits are received at the next location within their respective tracks.

[0204] Thus, at time t4, the following interactions become effective: Each of the described interactions between qubit pairs becomes effective due to the qubit pairs being in close proximity such that an exchange interaction is possible, i.e., the qubit pairs are positioned within a quantum interaction distance.

[0205] At time t4, an interaction between the first and fifth qubits 421, 425 of the first plurality of qubits 420 becomes effective. At time t4, the first qubit 421 of the first plurality of qubits 420 is at the fourth location 464 in the first track 401. The fifth qubit 425 of the first plurality of qubits 420 is at the fourth location 484 in the fifth track 405.

[0206] At time t4, another interaction becomes effective between the first and second qubits 431, 432 of the second plurality of qubits 430. At time t4, the first qubit 431 of the second plurality of qubits 430 is at a first location 461 in the first track 401. The second qubit 432 of the second plurality of qubits 430 is at a first location 466 in the second track 402.

[0207] At time t4, another interaction becomes effective between the first and third qubits 441, 443 of the third plurality of qubits 440. At time t4, the first qubit 441 of the third plurality of qubits 440 is at a second location 462 in the first track 401. The third qubit 443 of the third plurality of qubits 440 is at a second location 472 in the third track 403.

[0208] At time t4, another interaction becomes effective between the first and fourth qubits 451, 454 of the fourth plurality of qubits 450. At time t4, the first qubit 451 of the fourth plurality of qubits 450 is at a third location 463 in the first track 401. The fourth qubit 454 of the fourth plurality of qubits 450 is at a third location 478 in the fourth track 404.

[0209] Following the above two-qubit interaction, each of the plurality of qubits 420, 430, 440, 450 is shuttled clockwise along tracks 401-405 from a location at time t4 to a next location along tracks 401-405. At time t5, where t5>t4, the shuttling step is completed and the qubits are received at the next location within their respective tracks.

[0210] At time t5, qubits 421-425, 431-435, 441-445, 451-455 are in locations 461-464, 466-469, 471-474, 476-479, 481-484 in the same tracks 401-405 as at time t1. Thus, the set of interactions that are active at time t5 is equal to the set of interactions that are active at time t1 above. The qubits in each track 401-405 cycle through their respective tracks and when positioned sufficiently close, i.e., within the quantum interaction distance, with qubits in adjacent tracks, they will interact.

[0211] The interactions occur (i) at the first gate device 415 between a quantum bit at a first location 461 in the first track 401 and a quantum bit at a first location 466 in the second track 402, (ii) at the second gate device 416 between a quantum bit at a second location 462 in the first track 401 and a quantum bit at a second location 472 in the third track 403, (iii) at the third gate device 417 between a quantum bit at a third location 463 in the first track 401 and a quantum bit at a third location 478 in the fourth track 404, and (iv) at the fourth gate device 418 between a quantum bit at a fourth location 464 in the first track 401 and a quantum bit at a fourth location 484 in the fifth track 405.

[0212] In this example, the same interaction occurs at each of the gate devices 415-418 with each of the multiple qubits 420, 430, 440, 450. In alternative examples, one or more of the gate devices 415-418 may be reconfigured before or during operation of the quantum circuit.

[0213] Optionally, one or more qubits may be transferred from a fourth location 464, 469, 474, 479, 484 in the tracks 401-405 to the manipulation devices 410-414. Additionally, one or more qubits may be transferred from the manipulation devices 410-414 to a first location 461, 466, 471, 476, 481 in the tracks 401-405. In one example, the qubits transferred from the fourth location 464, 469, 474, 479, 484 to the manipulation devices 410-414 are subsequently transferred to the first location 461, 466, 471, 476, 481.

[0214] In another example, the qubits transferred from the manipulation devices 410-414 to the first locations 461, 466, 471, 476, 481 are not the particular qubits transferred from the fourth locations 464, 469, 474, 479, 484 to the manipulation devices 410-414. However, the functionality of the qubits removed from the tracks 401-405 by being transferred from the fourth locations 464, 469, 474, 479, 484 to the manipulation devices 410-414 is provided by the qubits transferred from the manipulation devices 410-414 to the first locations 461, 466, 471, 476, 481. For example, the qubits may be transferred from the manipulation devices into an electron reservoir or from the electron reservoir to the first locations.

[0215] The interactions described above in connection with FIG. 4B were between qubits in the same qubit matrix. Such interactions involve one qubit in one track (here the first track 401) and a corresponding qubit in an adjacent track (here any one of the second through fifth tracks 402-405). This enables simultaneous processing of multiple qubit arrays in the same qubit processor. Non-interacting qubits are kept sufficiently far away (i.e., at a distance greater than the quantum interaction distance) from other qubits in the processor, but qubits are periodically brought closer to each other (i.e., within the quantum interaction distance) when desired for interactions. The qubit density of the qubit processor is increased due to the presence of multiple qubits complexing within the same area. Shuttling around defined tracks, or loops, ensures that the qubits are kept separate when not interacting.

[0216] In addition to the interactions described above, the architecture illustrated in Figure 4B allows for interactions between qubits in the same track. These interactions involve a qubit in one qubit (e.g., the i th qubit) with a corresponding qubit in an adjacent qubit (either the i-1 th qubit or the i+1 th qubit).

[0217] Within each track, corresponding quantum bits from the i+1th plurality of quantum bits are located between quantum bits from the ith and i+2th plurality of quantum bits, such that direct interaction between corresponding quantum bits from the ith and i+2th plurality of quantum bits is not possible.

[0218] Interaction between two qubits in the same track is enabled by positioning the two qubits within a quantum interaction distance along the track. Methods for positioning qubit pairs that may enable interaction are described in detail in relation to FIG. 1. The positioning that enables interaction is temporary. Interactions between qubit pairs in the same track can occur simultaneously with corresponding qubit pairs in other tracks. For example, simultaneous interactions can occur between first qubits 421, 431 of the first and second pluralities of qubits 420, 430, between second qubits 422, 432 of the first and second pluralities of qubits 420, 430, between third qubits 423, 433 of the first and second pluralities of qubits 420, 430, between fourth qubits 424, 434 of the first and second pluralities of qubits 420, 430, and between fifth qubits 425, 435 of the first and second pluralities of qubits 420, 430.

[0219] Instead, interactions between qubit pairs in the same track can occur individually and locally within only one track or within a subset of tracks.

[0220] In addition to the interactions discussed above, the architecture illustrated in Figure 4B further enables interactions between qubits from different tracks and different plurality of qubits. For reference, it was stated above that the first qubit 421 of the first plurality of qubits 420 in the first track 401 can interact with the second through fifth qubits 422-425 of the first plurality of qubits 420 in the second through fifth tracks 402-405, respectively.

[0221] In another example, it is possible to enable interaction between a first qubit 421 of the first plurality of qubits 420 in the first track 401 and each of the second through fifth qubits 432-435, 442-445, 452-455 of the second through fourth plurality of qubits 430, 440, 450 in the second through fifth tracks 402-405. This can be achieved, for example, by selectively shuttling qubits around some tracks and not others. In one example, qubits 421, 431, 441, 451 in the first track 401 are shuttled clockwise around that track while the qubits in the second through fifth tracks 402-405 remain stationary.

[0222] 4B, this allows a first qubit 421 of first plurality of qubits 420 to interact with (1) a second qubit 422 of first plurality of qubits 420 in second track 402, (2) a third qubit 433 of second plurality of qubits 430 in third track 403, (3) a fourth qubit 444 of third plurality of qubits 440 in fourth track 404, and (4) a fifth qubit 455 of fourth plurality of qubits 450 in fifth track 405. In this way, each qubit in a track is capable of interacting with any qubit in an adjacent track, i.e., a track that is within the quantum interaction distance of that track.

[0223] Together, the possibilities for inter-track and intra-track interactions provide a pseudo-3D architecture as shown diagrammatically in Figure 4A, but which is strictly 2D as can be seen in Figure 4B. Inter-track interactions are diagrammatically shown as interactions within planes 406-409. Intra-track interactions are diagrammatically shown as interactions between planes 406-409.

[0224] 4B, the number of qubits in each track 401-405 is the same. However, in different examples, the number of qubits may vary between tracks.

[0225] FIG. 5A diagrammatically illustrates a qubit processor having multiple arrays of qubits. Each of the qubit arrays 511, 512, 513, 514, 515, 516 is diagrammatically shown in a separate plane 531, 532, 533, 534, 535, 536. Although the qubit processor is diagrammatically shown as stacked planes 531-536, interactions between qubit pairs can occur between and within them. This qubit processor is similar to that described in connection with FIGS. 4A and 4B. In addition to the inter-plane interactions 591 between corresponding qubits from adjacent arrays illustrated, interactions between corresponding qubits from the first plane 531 and the sixth plane 536 are possible, as described in connection with FIG. 4A. Available in-plane interactions 592 are illustrated.

[0226] Figure 5B diagrammatically illustrates the qubit processor of Figure 5A at time t1. The qubit processor includes seven defined tracks 501, 502, 503, 504, 505, 506, 507. Each track includes a manipulation device 521, 522, 523, 524, 525, 526, 527. Within each track 501-507 there are six qubits corresponding to six separate pluralities of qubits 511, 512, 513, 514, 515, 516. Each qubit in the plurality of qubits 511-516 is in a separate track 501-507. In this example, each plurality of qubits includes seven qubits.

[0227] In Figure 5B, first defined track 501 is substantially hexagonal. First track 501 has six locations 551, 552, 553, 554, 555, 556, each located at a corner of hexagonal track 501. At time t1, each qubit in first track 501 is at a location 551-556 in first track 501. Each qubit 551-556 is within a different number of qubits 511-516.

[0228] The second through seventh defined tracks 502-507 in FIG. 5B are substantially triangular. Each of the second through seventh defined tracks 502-507 has three locations, each location positioned at a corner of the triangular track 502-507. At time t1, three locations in each triangular track 502-507 are occupied by one qubit. In addition, the remaining three qubits in each of the second through seventh tracks 502-507 are at intermediate locations positioned along the edges of the triangular loop.

[0229] The tracks 501-507 in FIG. 5B are arranged such that a quantum bit in the first track 501 can interact with a quantum bit in each of the second, third, fourth, fifth, sixth and seventh tracks 502-507.

[0230] At time t1, an interaction becomes effective between a first and a second qubit of the first plurality of qubits 511. At time t1, a first qubit of the first plurality of qubits 511 is at a first location 551 in the first track 501 and a second qubit of the first plurality of qubits 511 is at a second location 561 in the second track 502. This interaction proceeds according to a first gate device 541.

[0231] At time t1, an interaction between a first qubit and a third qubit of the second plurality of qubits 512 becomes effective. At time t1, the first qubit of the second plurality of qubits 512 is at a second location 552 in the first track 501 and the third qubit of the second plurality of qubits 512 is at a third location 562 in the third track 503. This interaction proceeds according to the second gate device 542.

[0232] At time t1, an interaction between a first qubit and a fourth qubit of the third plurality of qubits 513 becomes effective. At time t1, the first qubit of the third plurality of qubits 513 is at a third location 553 in the first track 501 and the fourth qubit of the third plurality of qubits 513 is at a third location 563 in the fourth track 504. This interaction proceeds according to the third gate device 543.

[0233] At time t1, an interaction becomes effective between a first qubit and a fifth qubit of the fourth plurality of qubits 514. At time t1, the first qubit of the fourth plurality of qubits 514 is at a fourth location 554 in the first track 501, and the fifth qubit of the fourth plurality of qubits 514 is at a first location 564 in the fifth track 505. This interaction proceeds according to the fourth gate device 544.

[0234] At time t1, an interaction between a first qubit and a sixth qubit of the fifth plurality of qubits 515 becomes effective. At time t1, the first qubit of the fifth plurality of qubits 515 is at a fifth location 555 in the first track 501, and the sixth qubit of the fifth plurality of qubits 511 is at a first location 565 in the sixth track 506. This interaction proceeds according to the fifth gate device 545.

[0235] At time t1, an interaction between a first qubit and a seventh qubit of the sixth plurality of qubits 516 becomes effective. At time t1, the first qubit of the sixth plurality of qubits 516 is at a sixth location 556 in the first track 501, and the seventh qubit of the first plurality of qubits 516 is at a second location 566 in the seventh track 507. This interaction proceeds according to the sixth gate device 546.

[0236] In each of the second through seventh tracks 502-507, the first location is at the first corner in the clockwise direction of the controls 522-527. Thus, the corner of the second track 502 closest to the first track 501 includes the second location 561 of the second track 502, the corner of the third track 503 closest to the first track 501 includes the third location 562 of the third track 503, the corner of the fourth track 504 closest to the first track 501 includes the third location 563 of the fourth track 504, the corner of the fifth track 505 closest to the first track 501 includes the first location 564 of the fifth track 505, the corner of the sixth track 506 closest to the first track 501 includes the first location 565 of the sixth track 506, and the corner of the seventh track 507 closest to the first track 501 includes the second location 566 of the seventh track 507.

[0237] After the above mentioned interactions are completed, the qubits are shuttled clockwise around the tracks 501-507. Interactions between six different qubit pairs (first and second, first and third, first and fourth, first and fifth, first and sixth, first and seventh) from the first plurality of qubits 511 will occur continuously and periodically at the first gate device 541, the second gate device 542, the third gate device 543, the fourth gate device 544, the fifth gate device 545, and the sixth gate device 546, respectively. The interaction between the first and seventh qubits from the first plurality of qubits 511 at the sixth gate device 546 is followed by the shuttling of qubits around the tracks of the qubit processor. The next interaction is between the first and second qubits from the first plurality of qubits 511 at the first gate device 541.

[0238] A second through sixth plurality of qubits 512-516 follow the first plurality of qubits 511 around the qubit processor, with a different pair of qubits interacting at each gate device 541-546 within the qubit processor. In this manner, six arrays of qubits 511-516 are processed sequentially and optionally independently within the qubit processor, thereby increasing the throughput of the qubit processor.

[0239] In this example, in addition to the inter-track interactions described, intra-track interactions are possible: enabling intra-track interactions by positioning qubit pairs within a track within the quantum interaction distance provides a quasi-three-dimensional architecture, although strictly two-dimensional.

[0240] 5A and 5B can be used for surface code or color code parity checking. Each plane 431-436 diagrammatically represents a parity check layer.

[0241] In Figures 1, 2, 3B, and 4B, the tracks are illustrated as substantially square loops. However, the tracks can be of any shape, as illustrated in Figure 5B. The tracks are designed according to experimental requirements, which can include fit within spatial or other design constraints, or can relate to the number and arrangement of different arrays that can be processed by the qubit processor at any one time. The tracks are typically polygonal loops, as they allow for the best interaction sites at corners (as previously discussed) or along straight edges (see Figures 7B and 8B for examples).

[0242] 6 illustrates generally a qubit processor including a number of tracks 601, 602, 603, 604, each forming a polygonal loop. In this example, a first defined track 601 is a square, a second defined track 602 is a pentagon, a third defined track 603 is a triangle, and a fourth defined track 604 is a hexagon.

[0243] The tracks 601-604 are arranged and connected such that a first interaction location 621 allows interaction between qubits in the first and second tracks 601, 602, a second interaction location 622 allows interaction between qubits in the second and third tracks 602, 603, a third interaction location 623 allows interaction between qubits in the third and fourth tracks 603, 604, and a fourth interaction location 624 allows interaction between qubits in the first and fourth tracks 601, 604. Additionally illustrated is an interaction location 625 which enables interaction between a qubit of one of the illustrated tracks 601-604 and another qubit in another track (not shown).

[0244] At interaction locations 621-625, pairs of qubits can interact if the associated locations in a pair of adjacent tracks are occupied. The tracks are arranged such that the positioning of locations in adjacent tracks at interaction locations 621-625 brings qubits at those locations within quantum interaction distance to enable interaction.

[0245] As previously mentioned, qubits 611-614 move around their respective tracks 601-604. The qubits 611-614 within a track 601-604 can move in the same direction as adjacent tracks 601-604 or in the opposite direction.

[0246] Each track 601-604 contains a number of quantum bits 611, 612, 613, 614. The maximum number of quantum bits in each track 601-604 is determined by the total time T loop , the time τ required to execute the rate limiting processing step max However, the maximum number of qubits can be increased by incorporating a buffering step.

[0247] Figure 7A diagrammatically illustrates a qubit processor having multiple arrays of qubits. The qubit processor illustrated in Figure 7A is similar to the qubit processor illustrated in Figure 4A. Each array of qubits 720, 730, 740, 750 is diagrammatically illustrated by a plane 706, 707, 708, 709. Qubit-to-qubit interactions can occur within and / or between the arrays 720, 730, 740, 750.

[0248] In the first plane 706, first, second, third, and fourth gate devices 715, 716, 717, 718 can be used to create two-qubit interactions between a first qubit 721 and second, third, fourth, and fifth qubits 722, 723, 724, 725. Corresponding interactions can occur in the second, third, and fourth planes 707, 708, 709. Gate devices 715-718 enable interactions between qubit pairs within the array for all arrays.

[0249] As described in relation to Figure 4A, two-qubit interactions 791 can occur between corresponding qubits in adjacent planes 706-709. As in Figure 4A, the two-qubit interaction between the fourth plane 709 and the first plane 706 is not shown in the figure.

[0250] Figure 7B diagrammatically illustrates the qubit processor of Figure 7A at time t1. Similar to the qubit processor illustrated in Figure 4B, the qubit processor includes five defined tracks 701, 702, 703, 704, 705. Each track includes a manipulation device 710, 711, 712, 713, 714. Each manipulation device 710-714 includes one or more manipulation elements, as described in relation to Figure 2.

[0251] In Figure 7B, the portions of the second through fifth tracks 702-705 that are within quantum interaction distance from the first track 701 have been expanded compared to the qubit processor of Figure 4B. This enables interaction between a qubit in the first track 701 and a qubit in the second, third, fourth, or fifth tracks 702-705 anywhere within the overlap between adjacent tracks. The two-qubit interaction is defined using first, second, third, and fourth gate devices 715, 716, 717, 718.

[0252] In Figure 7B, there are four qubit pluralities 720, 730, 740, 750, each containing five qubits. There are five tracks 701-705 in Figure 7B, each containing one qubit from each of the qubit pluralities 720, 730, 740, 750.

[0253] The first plurality of qubits 720 includes five qubits 721, 722, 723, 724, 725. The second plurality of qubits 730 includes five qubits 731, 732, 733, 734, 735. The third plurality of qubits 740 includes five qubits 741, 742, 743, 744, 745. The fourth plurality of qubits 750 includes five qubits 751, 752, 753, 754, 755. The first, second, third, and fourth qubits of each plurality of qubits 720, 730, 740, 750 are positioned within the processor as described in connection with FIG.

[0254] Each track 701-705 includes four locations, similar to the processor of Figure 4B. However, in Figure 7B, each location is positioned along an edge of a substantially rectangular track 701-705. In this example, each location is a portion of the second through fifth tracks 702-705 that extends a length and is within a quantum interaction distance of the first track 701. Alternatively, each location can be positioned within less than the entire length of the overlap between adjacent tracks.

[0255] The rate-limiting steps in this example are one or more interactions performed according to gate devices 715-718. The effective processing time of the interactions is reduced by extending each interaction over a portion of the edge of the loop and by performing the interactions in conjunction with shuttling along track 701.

[0256] The first track 701 includes first, second, third, and fourth locations 761, 762, 763, 764. The second track 702 includes first, second, third, and fourth locations 766, 767, 768, 769. The third track 703 includes first, second, third, and fourth locations 771, 772, 773, 774. The fourth track 704 includes first, second, third, and fourth locations 776, 777, 778, 779. The fifth track 705 includes first, second, third, and fourth locations 781, 782, 783, 784.

[0257] 7B diagrammatically illustrates a qubit processor at time t1. At time t1, a first qubit 721 of the first plurality of qubits 720 is in a third location 763 in the first track 701. A first qubit 731, 741, 751 of the second, third, and fourth pluralities of qubits 730, 740, 750 are in second, first, and fourth locations 762, 761, 764, respectively, in the first track 701. A second qubit 722 of the first plurality of qubits 720 is in a second location 767 in the second track 702. A second qubit 732, 742, 752 of the second, third, and fourth pluralities of qubits 730, 740, 750 are in first, fourth, and third locations 766, 769, 768, respectively, in the second track 702. A third qubit 723 of the first plurality of qubits 720 is in a fourth location 774 in the third track 703. A third qubit 733, 743, 753 of the second, third, and fourth pluralities of qubits 730, 740, 750 are in third, second, and first locations 773, 772, 771, respectively, in the third track 703. A fourth qubit 724 of the first plurality of qubits 720 is in a second location 777 in the fourth track 704. A fourth qubit 734, 744, 754 of the second, third, and fourth pluralities of tracks 730, 740, 750 are in first, fourth, and third locations 776, 779, 778, respectively, in the fourth track 704. The fifth qubit 725 of the first plurality of qubits 720 is in a fourth location 784 in the fifth track 705. The fifth qubits 735, 745, 755 of the second, third, and fourth pluralities 730, 740, 750 are in third, second, and first locations 783, 782, 781, respectively, in the fifth track 705.

[0258] Thus, at time t1, the first and second qubits 421, 422 of the first plurality of qubits 420 are positioned within a quantum interaction distance such that at this time an interaction between the first and second qubits 721, 722 of the first plurality of qubits 720 is valid. This two-qubit interaction will proceed according to the first gate device 715.

[0259] Similarly, at time t1, an interaction becomes effective between the first and fifth qubits 731, 735 of the second plurality of qubits 730. This two-qubit interaction will proceed according to the second gate device 716.

[0260] At time t1, an interaction between the first and fourth qubits 741, 744 of the third plurality of qubits 740 also becomes effective. This two-qubit interaction will proceed according to the third gate device 717.

[0261] Additionally, at time t1, an interaction between a first qubit 751 and a third qubit 753 of the fourth plurality of qubits 750 becomes effective. This two-qubit interaction will proceed according to the fourth gate device 718.

[0262] In this example, interactions at gate devices 715-718 proceed while qubits are shuttled around tracks 701-705. It is therefore important that the direction of movement of the qubits around the first track 701 is opposite to the direction of movement of the qubits around the second, third, fourth and fifth tracks 702-705. This ensures that the interacting qubits move in the same direction through each gate device 715-718.

[0263] In another example, the interactions at the gating devices 715 - 718 can occur at particular points along portions of the second and fifth tracks 702 - 705 that are within a quantum interaction distance from the first track 701 .

[0264] Following the above two-qubit interaction, each of the plurality of qubits 720, 730, 740, 750 is shuttled along tracks 701-705 from a location at time t1 to a next location along tracks 701-705. In this example, the shuttle is counterclockwise in the first track 701 and clockwise in the second through fifth tracks 702-705. The arrows in Figure 7B indicate the direction of qubit movement. In this example, the shuttle of all qubits 721-725, 731-735, 741-745, 751-755 is performed simultaneously.

[0265] At time t2, where t2>t1, the shuttling process is completed and the qubit is received at the next location in the track, as described in connection with FIG. 4B.

[0266] Thus, at time t2, the following interaction becomes effective: At time t2, an interaction becomes effective between a first qubit 721 and a third qubit 723 of the first plurality of qubits 720. At time t2, the first qubit 721 of the first plurality of qubits 720 is at a fourth location 764 in the first track 701. The third qubit 723 of the first plurality of qubits 720 is at a first location 771 in the third track 703.

[0267] At time t2, an interaction between first qubit 731 and second qubit 732 of second plurality of qubits 730 becomes effective. At time t2, first qubit 731 of second plurality of qubits 730 is at third location 763 in first track 701. Second qubit 732 of second plurality of qubits 730 is at second location 767 in second track 702.

[0268] At time t2, an interaction between the first qubit 741 and the fifth qubit 745 of the third plurality of qubits 740 also becomes effective. At time t2, the first qubit 741 of the third plurality of qubits 740 is at a second location 762 in the first track 701. The fifth qubit 745 of the third plurality of qubits 440 is at a third location 783 in the fifth track 705.

[0269] At time t2, an interaction between first qubit 751 and fourth qubit 754 of fourth plurality of qubits 750 becomes effective. At time t2, first qubit 751 of fourth plurality of qubits 750 is at first location 761 in first track 701. Fourth qubit 754 of fourth plurality of qubits 750 is at fourth location 779 in fourth track 704.

[0270] In this example, the interactions occur simultaneously. Following the above two-qubit interaction, each of the plurality of qubits 720, 730, 740, 750 continues around the tracks 701-705 of the qubit processor. The qubits in the first track 701 are shuttled counterclockwise, and the qubits in the second through fifth tracks 702-705 are shuttled clockwise. When they are received at the next location, the next four interaction sets are set up for the four qubit pairs, each of which is included in one of the plurality of qubits 720, 730, 740, 750. The interactions are enabled according to the relative positioning of the qubits, as described in connection with FIG. 4B.

[0271] The shuttling of qubits 721-725, 731-735, 741-745, 751-755 around tracks 701-705 can continue multiple times around tracks 701-705. Following a complete revolution of tracks 701-705, the qubits return to the same positions and the cycle of interactions between the various qubit pairs continues in the same manner as described.

[0272] In the qubit processor of FIG. 7B , interactions occur (i) between a qubit at a third location 763 in the first track 701 and a qubit at a second location 767 in the second track 702 at a first gate device 715, (ii) between a qubit at a second location 762 in the first track 701 and a qubit at a third location 783 in the fifth track 705 at a second gate device 716, (iii) between a qubit at a first location 761 in the first track 701 and a qubit at a fourth location 779 in the fourth track 704 at a third gate device 717, and (iv) between a qubit at a fourth location 764 in the first track 701 and a qubit at a first location 771 in the third track 703 at a fourth gate device 718.

[0273] In this example, the same interaction occurs at each of the gate devices 715-718 with each of the multiple qubits 720, 730, 740, 750. In alternative examples, one or more of the gate devices 715-718 may be reconfigured before or during operation of the quantum circuit.

[0274] Optionally, one or more qubits may be transferred from a fourth location 764, 769, 774, 779, 784 in the tracks 701-705 to the manipulation devices 710-714. Additionally, one or more qubits may be transferred from the manipulation devices 710-714 to a first location 761, 766, 771, 776, 781 in the tracks 701-705. In one example, the qubits transferred from the fourth location 764, 769, 774, 779, 784 to the manipulation devices 710-714 are subsequently transferred to the first location 761, 766, 771, 776, 781.

[0275] Similar to the architecture shown in Figure 4B, the architecture illustrated in Figure 7B also allows for interactions between qubits in the same track. These interactions involve a qubit in one qubit (e.g., the i th qubit) and a corresponding qubit in an adjacent qubit (either the i-1 th qubit or the i+1 th qubit). Intra-track interactions are discussed further in relation to Figure 4B.

[0276] Further arrangements of tracks within the qubit processor are possible. In one example, one or more corners or edges of the tracks can be designed as non-interacting regions. In another example, the qubit processor includes first, second, third, and fourth substantially square tracks arranged similarly to the first through fourth tracks of FIG. 7B, but without the fifth track adjacent to the first track.

[0277] Figure 8A diagrammatically illustrates a qubit processor having multiple arrays of qubits. The qubit processor illustrated in Figure 8A is similar to the qubit processor of Figure 7A. Each array of qubits 811, 812, 813, 814, 815, 816 is diagrammatically illustrated by a plane. Qubit interactions can occur within and / or between arrays 811-816.

[0278] First, second, third, and fourth gate devices 817, 818, 819, 820 may be used to create two-qubit interactions between adjacent qubits in each array 811-816. Gate devices 817-820 enable interactions between qubit pairs within the array for all arrays. As described in connection with FIG. 4A, two-qubit interactions 891 may occur between corresponding qubits between adjacent planes.

[0279] Figure 8B shows a schematic of the qubit processor of Figure 8A at time t1. The qubit processor includes five tracks 801, 802, 803, 804, 805. Each track includes a manipulation device 821, 822, 823, 824, 825. Each track is populated by six qubits, one from each of a plurality of qubits 811-816.

[0280] In FIG. 8B, each track 801-805 has four locations 831-834, 841-844, 851-854, 861-864, 871-874, each along an edge of the substantially square loop that forms each track 801-805.

[0281] The rate-limiting steps in this example are one or more interactions performed according to gate devices 817-820. The effective processing time of the interactions is reduced by extending each interaction over substantially the entire edge of the loop and performing the interaction simultaneously with the shuttling of qubits along track 801.

[0282] In this example, the interaction is effectively decomposed into multiple partial interactions performed in succession, and the shuttling is decomposed into multiple partial shuttling steps. The interaction proceeds by alternating partial interactions and partial shuttling steps, where each partial shuttling step involves shuttling a qubit by a small amount along the track, with the qubit continuing to be transferred around the track such that it is not separated from the other qubit of the interacting pair while the interaction is ongoing.

[0283] In another example, the steps of partial interaction and partial shuttling can be performed in parallel to further reduce the processing time of the qubits.

[0284] In this example, the interaction at the gate devices 817-820 proceeds while a number of qubits 811-816 are shuttled around the tracks 801-805. It is therefore important that the direction of movement of the qubits around the first track 801 is opposite to the direction of movement of the qubits around the second, third, fourth and fifth tracks 802-805. This ensures that the interacting qubits move in the same direction through each gate device 817-820. In this example, the qubits are shuttled clockwise around the first track 801 and the qubits are shuttled counterclockwise around each of the second, third, fourth and fifth tracks 802-805. The arrows in the figure indicate the direction of movement of the qubits around each track.

[0285] The quantum bits in each track 801-805 progress sequentially around the track and interact with other quantum bits when they come within quantum interaction distance due to the arrangement of tracks 801-805.

[0286] At time t1, an interaction between a first qubit and a second qubit of the first plurality of qubits 811 is enabled at the first gate device 817. The first qubit of the first plurality of qubits 811 is at a first location 831 of the first track 801 and the second qubit of the first plurality of qubits 811 is at a third location 843 of the second track 802. The first and second qubits of the first plurality of qubits 811 are approximately centered at their respective locations 831, 843 along the edges of the tracks 801, 802. The qubit pair are purposely positioned at the same location along the edges of the tracks 801, 802 to ensure strong coupling during the interaction.

[0287] As time progresses, the interaction between the first and second qubits of the first plurality of qubits 811 at the first gate device 817 continues as the first and second qubits of the first plurality of qubits 811 are shuttled along their respective tracks 801, 802 until the qubits leave their respective locations 831, 843. The qubits continue to be transferred along the tracks. The first qubit of the first plurality of qubits 811 will continue to interact with the third qubit of the first plurality of qubits 811 at the second gate device 818.

[0288] At time t1, an interaction between a first and a third qubit of the second and third pluralities of qubits 812, 813 at the second gate device 818 is enabled. A first qubit of the second and third pluralities of qubits 812, 813 is at a second location 832 of the first track 801 and a third qubit of the second and third pluralities of qubits 812, 813 is at a second location 852 of the third track 803. The first and third qubits of the second plurality of qubits 812 are generally at a first end of their respective locations 832, 852 along the edge of the tracks 801, 803. The first and third qubits of the third plurality of qubits 813 are generally at a second end of their respective locations 832, 852 along the edge of the tracks 801, 803. The second end is beyond the first end clockwise along the first track 801. Each qubit pair is purposefully positioned at the same location along the edge of the tracks 801, 802 to ensure strong coupling during interaction.

[0289] Over time, the interaction between the qubit pairs of the third plurality of qubits 813 is completed while the interaction between the qubit pairs of the second plurality of qubits 812 continues. The first qubit of the third plurality of qubits 813 then interacts with a fourth qubit of the third plurality of qubits 813 at third gate device 819. Meanwhile, at second gate device 818, an interaction between the qubit pairs of the first plurality of qubits 811 begins while the qubit pairs of the second plurality of qubits 812 are still undergoing an interaction.

[0290] At time t1, an interaction at third gate device 819 between a first and a fourth qubit of the fourth plurality of qubits 814 is enabled. The first qubit of the fourth plurality of qubits 814 is at a third location 833 of the first track 801 and the fourth qubit of the fourth plurality of qubits 814 is at a first location 861 of the fourth track 804. The first and fourth qubits of the fourth plurality of qubits 814 are approximately centered at respective locations 833, 861 along the edges of the tracks 801, 804. The qubit pairs are purposely positioned at the same locations along the edges of the tracks 801, 804 to ensure strong coupling during the interaction.

[0291] As time progresses, the interaction between the first and fourth qubits of the fourth plurality of qubits 814 at the third gate device 819 continues as the first and fourth qubits of the fourth plurality of qubits 814 are shuttled along their respective tracks 801, 804 until the qubits leave their respective locations 833, 861. The qubits continue to be transferred along the tracks. The first qubit of the fourth plurality of qubits 814 will continue to interact with the fifth qubit of the fourth plurality of qubits 814 at the fourth gate device 820.

[0292] At time t1, an interaction between a first and a fifth qubit of the fifth and sixth pluralities 815, 816 at the fourth gate device 820 is enabled. The first qubit of the fifth and sixth pluralities 815, 816 is at a fourth location 834 of the first track 801 and the fifth qubit of the fifth and sixth pluralities 815, 816 is at a fourth location 874 of the fifth track 805. The first and fifth qubits of the fifth plurality 815 are generally at a first end of the respective locations 834, 874 along the edge of the tracks 801, 805. The first and fifth qubits of the sixth plurality 816 are generally at a second end of the respective locations 834, 874 along the edge of the tracks 801, 805. The second end is beyond the first end in a clockwise direction along the first track 801. Each qubit pair is purposefully positioned at the same location along the edge of the tracks 801, 805 to ensure strong coupling during interaction.

[0293] Over time, the interaction between the qubit pairs of the sixth plurality of qubits 816 is completed, but the interaction between the qubit pairs of the second plurality of qubits 815 continues. A first qubit of the sixth plurality of qubits 816 will continue to interact with a second qubit of the sixth plurality of qubits 816 at a first gate device 817. Meanwhile, an interaction between the qubit pairs of the fourth plurality of qubits 814 begins at the fourth gate device 820, while the qubit pairs of the fifth plurality of qubits 815 are still undergoing an interaction at the fourth gate device 820.

[0294] The qubits move continuously around the tracks and qubit pairs interact whenever the pair is within the quantum interaction distance. In addition to inter-track interactions, intra-track interactions are also possible.

[0295] FIG. 9A diagrammatically illustrates a qubit processor for performing parity checks. The qubit processor includes alternating data qubits 911 and ancillary qubits 912. The qubit processor implements a surface code in which X checks 941 and Z checks 951 are performed. FIG. 9A illustrates a two-dimensional plane around which two-dimensional arrays of qubits can be transferred and interacted with. However, as will be described in connection with FIG. 9B, the qubit processor can be diagrammatically illustrated to further include identical planes stacked vertically, illustrating the possibility of interaction between arrays of qubits, not just between qubits within a single array.

[0296] Figure 9B shows a schematic of the qubit processor of Figure 8B. The qubit processor includes a number of tracks 901, 902. Data qubits 911 are transferred around the data track 901 and auxiliary qubits 912 are transferred around the auxiliary track 902. Each track 901, 902 includes four locations at the corners of the substantially rectangular track 901, 902. Each location has a gate device 921. Each track 901, 902 also includes a manipulation device 931.

[0297] In this example, data qubits 911 travel clockwise around data track 901, and ancillary qubits 912 travel clockwise around auxiliary track 902. In another example, data qubits 911 and ancillary qubits 912 may travel in opposite directions to each other around their respective tracks 901, 902. The data qubits 911 and ancillary qubits 912 periodically interact to perform X-checks 941 and Z-checks 951.

[0298] In this example, the tracks 901, 902 are substantially rectangular and arranged in a uniform array, due to certain desirable properties of the surface code architecture, in other examples the tracks 901, 902 can be any polygonal shape and arranged in any manner desired by the experimenter.

[0299] In this example, each data track 901 is substantially similar to the other data tracks 901, and data qubits 911 are simultaneously manipulated throughout the qubit processor. The manipulation devices in one or more data tracks 901 have initialization and / or gating functionality. The manipulation devices in these data tracks 901 may not have readout functionality, since the states of the qubits in these tracks may not be directly measurable. Typically, the states of these qubits can be measured indirectly, for example by measuring ancillary qubits 912.

[0300] Like the data tracks 901, each auxiliary track 902 is substantially similar to the other auxiliary tracks 902, such that auxiliary qubits 912 are simultaneously manipulated throughout the qubit processor. The manipulation devices in one or more auxiliary tracks 902 have read and / or gating functions. In practice, the manipulation devices in all auxiliary tracks 902 will have read and initialization functions. The simultaneous control of multiple data qubits 911 and multiple auxiliary qubits 912 advantageously reduces the number of control lines required, improving the efficiency of the qubit processor.

[0301] In another example, one or more data qubits 911 in one or more data tracks 901 may interact with, be manipulated, or be shuttled along the track separately from the other data qubits 911. Similarly, one or more ancillary qubits 912 in one or more auxiliary tracks 902 may interact with, be manipulated, or be shuttled along the track separately from the other ancillary qubits 912.

[0302] Each qubit processor illustrated generally herein is an illustration of a portion of a qubit processor, and each portion described is designed to be architecturally easily scalable.

[0303] 10 is a flow chart describing a qubit processing method. In step S101, a plurality of qubits are received by the operation devices in the respective defined tracks. The reception of the plurality of qubits by the operation devices in the respective defined tracks includes reception of a first qubit by the operation device in the first defined track, reception of a second qubit by the operation device in the second defined track, at least a portion of which is within a quantum interaction distance from the first track, reception of a third qubit by the operation device in the third defined track, at least a portion of which is within a quantum interaction distance from the first track, and reception of a fourth qubit by the operation device in the fourth defined track, at least a portion of which is within a quantum interaction distance from the first track.

[0304] In this example, the four tracks are arranged such that the first track is surrounded by the second, third, and fourth tracks. At least a portion of each of the second, third, and fourth tracks is within quantum interaction distance from the first track. At least another portion of each of the second, third, and fourth tracks is outside the quantum interaction distance from the first track. In this example, the portions of the second through fourth tracks that are within quantum interaction distance from the first track are corners of the tracks.

[0305] In step S102, the states of the multiple qubits are manipulated in the manipulation devices in the respective tracks, including manipulation of the state of the first qubit in the manipulation device in the first track, manipulation of the state of the second qubit in the manipulation device in the second track, manipulation of the state of the third qubit in the manipulation device in the third track, and manipulation of the state of the fourth qubit in the manipulation device in the fourth track.

[0306] Manipulating the state of a qubit includes initializing the state of the qubit, reading the state of the qubit, and / or performing single-qubit operations on the state of the qubit.

[0307] In step S103, the multiple qubits are transferred from the manipulation device to first locations in their respective tracks. The transfer of the multiple qubits from the manipulation device to first locations in their respective tracks includes a transfer of a first qubit from the manipulation device in the first track to the first location in the first track, a transfer of a second qubit from the manipulation device in the second track to the first location in the second track, a transfer of a third qubit from the manipulation device in the third track to the first location in the third track, and a transfer of a fourth qubit from the manipulation device in the fourth track to a fourth location in the first track.

[0308] In step S104, an interaction between the first qubit and the second qubit is enabled. The interaction is enabled when the first qubit is at a first location in the first track and the second qubit is at a first location in the second track by positioning the first location in the first track and the first location in the second track within a quantum interaction distance. In this example, the first location in the first track is at a corner of the first track and the first location in the second track is at a corner of the second track. The first location in the first track is closest to the second track and the first location in the second track is closest to the first track.

[0309] In step S105, a plurality of qubits are transferred from a first location to a second location within their respective tracks, the transfer of the plurality of qubits from the first location to the second location within their respective tracks including a transfer of a first qubit from a first location within the first track to a second location within the first track, a transfer of a second qubit from a first location within the second track to a second location within the second track, a transfer of a third qubit from a first location within the third track to a second location within the third track, and a transfer of a fourth qubit from a first location within the fourth track to a second location within the fourth track.

[0310] In step S106, an interaction between the first quantum bit and the third quantum bit is enabled. The manner in which the interaction is enabled is similar to that in step S104. Since the second location in the first track and the second location in the third track are arranged to be within a quantum interaction distance, when the first quantum bit is at the second location in the first track and the third quantum bit is at the second location in the third track, the first quantum bit and the third quantum bit are positioned within a quantum interaction distance.

[0311] In step S107, the qubits are transferred from the second location to a third location within their respective tracks, as described above in relation to step S105, with each qubit being transferred around the track to the next location within their tracks.

[0312] In step S108, an interaction between the first quantum bit and the fourth quantum bit is enabled. The manner in which the interaction is enabled is similar to steps S104 and S106. Because the third location in the first track and the third location in the fourth track are positioned within the quantum interaction distance, the interaction is enabled when the first quantum bit is at the third location in the first track and the fourth quantum bit is at the third location in the fourth track.

[0313] Following step S108, either step S109 or step S111 is performed. In step S109, the qubits are transferred from the third location in their respective tracks to the first location. As described above in connection with step S105, each qubit is transferred around the track to the next location within its track.

[0314] If step S109 is performed, then step S110 is performed after step S109. In step S110, an interaction between the first qubit and the second qubit is enabled when the first qubit is at a first location in the first track and the second qubit is at a first location in the second track. In this example, this is the same as step S104. Between steps S104 and S110, the first and second qubits orbit once around the first and second tracks, respectively, so that in step S110, the positions of the first and second qubits are the same as in step S104.

[0315] As an alternative to step S109, step S111 may be performed. In step S111, multiple qubits are transferred from the third locations in their respective tracks to a manipulation device. This is similar to the transfer step described above. A first qubit is transferred from the third location in the first track to a manipulation device in the first track, a second qubit is transferred from the third location in the second track to a manipulation device in the second track, a third qubit is transferred from the third location in the third track to a manipulation device in the third track, and a fourth qubit is transferred from the third location in the fourth track to a manipulation device in the fourth track.

[0316] When step S111 is performed, step S112 is performed after step S111. In step S112, the states of each of the multiple quantum bits are manipulated in the manipulation devices in the respective tracks. Step S112 includes manipulating the state of the first quantum bit in the manipulation device in the first track, manipulating the state of the second quantum bit in the manipulation device in the second track, manipulating the state of the third quantum bit in the manipulation device in the third track, and manipulating the state of the fourth quantum bit in the manipulation device in the fourth track.

[0317] Optionally, one or more qubits of the plurality of qubits are subjected to steps S109 and S110, while remaining qubits of the plurality of qubits are subjected to steps S111 and S112.

[0318] 11 is a flow chart describing a qubit processing method. In step S201, the state of a first qubit is manipulated on a manipulation device in a defined track. In step S202, the first qubit is transferred from the manipulation device to a first location in the track. In step S203, the first qubit is transferred from the first location in the track to a second location in the track. The first qubit is transferred from the manipulation device to the first location and from the first location to the second location using electronic shuttling.

[0319] In step S204, the state of the second qubit is manipulated in a manipulation device in the track. The manipulation device is used to manipulate the states of the first and second qubits. In one example, the manipulation device includes multiple manipulation elements. In that example, a first manipulation element is used to manipulate the state of the first qubit and a second initialization element is used to manipulate the state of the second qubit.

[0320] In step S205, the second quantum bit is transferred from the manipulation device to a first location in the track. In step S206, the first quantum bit is transferred from the second location in the track to a third location in the track. In step S207, the second quantum bit is transferred from the first location in the track to a second location in the track.

[0321] After step S207, either step S208 or step S209 is performed. In steps S208 and S209, the first quantum bit is transferred away from the third location in the track. In step S208, the first quantum bit is transferred from the third location in the track to the first location in the track. In step S209, the first quantum bit is transferred from the first location in the track to a manipulation device in the track. If step S209 is performed, then step S210 is performed after S209. In step S210, the state of the first quantum bit is manipulated in the manipulation device. The manipulation of the quantum bit state performed in step S210 can be the same as or different from the manipulation of the quantum bit state performed in step S201.

[0322] Step S211 is performed after step S208 if step S208 is performed, or after step S210 if steps S209 and S210 are performed. In step S211, the second quantum bit is transferred from a second location in the track to a third location in the track. After step S211, the second quantum bit is transferred from the third location. The second quantum bit, like the first quantum bit, is transferred to either the first location or a manipulation device (similar to steps S208 and S209).

[0323] The method of FIG. 11 describes the movement of a qubit pair around a defined track in a qubit processor. Within a track, there may be more than two qubits that move sequentially around the track. Qubits may be transferred between locations within the track and, optionally, to intermediate locations between the first, second, and third locations. One or more qubit operations and / or interactions are enabled for the first and second qubits (and any additional qubits) on the track. An interaction may be enabled between the first and second qubits by positioning them within a quantum interaction distance along the track, or a quantum gate operation (such as a rotation or phase shift) may be performed on the first or second qubit at one or more locations, or an interaction may be enabled between the first or second qubit and another qubit in an adjacent track.

[0324] The steps in Figure 11 are performed sequentially such that the first and second qubits are processed simultaneously within the qubit processor. The second qubit follows the first qubit around the track and undergoes the same processing steps immediately thereafter. This increases the throughput of the qubit processor.

[0325] As will be appreciated, the qubit processor comprises a number of defined tracks and a number of qubits within each track. A method of qubit processing using the qubit processor is provided in which inter-track and intra-track interactions are enabled between pairs of qubits by positioning the qubits within a quantum interaction distance. Thus, the qubit processing method of the present invention enables a pseudo-three-dimensional architecture using a qubit processor having a strictly two-dimensional architecture.

[0326] The above embodiments have been described in terms of qubits corresponding to quantum systems having two states. However, those skilled in the art will appreciate that the present disclosure is not limited to quantum systems with only two states, and that any "qudit" can be used, where the number of quantum states, "d", is an integer greater than or equal to two.

[0327] In this disclosure, exemplary dimensions and time scales are provided in terms of a qudit processor including silicon electron spin qubits, and one of ordinary skill in the art will appreciate that different dimensions and time scales may be appropriate in other qudit processor implementations. [Explanation of symbols]

[0328] 101, 201 tracks 111~114 Location 111~116 qubits 115~118 Gate device 121~126 qubits 131 Initialization device 131, 132 Operating device 132 Readout device 211~214 Location 215~218 Gate device 221~223 Quantum Bits 221~226 Quantum Bits 231~232 Initialization elements 231~234 Operation elements 231~234 elements 232~234 elements 233~234 Read elements Tracks 301-305 315~318 Gate device 321, 341, 351, 361, 371 qubits 322-325, 342-345, 352-355, 362-365, 372-375 Location 331~335 Operating device Tracks 401-405 406~409 plane 410~414 Operating device 415~418 Gate device 420~425 qubits 420, 430, 440, 450 Array 420, 430, 440, 450 Multiple qubits 422~425 qubits 430~435 qubits 430435 Quantum Bits 431~435, 441~445, 451~455 qubits 431~436 plane 432~435 qubits 440~445 qubits 440445 qubit 450~455 qubits 461~464, 466~469, 471~474, 476~479, 481~484 Location 471, 472, 476, 478, 481, 484 Location 491 Two-qubit interaction Tracks 501-507 511~516 qubits 511, 720~750 Array 512~516 qubits 521~527 Operating device 531~536 plane 541~546 Gate device 551~556 Quantum Bits 551~556, 561~566 Location Tracks 601-604 611~614 Quantum Bits 621~625 Location 621~625 Interaction location Tracks 701-705 706~709 plane 710~714 Operating device 715~718 Gate device 720~725 qubits 720~725, 731~735, 741~745, 751~755 qubits 730 Trucks 730~735 qubits 740, 720, 730, 750 Multiple qubits 740, 741, 745 qubits 750~754 qubits 761~767, 771, 773, 774, 776, 777, 779, 781, 783, 784 Location Tracks 801-805 811~816 Array 811~816 Multiple qubits 811~816 Quantum Bits 817~820 Gate device 821~825 Operating device 831~834, 843, 852, 861, 874 Location 901, 902 Trucks 902 Auxiliary Truck 911, 912 qubits 912 Auxiliary qubits 921 Gate device 931 Operating device 941 X Check 951 Z Check

Claims

1. 1. A method for performing quantum computing in a qudit processor, comprising: receiving a plurality of qudits at a manipulation device within each respective defined track; Receiving a first qudit at a manipulation device within a first defined track; receiving a second qudit at a manipulation device in a second defined track, at least a portion of which is within a quantum interaction distance from the first track; receiving a third qudit at a manipulation device in a third defined track, at least a portion of which is within the quantum interaction distance from the first track; receiving a fourth qudit at a manipulation device in a fourth defined track, at least a portion of which is within the quantum interaction distance from the first track; a receiving step including: manipulating the states of the qudits in their respective tracks at the manipulation device; transferring the plurality of qudits from the manipulation device to first locations within their respective tracks; enabling an interaction between the first qudit and the second qudit when the first qudit is at the first location in the first track and the second qudit is at the first location in the second track by positioning the first location in the first track and the first location in the second track within the quantum interaction distance; transferring the plurality of qudits from the first location to a second location within their respective tracks; enabling an interaction between the first qudit and the third qudit when the first qudit is at the second location in the first track and the third qudit is at the second location in the third track by positioning the second location in the first track and the second location in the third track within the quantum interaction distance; transferring the plurality of qudits from the second location to a third location within their respective tracks; enabling an interaction between the first qudit and the fourth qudit when the first qudit is at the third location in the first track and the fourth qudit is at the third location in the fourth track by positioning the third location in the first track and the third location in the fourth track within the quantum interaction distance; transferring the plurality of qudits from the third location to the first location within their respective tracks; enabling an interaction between the first qudit and the second qudit when the first qudit is at the first location in the first track and the second qudit is at the first location in the second track; transferring the plurality of qudits from the third location to the manipulation device within their respective tracks; manipulating the states of the plurality of qudits in the manipulation device within their respective tracks; The method includes:

2. The plurality of qudits is a first plurality of qudits, the method further comprising, after the step of transferring the first plurality of qudits from the first location to the second location within their respective tracks, receiving a second plurality of qudits at the first locations within each of the defined tracks, such that each track contains two qudits; Inclusive of each qudit of the second plurality of qudits follows a corresponding qudit of the first plurality of qudits within their respective tracks. The method of claim 1.

3. further comprising enabling an interaction between the first qudit of the first plurality of qudits and the first qudit of the second plurality of qudits by positioning the first qudit of the first and second plurality of qudits within the quantum interaction distance along the first track; The method of claim 2, comprising:

4. 3. The method of claim 2, further comprising: transferring the qudits from the third location to the first location within their respective tracks. transferring the qudits within their respective tracks from the third location to the manipulation device; transferring the plurality of qudits from the manipulation device to the first location within the first track; The method according to any one of claims 1 to 3, comprising:

5. The method of claim 1 , wherein each of the transferring steps comprises shuttling.

6. A method according to any one of claims 1 to 5, wherein each of the tracks forms a substantially polygonal loop.

7. The method of claim 6 , wherein one or more locations in each track are located at corners of the polygonal loop.

8. The method of claim 6 or 7, wherein one or more locations in each track lie along an edge of a loop of the polygon.

9. 1. A qudit processor, comprising: a first defined track forming a loop; second through kth defined tracks, where k>3, each of which forms a loop; Inclusive of each track configured to receive one or more qudits and to transfer the one or more qudits of that track along the track; each of the second through kth defined tracks is distinct from the first defined track, but is positioned such that at least a portion of each of the second through kth tracks is within a quantum interaction distance of the first track, thereby enabling interactions between qudits in the first track and the second through kth tracks; Quantum Dit Processor.

10. The qudit processor of claim 9 , wherein each track further comprises a manipulation device configured to manipulate the state of the qudits in that track.

11. The qudit processor of claim 10 , wherein the manipulation device of one or more tracks comprises a plurality of manipulation elements, each manipulating element configured to manipulate the state of a qudit in that track.

12. 1. A method for performing quantum computing in a qudit processor, comprising: manipulating a state of a first qudit at a manipulation device within a defined track; transferring the first qudit from the handling device to a first location within the track; transferring the first qudit from the first location in the track to a second location in the track; manipulating a state of a second qudit at the manipulation device in the track; transferring the second qudit from the handling device to the first location within the track; transferring the first qudit from the second location in the track to a third location in the track; transferring the second qudit from the first location in the track to the second location in the track; transferring the first qudit from the third location in the track to the first location in the track; transferring the first qudit from the third location in the track to the handling device in the track; manipulating a state of the first qudit with the manipulation device; transferring the second qudit from the second location in the track to the third location in the track; Inclusive of one or more qudit operations and / or interactions are enabled for the first and second qudits on the track; method.

13. The defined track is a first defined track, and the method further comprises: manipulating a state of another first qudit in a manipulation device in a second predefined track separate from the first predefined track; transferring the another first qudit from the manipulation device in the second track to a first location in the second track; transferring the another first qudit from the first location in the second track to a second location in the second track; manipulating a state of another second qudit in the manipulation device in the second track; transferring the another second qudit from the manipulation device in the second track to the first location in the second track; transferring the another first qudit from the second location in the second track to a third location in the second track; transferring the another second qudit from the first location in the second track to the second location in the second track; transferring the another first qudit from the third location in the second track to the first location in the second track; transferring the another first qudit from the third location in the second track to the manipulation device in the second track; manipulating a state of the other first qudit at the manipulation device in the second track; transferring the another second qudit from the second location in the second track to the third location in the second track; Inclusive of the operation and / or interaction of one or more qudits is effected on the other first and other second qudits on the second track; The method of claim 12.

14. The first location in the first track and the first location in the second track are within a quantum interaction distance, and the method further comprises: enabling an interaction between the first qudit and the other first qudit when the first qudit is at the first location in the first track and the other first qudit is at the first location in the second track; enabling an interaction between the second qudit and the other second qudit when the second qudit is at the first location in the first track and the other second qudit is at the first location in the second track; The method of claim 13, comprising:

15. 1. A qudit processor, comprising: a manipulation device and a defined track forming a loop leading from said manipulation device to said manipulation device, with at least first, second and third gating devices configured to perform quantum operations at respective first, second and third locations along said track, said track comprising: Receive multiple qudits, transferring the plurality of qudits in a first direction from the manipulation device to the first location, the second location, and the third location sequentially around the track in the loop; and a qudit processor configured to enable one or more qudit operations and / or one or more quantum interactions at the first, second, and third gate devices for one or more qudits of the plurality of qudits.

Images