Frequency patterns for reducing parasitic interactions in a quantum grid

Abstract

Methods, systems, and apparatus for operating qubits. In one aspect, a method includes: operating a first qubit from a first plurality of qubits at a first qubit frequency from a first qubit frequency region; and operating a second qubit from the first plurality of qubits at a second qubit frequency from a second first qubit frequency region, the second qubit frequency and the second first qubit frequency region being different from the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubit is diagonally opposite the first qubit in a two-dimensional qubit lattice.

Description

[0001] This application is a divisional application of the invention patent application filed on August 9, 2017, with application number 201780095621.4 and entitled "For reducing the frequency modes of parasitic interactions in quantum lattices". Technical Field

[0002] This specification relates to reducing parasitic interactions between qubits. For example, this specification describes systems and methods for operating qubits in frequency modes that reduce parasitic interactions, such as during the idling, measurement, and application of quantum logic gates. Background Technology

[0003] Large-scale quantum computers have the potential to provide rapid solutions to certain classes of difficult problems. To make large-scale quantum computing feasible, several challenges in designing and implementing the quantum architectures used to control and program quantum hardware must be overcome. Reducing the complexity of the quantum architecture while maintaining a high degree of control over the qubits included within it is a key step in building scalable quantum computers. Summary of the Invention

[0004] Typically, an innovative aspect of the subject matter described in this specification can be embodied in a method of operating a system of qubits, the method comprising actions of operating the qubit system, wherein the qubit system comprises: a first plurality of qubits, wherein each of the first plurality of qubits is configured to operate at a qubit frequency of one of a plurality of first qubit frequency regions; a second plurality of qubits, wherein each of the second plurality of qubits is configured to operate at a qubit frequency from one of a plurality of second qubit frequency regions; and a plurality of qubit couplers, each of the plurality of qubit couplers defining a corresponding qubit from the first plurality of qubits and a corresponding qubit from the second plurality of qubits. The nearest neighbor interaction between qubits, wherein the qubit system is arranged in a two-dimensional grid, and each of the first plurality of qubits is coupled to a plurality of qubits in the second plurality of qubits via a plurality of qubit couplers; wherein operating the qubit system includes: operating the first qubits of the first plurality of qubits at a first qubit frequency from a first qubit frequency region; and operating the second qubits of the first plurality of qubits at a second qubit frequency from a second first qubit frequency region, wherein the second qubit frequency and the second first qubit frequency region are different from the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubits are diagonally opposite the first qubits in the two-dimensional grid.

[0005] Other embodiments of this aspect include corresponding computer systems, apparatuses, and computer programs recorded on one or more computer storage devices, each computer storage device being configured to perform the actions of the method. A system of one or more computers may be configured to perform specific operations or actions by means of software, firmware, hardware, or a combination thereof installed on the system, which, in operation, causes the system to perform these actions. One or more computer programs may be configured to perform specific operations or actions by means of instructions that, when executed by a data processing device, cause the device to perform the actions.

[0006] The foregoing and other embodiments may optionally include one or more of the following features, individually or in combination. In some embodiments, the plurality of first qubits include data qubits, and the plurality of second qubits include measurement qubits.

[0007] In some embodiments, the method further includes operating a third data qubit from a plurality of data qubits at a second data qubit frequency, wherein the third data qubit is different from the second data qubit and is diagonally opposite the first data qubit in a two-dimensional grid.

[0008] In some embodiments, the method further includes: operating a fourth data qubit from a plurality of data qubits at a fourth data qubit frequency from a third data qubit frequency region, the third data qubit frequency region being different from the first data qubit frequency region, wherein the fourth data qubit is different from the second and third data qubits and is diagonally opposite to the first data qubit in a two-dimensional grid; and operating a fifth data qubit from a plurality of data qubits at a fifth data qubit frequency from the third data qubit frequency region, wherein the fifth data qubit is different from the second, third, and fourth data qubits and is diagonally opposite to the first data qubit in a two-dimensional grid.

[0009] In some implementations, the frequency region of the third data qubit is the same as that of the second data qubit.

[0010] In some implementations, the frequency region of the third data qubit differs from that of the second data qubit.

[0011] In some implementations, the frequency of the first data qubit differs from the frequency of the second data qubit by 2η, where η represents the nonlinearity of the system.

[0012] In some implementations, the frequency of the first data qubit differs from any one of the frequencies of (i) the third, (ii) the fourth, or (iii) the fifth data qubit by 2η, where η represents the nonlinearity of the system.

[0013] In some implementations, η = 0.2 GHz.

[0014] In some implementations, the second data qubit frequency region includes a predetermined frequency region, optionally including a frequency region with a width of 10 MHz.

[0015] In some implementations, the difference between the frequency of the second data qubit and the frequency of the third data qubit within the second data qubit frequency region is greater than the next nearest neighbor coupling strength g between the second data qubit and the third data qubit.

[0016] In some implementations, the third data qubit frequency region includes a predetermined frequency region, optionally including a frequency region with a width of 10 MHz.

[0017] In some implementations, the difference between the frequency of the fourth data bit and the frequency of the fifth data bit in the third data bit frequency region is greater than the second nearest neighbor coupling strength g between the fourth data bit and the fifth data bit.

[0018] In some implementations, the multiple data qubit frequency regions include four data qubit frequency regions, optionally including: a first idle frequency region, a first echo operation frequency region, a first single qubit gate frequency region, and a first interaction frequency region.

[0019] In some embodiments, the system for operating qubits further includes: operating a first measurement qubit from a plurality of measurement qubits at a first measurement qubit frequency from a first measurement qubit frequency region; and operating a second measurement qubit from a plurality of measurement qubits at a second measurement qubit frequency from a second measurement qubit frequency region, the second measurement qubit frequency and the second measurement qubit frequency region being different from the first measurement qubit frequency and the first measurement qubit frequency region, respectively, wherein the second measurement qubit is diagonally opposite the first measurement qubit in a two-dimensional grid.

[0020] In some embodiments, the method further includes operating a third measurement qubit from the plurality of measurement qubits at a second measurement qubit frequency, wherein the third measurement qubit is different from the second measurement qubit and is diagonally opposite the first measurement qubit in a two-dimensional grid.

[0021] In some embodiments, the method further includes operating a fourth measurement qubit from the plurality of measurement qubits at a fourth measurement qubit frequency from a third measurement qubit frequency region, the third measurement qubit frequency region being different from the first measurement qubit frequency region, wherein the fourth measurement qubit is different from the second and third measurement qubits and is diagonally opposite to the first measurement qubit in a two-dimensional grid; and operating a fifth measurement qubit from the plurality of measurement qubits at a fifth measurement qubit frequency from the third measurement qubit frequency region, wherein the fifth measurement qubit is different from the second, third, and fourth measurement qubits and is diagonally opposite to the first measurement qubit in a two-dimensional grid.

[0022] In some implementations, the frequency region of the third measurement qubit is the same as that of the second measurement qubit.

[0023] In some implementations, the frequency region of the third measurement qubit differs from that of the second measurement qubit.

[0024] In some implementations, the frequency of the first measured qubit and the frequency of the second measured qubit differ by 2η, where η represents the nonlinearity of the system.

[0025] In some implementations, the frequency of the first measured qubit differs from any one of the frequencies of (i) the third, (ii) the fourth, or (iii) the fifth measured qubit by 2η, where η represents the nonlinearity of the system.

[0026] In some implementations, η = 0.2 GHz.

[0027] In some implementations, the second measurement qubit frequency region includes a predetermined frequency region, optionally including a frequency region with a width of 10 MHz.

[0028] In some implementations, the difference between the frequency of the second measured qubit and the frequency of the third measured qubit within the second measured qubit frequency region is greater than the next nearest neighbor coupling strength g between the second and third measured qubits.

[0029] In some implementations, the third measurement qubit frequency region includes a predetermined frequency region, optionally including a frequency region with a width of 10 MHz.

[0030] In some implementations, the difference between the frequency of the fourth and fifth measurement qubits within the third measurement qubit frequency region is greater than the second nearest neighbor coupling strength g between the fourth and fifth measurement qubits.

[0031] In some implementations, the multiple measurement qubit frequency regions include four measurement qubit frequency regions, optionally including: a first idle frequency region, a first echo operation frequency region, a first single qubit gate frequency region, and a first interaction frequency region.

[0032] In some implementations, the multiple measurement qubit frequency regions and the multiple data qubit frequency regions also include a readout and reset frequency region adjacent to one of the multiple measurement qubit frequency regions.

[0033] In some embodiments, an apparatus for operating a system of qubits includes a first plurality of qubits, each of which is configured to operate at a qubit frequency from one of a plurality of first qubit frequency regions; a second plurality of qubits, each of which is configured to operate at a qubit frequency from one of a plurality of second qubit frequency regions; and a plurality of qubit couplers, each of which defines a nearest-neighbor interaction between a corresponding qubit from the first plurality of qubits and a corresponding qubit from the second plurality of qubits, wherein the system of qubits is arranged in a two-dimensional network. The system comprises: a lattice, wherein each of the first plurality of qubits is coupled to a plurality of qubits in the second plurality of qubits via a plurality of qubit couplers; and a qubit controller module configured as a system for operating qubits, wherein the system for operating qubits includes: operating a first qubit from the first plurality of qubits at a first qubit frequency from a first qubit frequency region; and operating a second qubit from the first plurality of qubits at a second qubit frequency from a second first qubit frequency region, the second qubit frequency and the second first qubit frequency region being different from the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubit is diagonally opposite the first qubit in a two-dimensional lattice.

[0034] In some implementations, the qubit controller module includes an excitation pulse generator and one or more excitation drive systems, and wherein operating the qubit at a qubit frequency from the qubit frequency region includes controlling the qubit via excitation pulses on the excitation drive system.

[0035] In some implementations, one or more excitation drive systems include a global excitation drive system.

[0036] In some implementations, the first plurality of qubits includes data qubits, and the second plurality of qubits includes measurement qubits.

[0037] Another innovative aspect of the subject matter described in this specification can be embodied in a method for operating a system of qubits, wherein the system of qubits is arranged in a two-dimensional grid, the method comprising: operating a first qubit at a first qubit frequency within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; and operating a second qubit at a second qubit frequency within a second qubit frequency region, wherein the second qubit frequency covers a second frequency range, the second qubit frequency and the second qubit frequency region being different from the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubit is diagonally opposite the first qubit in the two-dimensional grid.

[0038] Another innovative aspect of the subject matter described in this specification can be embodied in an apparatus comprising: a system of qubits arranged in a two-dimensional grid, wherein the system of qubits comprises: a first qubit at a first qubit frequency within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; and a second qubit at a second qubit frequency within a second qubit frequency region, wherein the second qubit frequency region covers a second frequency range, the second qubit frequency and the second qubit frequency region being different from the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubit is diagonally opposite the first qubit in the two-dimensional grid.

[0039] Another innovative aspect of the subject matter described in this specification can be embodied in a method comprising: a first qubit in a system operating at a first qubit frequency within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; a second qubit in a system operating at a second qubit frequency within a second qubit frequency region, wherein the second qubit frequency region covers a second frequency range, the second qubit frequency and the second qubit frequency region being different from the first qubit frequency and the first qubit frequency region, wherein the first qubit frequency differs from the second qubit frequency by a multiple of the nonlinearity of the system by qubits; and a third qubit in a system operating at a third qubit frequency from the second qubit frequency region, the third qubit frequency being different from the first qubit frequency and the second qubit frequency, wherein the third qubit is different from the second qubit, and the first qubit frequency differs from the third qubit frequency by a multiple of the nonlinearity of the system by qubits.

[0040] Another innovative aspect of the subject matter described in this specification can be embodied in an apparatus comprising: a system of qubits, wherein the system of qubits comprises: a first qubit at a first qubit frequency within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; a second qubit at a second qubit frequency within a second qubit frequency region, wherein the second qubit frequency region covers a second frequency range, the second qubit frequency and the second qubit frequency region being different from the first qubit frequency and the first qubit frequency region, wherein the first qubit frequency differs from the second qubit frequency by a multiple of the nonlinearity of the system in qubits; and a third qubit at a third qubit frequency from the second qubit frequency region, the third qubit frequency being different from the first qubit frequency and the second qubit frequency, wherein the third qubit is different from the second qubit, and the first qubit frequency differs from the third qubit frequency by a multiple of the nonlinearity of the system in qubits.

[0041] The subject matter described in this specification can be implemented in specific embodiments to achieve one or more of the following advantages.

[0042] As described in this specification, a quantum computing system that implements methods for reducing parasitic interactions between qubits can perform quantum computing operations while minimizing these interactions and introducing minimal errors. The methods described in this specification can improve the robustness of the quantum computing system and enhance the accuracy of the computations performed by the system.

[0043] As described in this specification, the methods for reducing parasitic interactions between qubits are scalable and allow for tolerant, practical requirements on the physical quantum computing hardware needed to implement the methods and perform quantum computing. For example, the methods and systems described in this specification can be implemented using a qubit frequency control architecture.

[0044] Furthermore, as described in this specification, methods for reducing parasitic interactions between qubits can increase the computational efficiency performed by a quantum computing system implementing such methods. For example, these methods enable the synchronous implementation of some quantum logic gates, thereby reducing the time required to execute algorithms.

[0045] Furthermore, as described in this specification, the method for reducing parasitic interactions between qubits in a quantum computing system is enhanced by placing two echo pulses (rotations about the X and / or Y axes designed to reduce the sensitivity of the qubit pairing environment) on the idle qubit during entanglement operations on two other qubits, thereby greatly simplifying the algorithmic implementation of quantum computing performed by the quantum computing system. For example, using the two echo pulses, a noise-suppressed sequence with ideal unitarity can be constructed. In cases where the ability to place two echo pulses on the idle qubit during entanglement operations on two other qubits is not available, it may be necessary to modify the algorithmic implementation to handle the unitarity of the echo pulses commuted by the entanglement gate representing the entanglement operation. The system and method described in this specification avoid such modifications.

[0046] Furthermore, as described in this specification, the methods for reducing parasitic interactions between qubits are tolerant of the thresholds for desired qubit detuning and parasitic coupling strength. Therefore, the practicality and applicability of the methods described in this specification are far-reaching.

[0047] One approach to constructing and operating quantum computing devices is based on surface codes, which are used as stabilizer codes. Surface codes provide a practical method for identifying and handling errors in a two-dimensional array of qubits. However, standard implementations of surface codes, such as those different from those described in this specification, require nearest-neighbor entanglement operations in dense patterns. As discussed herein, such dense patterns can lead to parasitic coupling between qubits that are diagonally opposite each other.

[0048] As described in this specification, a quantum computing system implementing methods for reducing parasitic interactions between qubits can perform surface code loops using a specific configuration of paired qubits. This configuration enables the surface code to be reliably implemented using a dense, closely spaced two-dimensional qubit grid. Furthermore, compared to other surface code implementations, this configuration allows for the use of fewer layers of entanglement operations to implement the surface code.

[0049] Details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the following description. Other features, aspects, and advantages of the subject matter will become apparent from the specification, drawings, and claims. Attached Figure Description

[0050] Figure 1 This is a block diagram of an example quantum computing system.

[0051] Figure 2 This is a flowchart of an example process for operating a system of qubits.

[0052] Figure 3A An example schematic data qubit frequency pattern is shown.

[0053] Figure 3B An example graph is shown illustrating the relationship between the idle error due to parasitic interactions for a single qubit and the qubit frequency divided by the system nonlinearity.

[0054] Figure 4 Example data qubits and measured qubit frequencies are shown.

[0055] Figure 5 This is a flowchart of an example process for performing entanglement operations on a two-dimensional array of qubits.

[0056] Figure 6 An example pairing of data and measurement qubits is shown for performing entanglement operations on a two-dimensional array of qubits.

[0057] Figure 7 This is an example curve of the frequency trajectory of a controlled Z-quantum gate.

[0058] Figure 8 This is an example graph showing the relationship between the probability of parasitic occupation transfer and the strength of diagonal coupling.

[0059] Figure 9 An example quantum circuit for measuring a stabilizer used in a surface code detection cycle is shown.

[0060] Figure 10 This is a flowchart of an example process for performing a surface code error detection loop.

[0061] Figure 11 An example uniform stabilizer for surface code detection loops is shown.

[0062] In the various figures, the same reference numerals and labels indicate the same elements. Detailed Implementation

[0063] In quantum computing systems, qubits are arranged and manipulated in a two-dimensional grid using nearest-neighbor interactions. However, in such a grid, the coupling between diagonally opposite qubits is relatively large due to their proximity. This coupling is parasitic—unintended and uncontrolled. For example, if two diagonally opposite qubits form a parasitic coupling, the qubits may influence each other in unintended and uncontrolled ways, for example, by inducing unwanted transitions in one or both qubits. Unintended transitions in qubits may cause the state of the qubit to flip from one computational state to another, or to cause transitions to higher qubit levels outside the computational subspace. Such transitions may introduce errors into the computation performed by the qubits. Therefore, minimizing parasitic coupling between qubits, especially on a large scale, is a crucial task in quantum computing when operating quantum computers.

[0064] Example operating environment

[0065] Figure 1 This is a block diagram of an example quantum computing system 100. The example quantum computing system 100 includes multiple qubits 102 (represented as hollow and solid circles) and a qubit controller module 104. The example quantum computing system 100 is an example of a system that can be used to perform quantum algorithm operations, simulations, or computations.

[0066] Multiple qubits 102 are arranged in a two-dimensional grid 112. For clarity, Figure 1 The two-dimensional grid 112 depicted includes 7×7 qubits; however, in some embodiments, system 100 may include a smaller or larger number of qubits. Multiple qubits 102 interact with each other through multiple qubit couplers (e.g., qubit coupler 114). The multiple qubit couplers define the nearest-neighbor interactions between the multiple qubits 102. In some embodiments, the strength g of the multiple qubit couplers is an adjustable parameter. In some cases, the multiple qubit couplers included in the quantum computing system 100 may be couplers with a fixed coupling strength.

[0067] In some embodiments, the plurality of qubits 102 may include data qubits (e.g., hollow circles such as qubit 118) and measurement qubits (e.g., solid circles such as qubit 116). Data qubits are qubits that participate in computations performed by system 100. Measurement qubits are qubits that can be used to determine the result of the computation performed by the data qubits. That is, during computation, the unknown state of the data qubits is transferred to the measurement qubits using appropriate physical operations and is measured via appropriate measurement operations performed on the measurement qubits.

[0068] Each of the multiple data qubits is configured to operate at a qubit frequency from a corresponding frequency region. For example, each data qubit can be configured to operate at a corresponding data qubit frequency from one of the multiple data qubit frequency regions. Similarly, each measurement qubit can be configured to operate at a corresponding measurement qubit frequency from one of the multiple measurement qubit frequency regions.

[0069] A qubit frequency region can include a computational qubit frequency region. For example, each data or measurement qubit can be configured to operate at a qubit frequency from the corresponding computational qubit frequency region, for instance, when the qubit participates in computation or algorithmic operations. If transitions between the fundamental states of a qubit computation occur at a qubit frequency from the computational qubit frequency region, then the qubit can be said to operate at that qubit frequency.

[0070] A qubit frequency region can include an idle qubit frequency region. For example, when a qubit is idle and not participating in interaction or computation, each data or measurement qubit can be configured to operate at a qubit frequency from the corresponding idle qubit frequency region. If the expected unitary value of the qubit is unitary over the duration... This means the qubit can be said to operate at a qubit frequency from the idle qubit frequency region for a set duration. Therefore, the qubit does not participate in entangled quantum logic gate operations—only echo pulses with unitary values ​​are applied to the qubit, where the echo pulse is defined as a rotation about the X and / or Y axes designed to reduce the qubit's sensitivity to its environment. In other words, the qubit can be said to be stationary at a frequency from the idle qubit frequency region, a frequency that minimizes the interaction between this qubit and other qubits, while the other qubits perform interactions or undergo unitary operations.

[0071] The frequency region of a qubit can include the frequency region of interacting qubits. For example, data and measurement qubits can be configured to operate at the corresponding qubit frequencies from the respective interaction frequency regions, for example, when the data and measurement qubits interact.

[0072] The frequency region of a qubit can include readout and reset frequency regions. For example, a measurement qubit can be configured to operate at a qubit frequency from the corresponding readout and reset frequency regions, for instance, when a measurement operation is performed on the measurement qubit. If the qubit frequency is close to or aligned with the operating frequency of the readout resonator or other measurement device that causes the measurement or reset operation, then the qubit can be said to operate at a qubit frequency from the readout and reset qubit frequency regions.

[0073] Data qubits and measurement qubits are arranged such that qubit couplers define nearest-neighbor interactions between data qubits and measurement qubits. That is, each data qubit is coupled to multiple measurement qubits, and each measurement qubit is coupled to multiple data qubits.

[0074] In other embodiments, the plurality of qubits 102 may not be separated into a plurality of data qubits and a plurality of measurement qubits. For example, in the case where system 100 includes a quantum computer that does not implement surface code, such as a quantum computer for executing one or more quantum algorithms (such as a supremacy algorithm), the system may not need to distinguish between data and measurement qubits. In these examples, the disclosed systems and methods can be used to reduce the number of quantum logic gate layers required to execute quantum algorithms, thereby speeding up the algorithms and reducing their errors.

[0075] When there is no distinction between data qubits and measurement qubits, the same process described herein can be used. For example, qubits can be configured to operate at qubit frequencies within a corresponding frequency region. Some qubits can be configured to operate at a corresponding qubit frequency within one of a plurality of different first qubit frequency regions. Other qubits can be configured to operate at a corresponding qubit frequency within one of a plurality of different second qubit frequency regions. The qubit frequency regions within the plurality of first and second qubit frequency regions may include corresponding computation frequency regions, idle frequency regions, interaction frequency regions, and readout / reset frequency regions.

[0076] As described herein, the example two-dimensional grid 112 may include parasitic couplings between qubits diagonally opposite each other, for example, parasitic coupling 120. In some cases, parasitic couplings between qubits include non-zero parasitic coupling strength g. diag For example, in some cases, the parasitic coupling strength may take values ​​as high as g. diag / π~5MHz.

[0077] Multiple qubits 102 in the two-dimensional grid 112 are operated via a qubit controller module 104. The qubit controller module 104 can operate the qubits 102 by controlling their frequency, for example, according to a qubit operating frequency 108. The qubit operating frequency depends on the type of qubits included in the system 100 and the operation being performed by the system. (Refer to the following...) Figures 2 to 4 Describe in detail example qubit operation frequency modes used to reduce parasitic interactions between diagonal qubits.

[0078] For example, the qubit controller module 104 can control the respective frequencies of the qubits 102 such that the frequencies of one or more qubits are tuned toward or away from the frequencies of the excitation pulses generated by the excitation pulse generator 110 on the excitation driveline 124, such as the entanglement operation frequency 106. The excitation pulses generated by the excitation pulse generator 110 can include pulses whose frequencies implement quantum operations, such as those of quantum logic gates. For example, the excitation pulse generator 110 can be configured to generate excitation pulses whose frequencies cause one or more qubits to perform entanglement operations, such as those of controlled Z-gates. (Refer to below...) Figures 2 to 5 A more detailed description is given of performing entanglement operations on a two-dimensional grid of qubits.

[0079] Multiple qubits can be coupled to the excitation drive system via corresponding couplers (e.g., coupler 126). In some cases, the coupler can be a capacitive coupler, for example, implemented via a microwave line extending adjacent to the qubit capacitor. For convenience, in Figure 1 A global excitation drive system is shown. However, in some embodiments, system 100 may include, for example, multiple excitation drive systems corresponding to multiple qubits.

[0080] The qubit controller module 104 can be configured to tune the frequency of qubit 102 via one or more qubit frequency control lines (e.g., qubit frequency control line 122). For convenience, in Figure 1 The image shows a single qubit frequency control line. However, in some embodiments, system 100 may include, for example, multiple qubit frequency control lines corresponding to each of a plurality of qubits 102. The qubit frequency control lines can be supplied via in-plane wiring or out-of-plane wiring.

[0081] The type of qubit controller module 104 utilized by system 100 depends on the type of qubits used by the system. As an example, qubits realized via atomic, molecular, or solid-state quantum systems typically have energy separation at the level of the relevant qubit in the microwave or optical domain. The states of such qubits can be manipulated and controlled using external fields such as microwaves or optical fields. In this case, as an example, a mode-locked laser can be used as a qubit controller due to its broadband spectrum characterized by both radio frequency and microwave structures. In another example, the qubit controller may include a collection of individual qubit controllers implemented by a radio frequency generator, and a global excitation controller or a collection of global excitation controllers implemented by a radio frequency or microwave generator. In both cases, the qubit controller can be manually operated or connected to a computer and can be controlled via suitable software that allows the specification and automatic execution of desired qubit operations.

[0082] Hardware programming: Quantum bit frequency modes for reducing parasitic interactions

[0083] For your convenience, please refer to the following: Figures 2 to 4 The provided disclosure is described with reference to a system of multiple qubits comprising multiple data qubits and multiple measurement qubits, which interact via qubit couplers that define nearest-neighbor interactions between the data and measurement qubits. However, this is only one example of a system of qubits that can be programmed and operated using the techniques described herein. For example, in some embodiments, the following techniques can be used to program and operate a system of qubits that do not distinguish between data qubits and measurement qubits. For example, in cases where a system using qubits performs a quantum algorithm (e.g., a hegemony algorithm), the qubits may be indistinguishable. The following arrangements and processes can still be used in settings where it is not necessary to distinguish between data and measurement qubits.

[0084] Figure 2 This is a flowchart of an example process 200 for a system used to operate qubits. For convenience, process 200 will be described as being executed by a system of one or more quantum or classical computers located at one or more locations. For example, the above references can be used. Figure 1 The quantum bit controller 104 of the described system 100 implements process 200.

[0085] A qubit system comprises qubits interacting via qubit couplers that define nearest-neighbor interactions. In some embodiments, the qubit system may include multiple data qubits and multiple measurement qubits that interact via qubit couplers that define nearest-neighbor interactions between the data and measurement qubits. The qubit system is arranged in a two-dimensional grid, and each of the multiple data qubits is coupled to the multiple measurement qubits via the multiple qubit couplers. Each data qubit is configured to operate at a data qubit frequency from one of the multiple data qubit frequency regions. Each measurement qubit is configured to operate at a measurement qubit frequency from one of the multiple measurement qubit frequency regions. Example data qubit frequency regions and measurement qubit frequency regions are described below with reference to steps 202 and 204. (Reference) Figure 1 An example system of qubits is shown.

[0086] The system operates the first data qubit from multiple data qubits at a first data qubit frequency from the first data qubit frequency region (step 202). For example, see the following reference. Figure 3AAs shown in the illustrative data qubit frequency mode 300, the data qubit 302 can operate at a data qubit frequency b from the corresponding data qubit frequency region B.

[0087] The system operates a second data qubit from multiple data qubits at a second data qubit frequency from a second data qubit frequency region (step 204). The second data qubit is a data qubit diagonally opposite the first data qubit in a two-dimensional grid. For example, see the following reference. Figure 3A As shown in the illustrative data qubit frequency mode 300, the system can operate a second qubit, for example, qubit 304, at a data qubit frequency a from the corresponding data qubit frequency region A.

[0088] The frequency of the second data qubit and the frequency region of the second data qubit are different from the frequency and frequency region of the first data qubit, respectively. For example, see the following reference. Figure 3A As shown in the illustrative data qubit frequency mode 300, the first data qubit 302 can operate at a data qubit frequency b from the corresponding data qubit frequency region B, and the second data qubit 304 diagonally opposite the data qubit 302 can operate at a data qubit frequency a from a different data qubit frequency region A.

[0089] In some implementations, the system can further operate a third data qubit from the plurality of data qubits at the frequency of the second data qubit. The third data qubit differs from the second data qubit and is diagonally opposite the first data qubit in two dimensions. For example, see the following reference... Figure 3A As shown in the illustrative data qubit frequency mode 300, the system can operate the first data qubit 302 at a data qubit frequency b from the corresponding data qubit frequency region B, operate the second data qubit 304 diagonally opposite to the data qubit 302 at a data qubit frequency a from a different data qubit frequency region A, and operate the third data qubit 306, which is different from the second data qubit 304 and diagonally opposite to the first data qubit 302.

[0090] In some implementations, the system can further operate the fourth and fifth data qubits from a plurality of data qubits at corresponding fourth data qubit frequencies from the third data qubit frequency region and fifth data qubit frequencies from the third data qubit frequency region. The third data qubit frequency region differs from the first data qubit frequency region. The fourth and fifth data qubits are diagonally opposite to the first data qubit.

[0091] For example, see the reference below. Figure 3A As shown in the illustrative data qubit frequency mode 300, the system can operate the first data qubit 302 at a data qubit frequency b from the corresponding data qubit frequency region B, the second data qubit 304 at a data qubit frequency a from the data qubit frequency region A, the third data qubit 306 at a data qubit frequency a' from the data qubit frequency region A, the fourth data qubit 310 at a data qubit frequency a from the data qubit frequency region A, and the fifth data qubit 308 at a data qubit frequency a' from the data qubit frequency region A. In some embodiments, the third data qubit frequency region may be the same as the second data qubit frequency region. In other embodiments, the third data qubit frequency region may be different from the second data qubit frequency region; for example, data qubits 308 and 310 may operate at data qubit frequencies c' and c, respectively.

[0092] As in Figure 3A As illustrated in the schematic data qubit frequency pattern 300, in some embodiments, the multiple data qubit frequency regions include two data qubit frequency regions, for example, a first region A and a second region B. In these embodiments, the data qubit frequencies from each region can be offset by -2η, where η represents the nonlinearity of the system. For example, data qubit frequencies a∈A and b∈B can differ by 2η. One explanation for why the frequency difference depends on the nonlinearity of the system is as follows: Idle qubits may be affected by parasitic interactions from diagonal qubits. To minimize these effects, the frequency difference between diagonal qubits is optimally chosen. The effects of diagonal qubits can be expressed through the nonlinearity of the system. Therefore, by analyzing the nonlinearity of the system, a range of frequency values ​​that locally minimize the effects of diagonal qubits can be found. That is, the system nonlinearity provides an indication of how to minimize parasitic interactions between qubits and therefore how to minimize system errors. Figure 3B The following example graph is shown: This example graph shows the relationship between the idle ZZ error (y-axis) of a single qubit, which is caused by the frequency shift due to parasitic interactions from diagonal qubits, and the qubit frequency divided by the system nonlinearity (x-axis).

[0093] Additionally, in some embodiments, the data qubit frequency from a specific data qubit frequency region may include frequencies within a predetermined frequency region (e.g., a predetermined frequency region with a width of 10 MHz). For example, Figure 3AData qubits 304 and 306 can be operated at data qubit frequencies a and a', respectively, where a and a' differ by approximately 10 MHz.

[0094] Furthermore, in some implementations, swapping can be avoided by ensuring that the difference between the frequencies of the data qubits within a predetermined frequency region is greater than the second nearest neighbor coupling constant g. For example, the difference between the frequencies a and a' of the data qubits diagonally opposite qubit 304 and 306 to qubit 302 can be greater than g, for example, (aa′) >> g. For a second nearest neighbor coupling constant g = 1 MHz, a 10 MHz detuning between a and a' is acceptable.

[0095] like Figure 3A As illustrated in schematic data qubit frequency pattern 350, in some embodiments, multiple data qubit frequency regions include four data qubit frequency regions, such as regions A, B, C, and D. Multiple frequency regions allow the qubits to be "parked" and individually controlled, for example, using a global XY excitation drive system. For example, for η = 200 MHz, data qubits can be parked or operated at frequencies between 6 and 7 GHz, such as 6.7 GHz, 6.3 GHz, 6.8 GHz, and 6.2 GHz.

[0096] In these implementations, the multiple data qubit frequency regions may include a first idle frequency region. When a data qubit is not actively involved in algorithmic computations performed by the qubit system and is idle, the data qubit may be configured to operate at the idle frequency.

[0097] The multiple data qubit frequency regions may also include a first echo operation frequency region. The data qubits can be configured to operate at the echo operation frequency when an echo operation is performed on the data qubit.

[0098] The multiple data qubit frequency regions may also include a first single qubit gate frequency region. When a single qubit quantum gate (such as a Hadamard quantum logic gate or a Pauli X, Y, or Z quantum logic gate) is being executed on a data qubit, the data qubit can be configured to operate at the single qubit gate frequency region.

[0099] The frequency regions of multiple data qubits can also include interaction frequency regions. When a data qubit is interacting with a neighboring measurement qubit, such as when entanglement is performed on paired data and neighboring measurement qubits, the data qubit can be configured to operate at the interaction frequency region. (Reference) Figure 4 The frequency range of example data qubits is shown.

[0100] In an embodiment where the multiple data qubit frequency regions include four data qubit frequency regions, the system for operating the qubits may include: for each data qubit, operating the data qubit at a data qubit frequency from the data qubit frequency region, wherein each other data qubit diagonally opposite the data qubit operates at a corresponding other data qubit frequency from a different data qubit frequency region, and the other data qubit diagonally opposite the data qubit operates at a corresponding other data qubit frequency from a different data qubit frequency.

[0101] For example, as in Figure 3A As illustrated in the schematic data qubit frequency pattern 350, data qubit 352 can operate at a data qubit frequency b from its corresponding data qubit frequency region B, and each of the other data qubits diagonally opposite data qubit 352, such as data qubits 354, 356, 358, and 360, can operate at data qubit frequencies a, a', c, or c' from different data qubit frequency regions A and C. The other data qubits diagonally opposite data qubit 352, such as data qubits 356 and 358, or data qubits 354 and 360, operate at their respective data qubit frequencies from different data qubit frequency regions. That is, data qubit 356 operates at a frequency from data qubit frequency region A, and data qubit 358 operates at a frequency from a different data qubit frequency region C. Similarly, data qubit 354 operates at a frequency from data qubit frequency region A, and data qubit 360 operates at a frequency from a different data qubit frequency region C.

[0102] In these implementations, the data qubit frequencies corresponding to the diagonal data qubits can be offset by -2η, for example, (ab) / η ≥ 2. For example, in illustrative data qubit frequency pattern 350, the data qubit frequencies can be set to a = 0, b = -2η, c = 0.5η, d = -2.5η. In some implementations, given a frequency range of approximately 0.8–1.0 GHz in which similar qubits—data or measurement qubits—can be stationed, η = 0.2 GHz. For example, if all data qubits are stationed at frequencies between 6–7 GHz (e.g., in the 0.8–1 GHz range) and all measurement qubits are stationed between 4–5 GHz, interactions may occur between 5 GHz and 6 GHz. However, other layouts are also possible.

[0103] Additionally, in some embodiments, the data qubit frequency from a specific data qubit frequency region may include frequencies within a predetermined frequency region (e.g., a predetermined frequency region with a width of 10 MHz). For example, Figure 3A Data qubits 354 and 356 can be operated at data qubit frequencies a and a', respectively, where a and a' differ by approximately 10 MHz.

[0104] Furthermore, in some implementations, the difference between the frequencies of other data qubits diagonally opposite to this qubit (e.g., data qubit frequencies a, a' or c, c') can be greater than the nearest neighbor coupling constant g, for example, (aa′) >> g.

[0105] As described in this article, for example, refer to Figure 4 The aforementioned data qubit frequency patterns facilitate the execution of dense modes in entanglement operations, such as those of controlled Z quantum logic gates, even without nearest-neighbor (including diagonal) qubits of the same frequency. Therefore, parasitic interactions can be reduced.

[0106] The aforementioned characteristics of data qubits can also be applied to multiple measurement qubits in a qubit system. For example, a system for operating qubits may further include: for each measurement qubit, operating the measurement qubit at a measurement qubit frequency from a measurement qubit frequency region, wherein each other measurement qubit diagonally opposite the measurement qubit is operated at a corresponding other measurement qubit frequency from a different measurement qubit frequency region.

[0107] In some implementations, the multiple measurement qubit frequency regions include two measurement qubit frequency regions. The measurement qubit frequency and the other measurement qubit frequency can differ by 2η. The other measurement qubit frequencies can include frequencies within a predetermined frequency region, optionally including a predetermined frequency region with a width of 10 MHz. The difference between other measurement qubit frequencies within the predetermined frequency region can be greater than the nearest neighbor coupling constant g.

[0108] In some implementations, the multiple measurement qubit frequency regions may include four measurement qubit frequency regions, optionally including a second idle frequency region, a second echo operation frequency region, a second single qubit gate frequency region, and a second interaction frequency region. For example, data qubits may be stationary or operational at frequencies between 6 and 7 GHz, measurement qubits may be stationary or operational at frequencies between 4 and 5 GHz, and interactions between qubits may occur between 5 and 6 GHz.

[0109] In these examples, the system for operating qubits may further include: for each measurement qubit, operating the measurement qubit at a measurement qubit frequency from a measurement qubit frequency region, wherein each other measurement qubit diagonally opposite the measurement qubit is operated at a corresponding other measurement qubit frequency from a different measurement qubit frequency region, and wherein the other opposite measurement qubit diagonally opposite the measurement qubit is operated at a corresponding other measurement qubit frequency from a different measurement qubit frequency region.

[0110] In some implementations, the diagonal measurement qubits may be offset by 2η, optionally where η = 0.2 GHz. Other measurement qubit frequencies from the same measurement qubit frequency region may include frequencies within a predetermined frequency region (optionally including a predetermined frequency region with a width of 10 MHz). The difference between other measurement qubit frequencies from the same measurement qubit frequency region is greater than g.

[0111] In some implementations, a readout and reset frequency region may be included adjacent to one of the multiple measurement qubit frequency regions. Placing the readout and reset frequency region adjacent to the measurement qubit frequency region allows the qubit frequency to be tuned close to the readout resonator to obtain large dispersion, and thus a large measurement signal. Additionally, placing the readout and reset frequency region adjacent to the measurement qubit frequency region allows the measurement qubit to be reset using the readout resonator. Furthermore, placing the readout and reset frequency region adjacent to the measurement qubit frequency region allows the movement of the measurement qubit to extend beyond the readout resonator, thereby allowing the movement of the data qubit to approach the readout resonator to obtain large dispersion and a large signal without negatively impacting the measurement qubit.

[0112] Figure 3AExample schematic data qubit frequency patterns 300 and 350 are shown. Example schematic data qubit frequency pattern 300 shows multiple data qubits, such as data qubits 302, 304, 306, 308, and 310, coupled to multiple measurement qubits via nearest-neighbor interactions. Example schematic data qubit frequency pattern 300 shows data qubits operating at data qubit frequencies a, a', b, and b' from two data qubit frequency regions A and B. Each data qubit in example schematic data qubit frequency pattern 300 operates at a data qubit frequency different from that of its diagonally adjacent data qubits. For example, data qubit 302 operates at data qubit frequency b from frequency region B, while its diagonally adjacent data qubits 304, 306, 308, and 310 operate at data qubit frequencies a, a', a', and a, respectively, from frequency region A.

[0113] The example illustrative data qubit frequency pattern 350 shows multiple data qubits, such as data qubits 352, 354, 356, 358, and 360, which are coupled to multiple measurement qubits via nearest-neighbor interactions. The example illustrative data qubit frequency pattern 350 shows data qubits operating at data qubit frequencies a, a', b, b', c, c', and d, d'. The data qubit frequencies can be frequencies from four corresponding data qubit frequency regions (e.g., regions A, B, C, and D). Each data qubit in the example illustrative data qubit frequency pattern 350 operates at a data qubit frequency different from the data qubit frequencies at which its diagonally adjacent data qubits operate. Additionally, qubits diagonally adjacent to and opposite each other, such as qubits 356 and 358, operate at different data qubit frequencies. For example, data qubit 352 operates at data qubit frequency b from frequency region B, while its diagonally adjacent data qubits 354 and 360 operate at data qubit frequencies a and c' from frequency regions A and C, respectively, because they are diagonally opposite each other. Similarly, its diagonally adjacent data qubits 356 and 358 operate at data qubit frequencies a' and c, respectively, from frequency regions A and C, because they are diagonally opposite each other.

[0114] Figure 4The example data qubit and measurement qubit frequencies are shown at 400. The example data qubit and measurement qubit frequencies include nine different frequencies ranging from 410, 412, to 414. Four frequencies are data qubit frequencies at 402. Four frequencies are measurement qubit frequencies at 406. One of the data qubit frequencies is the interaction frequency at 404. Similarly, one of the measurement qubit frequencies is the interaction frequency at 404. One frequency is the readout and reset frequency at 408. This configuration of frequencies allows dense modes of entanglement operations, such as those of controlled Z quantum logic gates, to be performed without neighboring (including diagonal) qubits of the same frequency. Because the qubits are geometrically well separated, parasitic interactions can be reduced.

[0115] Data qubit frequencies 1 and 2 in frequency range 410 are idle data qubit frequencies. Similarly, measurement qubit frequencies 3 and 4 in frequency range 412 are idle measurement qubit frequencies. Data qubit frequencies 3 and 4 and measurement qubit frequencies 1 and 2 in frequency range 414 are qubit frequencies used for the qubit being manipulated. In some embodiments, one or more frequencies in frequency ranges 410 and 412 or frequency range 414 may also be selected for a single qubit gate in a global application.

[0116] The example data qubit and measurement qubit frequencies 400 also include an additional readout and reset frequency 416 for the data qubit. Referring to Figure 400, the additional readout and reset frequency 416 is shown at a higher frequency than the data qubit frequency 402, i.e., above the data qubit frequency 402. The additional readout and reset frequency 416 allows the data qubit to be read out or reset while interacting with other qubit pairs. This can be beneficial in various settings. An example setting involves performing surface code error detection in superconducting hardware, since the measurement qubit becomes a data qubit when the overexcited (leaking) state is removed, and vice versa. In this setting, it can be very advantageous to measure the data qubit while interacting with other qubit pairs.

[0117] Hardware programming: Synchronization qubit detuning for reducing parasitic interactions

[0118] For convenience, please refer to Figures 5 to 8The described techniques relate to a system of multiple qubits comprising multiple data qubits and multiple measurement qubits that interact via a qubit coupler that defines the nearest neighbor interaction between the data and measurement qubits. However, this is just one example of a system of qubits that can be programmed and operated using the following techniques. For example, in some implementations, the following techniques can be used to program and operate a system of qubits that do not distinguish between data and measurement qubits. For example, in cases where a system using qubits performs a quantum algorithm (e.g., a hegemony algorithm), the qubits may be indistinguishable. The following techniques and arrangements can still be used in settings where distinguishing between data and measurement qubits is not required.

[0119] Figure 5 This is a flowchart of an example process 500 for performing entanglement operations using a system employing qubits. For convenience, process 500 will be described as being performed by a system of one or more quantum or classical computers located at one or more locations. For example, the above references can be used... Figure 1 The quantum bit controller module 104 of the described system 100 implements process 500. In some embodiments, it may be combined with the above references. Figures 2 to 4 The frequency pattern described is used to execute process 500.

[0120] A qubit system comprises multiple qubits and multiple qubit couplers that define the nearest-neighbor interactions between the multiple qubits. In some embodiments, the multiple qubits may include multiple data qubits, multiple measurement qubits, and multiple qubit couplers that define the nearest-neighbor interactions between the data qubits and the measurement qubits. The qubit system is arranged as a two-dimensional grid, and each of the multiple data qubits is coupled to the multiple measurement qubits via a corresponding qubit coupler. (Refer to above) Figure 1 An example two-dimensional grid is shown.

[0121] The system pairs multiple data qubits with corresponding adjacent measurement qubits (step 502). In some embodiments, the system can pair multiple data qubits and measurement qubits into non-overlapping pairs. For example, each data qubit paired with a corresponding adjacent measurement qubit may not be paired with another adjacent measurement qubit. Similarly, each measurement qubit paired with a corresponding adjacent data qubit may not be paired with another adjacent data qubit. Figure 6 An example pairing of data qubits and adjacent measurement qubits forming non-overlapping pairs is shown in an example two-dimensional qubit grid 600.

[0122] Alternatively or additionally, the system can pair multiple data qubits and their corresponding adjacent measurement qubits into pairs with parallel qubit couplers. For example, refer to the above reference. Figure 1 The two-dimensional grid 112 shown allows the system to pair data qubits with measurement qubits located directly above or below the data qubits. In this configuration, the paired data and measurement qubits can be described as having north-south parallel couplers.

[0123] In systems where multiple data qubits are paired with their corresponding adjacent measurement qubits in non-overlapping pairs, the parallel couplers have the same orientation. That is, each measurement qubit can be paired with its corresponding adjacent data qubit to its north (or south). Figure 6 In the example two-dimensional grid 600, an example pairing of data qubits and adjacent measurement qubits into non-overlapping pairs with north-south parallel couplers is shown. In some cases, such as those where the system pairs multiple data qubits with corresponding adjacent measurement qubits into overlapping pairs, the parallel couplers can have different orientations. That is, some measurement qubits can be paired with a first data qubit in the north direction and a second data qubit in the south direction. In the example two-dimensional grid 600, the qubits are coupled only to the coupler in the north direction, as indicated by arrow 626.

[0124] As another example, refer to the above references. Figure 1 The two-dimensional grid 112 shown allows the system to pair data qubits with measurement qubits directly to the right or left of the data qubits. In this configuration, the paired data and measurement qubits can be described as having east-west parallel couplers.

[0125] When the system pairs multiple data qubits with their corresponding adjacent measurement qubits into non-overlapping pairs, the parallel coupler has the same orientation. That is, each measurement qubit can be paired with a corresponding adjacent data qubit to its west (or east). When the system pairs multiple data qubits with their corresponding adjacent measurement qubits into overlapping pairs, the parallel coupler can have different orientations. That is, some measurement qubits can be paired with a first data qubit in the west-facing direction and a second data qubit in the east-facing direction. Figure 6 An example pairing of data qubits and adjacent measurement qubits in an east-west parallel coupler with different orientations is shown in example two-dimensional grid 650. In example two-dimensional grid 650, as indicated by arrows 628 and 630, the qubits are coupled to the coupler in both the east and west directions.

[0126] In some implementations, the system can pair a subset of multiple data qubits with corresponding adjacent measurement qubits. For example, the system can pair multiple data qubits with corresponding adjacent measurement qubits such that each paired data qubit and measurement qubit is not adjacent to any other paired data qubit and measurement qubit. Figure 6 An example non-nearest pair of data qubits and corresponding adjacent measurement qubits is shown in an example two-dimensional grid 600.

[0127] In some implementations, the system can pair multiple data qubits with corresponding adjacent measurement qubits to form multiple subsets of paired data and measurement qubits. For example, the system can repeat the pairing process described above on multiple subsets, for example, until each qubit in the system is paired with at least one other qubit.

[0128] In some cases, multiple subsets of paired data and measurement qubits can include non-overlapping subsets of paired data and measurement qubits. For example, Figure 6 The example two-dimensional grid 600 illustrates multiple non-overlapping subsets of paired data and corresponding adjacent measurement qubits. In the example two-dimensional grid 600, each subset includes non-nearest pairs of paired data and corresponding adjacent measurement qubits. In other cases, multiple subsets of paired data and measurement qubits may include overlapping subsets of paired data and measurement qubits. For example, Figure 6 The example two-dimensional grid 650 shows multiple overlapping subsets of paired data and corresponding adjacent measurement qubits.

[0129] The system performs an entanglement operation in parallel for each paired data and measurement qubit (step 504). For example, the system can apply a two-qubit quantum logic gate, such as a controlled Z quantum logic gate, in parallel to each paired data and measurement qubit. Since the frequency amplitude of the applied entanglement operation may vary, performing the entanglement operation in parallel for each paired data and measurement qubit is understood to mean performing the entanglement operation in parallel for each paired data and measurement qubit to the extent allowed by the hardware used to execute process 500. Example variations are described in more detail below.

[0130] When the system generates multiple subsets of paired data qubits and corresponding adjacent measurement qubits, as described above with reference to step 504, the system can perform entanglement operations in parallel on each paired data and measurement qubit within a respective subset. To perform entanglement operations on each data and measurement qubit in the system of qubits, the system can sequentially perform entanglement operations on the paired data and measurement qubits within each subset. In some embodiments, the order in which the system selects subsets to perform entanglement operations on can be arbitrary.

[0131] Due to the configuration of the paired qubits, as described above with reference to step 504, each qubit involved in the entanglement operation (or each qubit involved in a sequential application of the entanglement operation on a subset of paired qubits) is either not adjacent to other qubits involved in the entanglement operation, or has the same type diagonally. For example, in the case where data qubits and adjacent measurement qubits have been paired into non-nearby pairs of data and adjacent measurement qubits, as... Figure 6 As shown in group 602, the qubits involved in one entanglement operation are not adjacent to the qubits involved in other entanglement operations. As another example, in the case where data qubits and adjacent measurement qubits have been paired into an overlapping subset of paired data and measurement qubits with parallel couplers, such as... Figure 6 As shown in group 608, the qubits involved in an entanglement operation are of the same type diagonally, for example, qubits 610 and 612.

[0132] Therefore, when entanglement is performed in parallel for each paired data and measurement qubit, each measurement qubit can be detuned without resonant crossover with another measurement qubit performing a similar frequency trajectory to its corresponding data qubit. In fact, since the entanglement is performed in parallel, the detuning Δf between diagonal qubits is constant (or nearly constant, see below), and therefore no occupation migration from diagonal interactions will occur. Furthermore, each data qubit can perform a portion of the trajectory—they do not have to maintain a constant frequency. For example, data qubits can perform a frequency trajectory moving toward the measurement qubit. The advantages of the method performed by the system remain.

[0133] To perform entanglement operations on each paired data and measurement qubit in parallel, the system detunes each measurement qubit in the paired data and measurement qubits in parallel. As described herein, detuning each measurement qubit in the paired data and measurement qubits in parallel may include maintaining a constant or nearly constant detuning Δf between the measurement qubits in the paired data and measurement qubits. For example, the system may maintain a detuning frequency from a predetermined frequency range, such as a frequency in the 100 MHz range (e.g., between 500 MHz and 400 MHz) or in the 200 MHz range (e.g., between 700 MHz and 500 MHz). Where the system pairs multiple data qubits with corresponding adjacent measurement qubits to form multiple non-overlapping subsets of paired data and measurement qubits, the system may perform entanglement operations on each paired data and measurement qubit in the subsets approximately in parallel for each subset.

[0134] In some implementations, the system can perform entanglement operations on each paired data and measurement qubit by applying an entanglement operation frequency trajectory to the paired data and measurement qubits. (See reference) Figure 7 An example controlled Z-gate frequency trajectory is shown that can be applied to one or more paired data and corresponding adjacent measurement qubits.

[0135] In some implementations, the system can apply corresponding entanglement operation frequency trajectories to different pairs of data and measurement qubits. In these implementations, variations between the corresponding entanglement operation frequency trajectories can be kept below a predetermined threshold. For example, due to variations in the control pulse amplitude, such as those referenced herein. Figure 1 This change will occur in the form of the excitation transmission system that is ignored.

[0136] Figure 6 An example pairing of data and measurement qubits for performing entanglement operations on a first qubit two-dimensional array 600 and a second qubit two-dimensional array 650 is shown. Both qubit two-dimensional arrays 600 and 650 include multiple data qubits, such as data qubits 614 and 616, and multiple measurement qubits, such as measurement qubits 618 and 620. Each of the multiple data qubits is coupled to multiple adjacent measurement qubits via a corresponding qubit coupler, as referenced herein. Figure 1 As stated above.

[0137] In the 2D array 600, each paired data and adjacent measurement qubit does not overlap with another paired data and adjacent measurement qubit. Furthermore, each paired data and adjacent measurement qubit has a parallel north-south qubit coupler in the same direction—that is, each measurement qubit is coupled to a data qubit to the south. For convenience, the couplers in each paired data and measurement qubit are shown as north-south couplers, but these couplers could also be north-south (where each measurement qubit is coupled to a data qubit to the north), east-west (where each measurement qubit is coupled to a data qubit to the west), or west-east (where each measurement qubit is coupled to a data qubit to the east).

[0138] The example first qubit two-dimensional array 600 comprises three non-overlapping subsets. Each subset includes multiple paired data and adjacent measurement qubits. (Reference) Figure 6 The first subset includes all qubits enclosed by solid lines, such as qubit pairs 602, 624, and 622. The second subset includes all qubits enclosed by thick dashed lines, such as qubit pair 604. The third subset includes all qubits enclosed by thin dashed lines, such as qubit pair 606. In some cases, as shown in qubit array 600, the pairing of data and adjacent measurement qubits may not be exhaustive. For example, some qubits on the periphery of the grid may not be paired with other qubits.

[0139] Each subset comprises non-neighbor pairs of data qubits and adjacent measurement qubits, where a qubit is said to be neighboring another qubit if it is coupled to or diagonally opposite to another qubit. That is, a pair in each subset is not neighboring any other pair in the subset. Therefore, when entanglement operations are performed approximately in parallel on each pair of data and adjacent measurement qubits in a corresponding subset, each qubit involved in the corresponding entanglement operation is not neighboring any other qubit involved in any other corresponding entanglement operation. For example, when entanglement operations are performed in parallel on the pairs included in the subset represented by the solid lines, the measurement qubits in pair 622 can change their frequencies without resonating with the frequencies of another measurement qubit performing a similar frequency trajectory, because the measurement qubits diagonally opposite the measurement qubits in pair 622 are members of other subsets represented by the thick and thin dashed lines. As described above, this configuration reduces the probability of parasitic occupancy qubit leakage.

[0140] In the two-dimensional array 650, each paired data and measurement qubit has parallel qubit couplers with different orientations, namely, east-west couplers (where each measurement qubit is coupled to a data qubit to the west) or west-east couplers (where each measurement qubit is coupled to a data qubit to the east). In other words, each measurement qubit in array 650 can be coupled to a data qubit via an east-west coupler, coupled to a data qubit via a west-east coupler, or both. Similarly, each data qubit in array 650 can be coupled to a measurement qubit via an east-west coupler, coupled to a measurement qubit via a west-east coupler, or both. For convenience, the couplers in each paired data and measurement qubit are shown as east-west and west-east couplers, but these couplers could also be north-south and north-south couplers.

[0141] In some implementations, a north-south coupler or a north-south coupler can be used to repeat the above pattern, so that all nearest-neighbor data qubits and measurement qubits can interact.

[0142] The example second qubit two-dimensional array 650 includes four overlapping subsets. Each subset includes multiple paired data and adjacent measurement qubits. (Reference) Figure 6 The first subset includes all qubits enclosed by solid lines, for example, qubit pair 654. The second subset includes all qubits enclosed by thick dashed lines, for example, qubit pair 658. The third subset includes all qubits enclosed by thin solid lines, for example, qubit pair 656. The fourth subset includes all qubits enclosed by dotted lines, for example, qubit pair 652. In some cases, as shown in qubit array 650, the pairing of data and measurement qubits can be exhaustive, i.e., each qubit can be paired with at least one other qubit.

[0143] Each subset comprises a pair of data qubits and adjacent measurement qubits. For example, a data qubit in a given subset is diagonally opposite to at least one other data qubit in that subset, or a measurement qubit in a given subset is diagonally opposite to at least one other measurement qubit in that subset. Therefore, when entanglement operations are performed approximately in parallel on each pair of data and adjacent measurement qubits within a given subset, each qubit involved in a corresponding entanglement operation is adjacent (diagonally opposite) to other qubits of the same type involved in other corresponding entanglement operations. However, by detuning each measurement qubit in a subset in parallel, for example by maintaining an approximately constant detuning Δf between the measurement qubits in the paired data and measurement qubits, each measurement qubit can be detuned without resonant crossover with another measurement qubit performing a similar frequency trajectory on its corresponding data qubit. As described above, this configuration reduces the probability of parasitic occupied qubit leakage.

[0144] Figure 7 This is a graph 700 showing the frequency trajectory 702 of an example controlled Z-quantum gate. Graph 700 illustrates the frequency trajectory as shown in the reference above. Figure 5 The example control frequency amplitude (ΔH) during the application of adiabatic controlled Z quantum gates is described. z The relationship between the control frequency amplitude and the normalized time. For example, the control frequency amplitude can be expressed as shown above. Figure 1 The amplitude of the control pulse for the controlled Z quantum gate is generated by the excitation pulse generator 110 and emitted by the excitation drive system 124.

[0145] The example frequency trajectory 702 can be applied to paired data qubits and measurement qubits to perform entanglement operations, such as controlled Z quantum gates. (See above reference.) Figure 5 As described, in some implementations, the frequency trajectories applied approximately in parallel to the corresponding pairs of data and measurement qubits may include variations in the amplitude of control pulses. For example, controlling the frequency amplitude (ΔH) z The value of ) may change, for example, by a factor of 100 MHz, to the value shown in graph 700.

[0146] Figure 8 The above should be considered. Figure 5 Example graph 800 shows the relationship between the probability of parasitic occupation leakage and the diagonal coupling strength when entanglement operations are performed in parallel on paired data and measurement qubits.

[0147] The probability of parasitic occupancy qubit leakage during standard entanglement operations (e.g., entanglement operations different from those described in this disclosure) of paired data and measurement qubits can be estimated using the framework of Landau-Zener transitions. The framework of Landau-Zener transitions is, for example, provided by J. Martinis and M. Geller in Phys. Rev. A90, 022307 (2014), “Fast adiabatic qubit gates using only σ z control (using only σ) z The controlled fast adiabatic quantum bit gate is described in "Controlled Fast Adiabatic Quantum Bit Gate", the disclosure of which is incorporated herein by reference in its entirety. Within this framework, the probability of occupying leakage can be given by the following formula:

[0148]

[0149] In the above formula, H x This represents the coupling strength of the qubit, and This represents the control pulse that enables the standard entanglement operation.

[0150] Pick The rate of frequency change during the entanglement operation frequency trajectory can be estimated as And the rate of change of the control pulse can be estimated as Plugging these values ​​into the above equation gives P = 0.04. This probability of parasitic occupancy qubit leakage is a significant and harmful occupancy leakage.

[0151] The probability P of parasitic occupation leakage during the entanglement operation as described in this specification can be estimated as:

[0152] P=|θ mr | 2 / 4

[0153]

[0154] In the above formula, θ = arctan(H) x / H z () is the phase associated with the control pulse that implements the entanglement operation. Where g represents the coupling strength between the data qubit and the measurement qubit, H z Represents the control pulse, θ mr This indicates the error angle during the movement and rotation of the frame, and

[0155] Using this framework, the probability of parasitic occupation leakage during entanglement operations according to this disclosure is plotted in graph 800 as a function of the parasitic coupling strength. In graph 800, as referenced above... Figure 5 The detuning frequency Δf, for example, changes from 500 MHz to 400 MHz due to variations in the amplitude of the control pulses between qubits, and η = 200 MHz. Graph 800 shows the detuning frequency for 10... 5 and 10 7 The diagonal coupling strength g between them diag / 2π(MHz), the probability of parasitic occupancy leakage remains <10 -11 This provides a significant improvement in the probability of diagonal qubit level crossover—an improvement of 10. 9 The order of magnitude.

[0156] Hardware programming: Surface code loop

[0157] In some settings, quantum computers can provide an efficient means of solving problems that might be difficult to solve efficiently using traditional classical computers. Examples include factoring very large numbers into their primes and searching large, unstructured datasets. However, physical systems such as ionic systems, spin circuits in semiconductors, and superconducting circuits may not always perform well enough to be used directly as computational qubits in quantum computing devices.

[0158] One approach to building quantum computing devices is based on surface codes. Surface codes provide a fault-tolerant method for representing information in quantum computing devices. Logical qubits are sets of physical qubits arranged in a way that allows logical qubits to perform better than individual physical qubits.

[0159] In some cases, surface code can operate as stabilizer code—a method of measuring the stabilizer to detect errors when they occur. By selecting appropriate options for stabilizer measurements, qubits can be manipulated to perform logical operations. Thus, measuring stabilizers on a system of qubits constitutes the basic repetitive loop of a quantum computer, upon which all higher-level functions can be built.

[0160] Figure 9 An example quantum circuit 900 is shown, which is used to measure a stabilizer for a surface code error detection loop. The example quantum circuit 900 includes a five-qubit register. The five-qubit register includes a measurement qubit, represented as |0>, and four data qubits representing the nearest neighbors of the measurement qubit. In the example quantum circuit, it is assumed that the measurement qubit is located in a two-dimensional grid, as shown in the reference... Figure 1Therefore, the four nearest-neighbor data qubits correspond to the data qubits |S> to the south, |W> to the west, |E> to the east, and |N> to the north.

[0161] In some cases, such as when the measurement qubit has fewer adjacent data qubits, a quantum circuit can have a smaller qubit register. For example, if the measurement qubit is at a corner of a two-dimensional grid, it may have only two adjacent data qubits. In this example, the corresponding quantum circuit could have a three-qubit register.

[0162] Example quantum circuit 900 demonstrates the execution of the above references. Figure 10 The sequence of quantum logic gates required for the surface code error detection loop 1000, as described herein. Figure 10 The example quantum circuit 900 includes a first Hadamard gate 952 applied to the measurement qubit |0>. Subsequently, a first entanglement operation 956 is performed on the measurement qubit register |0> and the south-facing data qubit register |S>. Then, a second Hadamard gate 958 is applied to the west-facing data qubit register |W>. Finally, a second entanglement operation 960 is applied to both the measurement qubit register |0> and the west-facing data qubit register |W>.

[0163] Example quantum circuit 900 includes a third hadamard gate 972 and a fourth hadamard gate 974. Hadamard gates 972 and 974 are sequentially applied to the west qubit |W> and the east qubit |E>, respectively. When example quantum circuit 900 is applied to the above reference... Figure 1 In the system of measurement qubits and data qubits, the Hadamard gate applied to the data qubit to the west (after the entanglement operation between the first measurement qubit and the data qubit to the east) is canceled out by the Hadamard gate applied to the data qubit to the east (before the entanglement operation between the second measurement qubit and the data qubit to the east).

[0164] The third entanglement operation 962 is applied to the measurement qubit register |0> and the east data qubit register |E>. Then, the fifth hadamard gate 964 is applied to the east data qubit register |E>. The fourth entanglement operation 966 is applied to the measurement qubit register |0> and the north data qubit register |N>. The sixth hadamard gate is applied to the measurement qubit register |0>, and then measurement operation 970 is performed.

[0165] Entanglement operations 956, 960, 962, and 966 can include controlled Z quantum logic gates. When Hadamard quantum logic gates are applied before and after the controlled Z quantum logic gates, such as Hadamard quantum logic gates 958 and 972 or 974 and 964, these three gates (Hadamard, controlled Z, and Hadamard) operate together as a controlled X quantum logic gate. Therefore, in general, if the measurement qubit is in the |1> state, then... Figure 9 The entanglement operation described in the text can represent the application of the operator ZXXZ (controlled Z, controlled X, controlled X, controlled Z).

[0166] Figure 10 It is used for multiple quantum circuits (e.g., Figure 9 The flowchart illustrates an example process 1000 of a quantum circuit (shown in the diagram) executing a surface code error detection loop. For convenience, process 1000 will be described as being executed by a system of one or more quantum or classical computers located in one or more locations. For example, the above reference can be used... Figure 1 The quantum bit controller 104 of the described system 100 implements process 1000. In some embodiments, it can be combined with the above reference. Figures 2 to 8 The described technology is used to execute process 1000.

[0167] Example process 1000 is described as being arranged by the system as a two-dimensional grid (e.g., Figure 1 Multiple data qubits and multiple measurement qubits of grid 112 are executed, as referenced above. Figure 1 Each of the plurality of data qubits is coupled to an adjacent measurement qubit via a corresponding qubit coupler.

[0168] The system initializes multiple measurement qubits (step 1002). For example, as... Figure 9 As shown in the example quantum circuit 900, initializing multiple measurement qubits may include preparing the measurement qubits in the computational fundamental state of |0>.

[0169] The system applies a Hadamard quantum logic gate to the initialized measurement qubit (step 1004). By initializing the measurement qubit in the computational fundamental state of |0> and applying the Hadamard quantum logic gate to the initialized measurement qubit, the measurement qubit is placed in a 50 / 50 superposition state of |0> and |1>. (Refer to above) Figure 9 The application of the Hadamard quantum logic gate 952 to the initialization of the measurement qubit is shown.

[0170] The system performs multiple entanglement operations on the first pair of paired measurement and data qubits (step 1006). For example, the entanglement operations may include a controlled Z quantum logic gate. Applying the controlled Z quantum logic gate to the paired measurement and data qubits includes applying a Z operator to the data qubit if the measurement qubit is in state |1>.

[0171] Each pair of measurement and data qubits in the first set includes a measurement qubit coupled to an adjacent data qubit in a first direction. For example, each pair may include a measurement qubit coupled to an adjacent data qubit below the measurement qubit (e.g., in a south-facing direction) via a corresponding qubit coupler. (References herein) Figure 6 A two-dimensional qubit grid 600 is used to illustrate and describe example pairs of measurement qubits coupled to corresponding adjacent data qubits in the south-facing direction. (Reference) Figure 9 This illustrates the application of entanglement operation 956 to a measurement qubit paired with a data qubit on the south side.

[0172] In some embodiments, performing multiple entanglement operations on the first set of paired measurement and data qubits includes separating the paired measurement and data qubits into multiple subsets of the paired qubits, the subsets comprising non-overlapping and non-nearest pairs. In these embodiments, non-nearest is understood to include diagonally non-nearest pairs. (Refer to above) Figure 6 The two-dimensional qubit grid 600 shows and describes several example subsets of paired qubits. For example... Figure 6 As shown in the two-dimensional qubit grid 600, in some embodiments, the multiple subsets may include three subsets 602, 604 and 606.

[0173] The system can then perform entanglement operations in parallel on pairs of qubits in each of multiple subsets. For example, as referenced... Figure 5 As described, performing entanglement operations in parallel on pairs of qubits in each of multiple subsets may include detuning each measurement qubit in each subset in parallel.

[0174] The system applies a Hadamard quantum logic gate to multiple data qubits in the second direction (step 1008). For example, the system can apply a Hadamard quantum logic gate to multiple data qubits in the west-facing direction from the measurement qubit. (See reference) Figure 9 This demonstrates the application of the Hadamard quantum logic gate 958 to the data qubits on the west side.

[0175] The system performs multiple operations on the second set of paired measurement and data qubits (step 1010). These operations may include controlled Z-gates and Hadamard quantum gates. For example, the system may perform a controlled Z-gate on the measurement qubit paired with the data qubit in the second direction, followed by a Hadamard quantum gate on the data qubit in the second direction. Then, the system may perform a Hadamard quantum gate on the data qubit in the third direction, followed by a controlled Z-gate on the measurement qubit paired with the data qubit in the third direction.

[0176] Each pair of measurement and data qubits in the second set includes a measurement qubit coupled to an adjacent data qubit in a second or third direction, the second and third directions being perpendicular to the first direction, with the second direction opposite to the third direction. For example, each pair may include a measurement qubit coupled to an adjacent data qubit to the right or left of the measurement qubit, i.e., in an east or west direction, via a corresponding qubit coupler. Due to the commutation of entanglement operations in the west and east directions, the system can perform a mixture of entanglement operations in the west and east directions.

[0177] The above reference Figure 6 A two-dimensional qubit lattice 650 is shown and described, illustrating example pairs of measurement qubits coupled to corresponding adjacent data qubits in the east and west directions. (Reference) Figure 9 Applications of entanglement operations 960 and 962 to measurement qubits paired with data qubits on the west and east sides are shown.

[0178] In some embodiments, performing multiple entanglement operations on the second set of paired measurement and data qubits includes separating the paired measurement and data qubits into multiple subsets of the paired qubits, the subsets including overlapping and neighboring pairs. In these embodiments, neighboring is understood to include diagonally neighboring pairs. (Refer to above) Figure 6 A two-dimensional qubit lattice 650 is shown and described, illustrating several examples of such paired qubits. For example... Figure 6 As shown in the two-dimensional qubit grid 650, in some embodiments, the multiple subsets may include four subsets 652, 654, 656 and 658.

[0179] The system can then perform operations in parallel on pairs of qubits in each of multiple subsets. For example, as referenced... Figure 5 As described, performing entanglement operations in parallel on pairs of qubits in each of multiple subsets may include detuning each measurement qubit in each subset in parallel.

[0180] The system applies a Hadamard quantum logic gate to multiple data qubits in a third-direction direction (step 1012). For example, the system can apply a Hadamard quantum logic gate to multiple data qubits in an eastward direction from the measurement qubit. (See reference) Figure 9 This illustrates the application of the Hadamard quantum logic gate 964 to the data qubits on the east side. (See reference...) Figure 9 As described, when the Hadamard quantum logic gate is applied before and after the controlled Z quantum logic gate, for example, as described with reference to steps 1010 and 1012, the three gates together act as the controlled X quantum logic gate.

[0181] The system performs multiple entanglement operations on the third set of paired measurement and data qubits (step 1014). As described above, the entanglement operations may include controlled Z quantum logic gates. Each pair in the third set of paired measurement and data qubits includes a measurement qubit coupled to an adjacent data qubit in a fourth direction opposite to the first direction. For example, each pair may include a measurement qubit coupled to an adjacent data qubit above the measurement qubit, i.e., in the north direction, via a corresponding qubit coupler. This can be directly modified. Figure 6 An example pair of measurement qubits coupled to corresponding neighboring data qubits in the north direction is generated using a two-dimensional qubit grid of 600. (See reference) Figure 9 The application of entanglement operation 966 to a measurement qubit paired with a north-facing data qubit is shown.

[0182] In some embodiments, performing multiple entanglement operations on a third set of paired measurement and data qubits includes separating the paired measurement and data qubits into multiple subsets of the paired qubits, the subsets comprising non-overlapping and non-nearest pairs. In these embodiments, non-nearest is understood to include diagonally non-nearest pairs. In some embodiments, the multiple subsets may include three subsets.

[0183] The system can then perform entanglement operations in parallel on pairs of qubits in each of multiple subsets. For example, as referenced... Figure 5 As described, performing entanglement operations in parallel on pairs of qubits in each of multiple subsets may include detuning each measurement qubit in each subset in parallel.

[0184] The system applies Hadamard quantum logic gates to multiple measurement qubits (step 1016). Reference Figure 9 This demonstrates the application of the Hadamard quantum logic gate 968 to the measurement of qubits.

[0185] The system measures multiple measurement qubits to detect errors (step 1018). Reference Figure 9 Example measurement operation 970 is shown.

[0186] As described above, performing multiple entanglement operations on the first set of paired measurement and data qubits requires three sequential applications of the array of entanglement operations—one application for each subset. If this scheme is applied individually to all four directions of nearest-neighbor interactions, such as north, south, east, and west, the complete surface code error detection loop 1000 would require 12 applications of entanglement operations. However, for example, according to the above reference... Figure 5 and Figure 6 The described technique detunes geometrically diagonally measured qubits in parallel, and the denser mode of entanglement operations makes all interactions perpendicular to the first direction (e.g., east and west) only in four layers of CZ gates—one application for each subset—resulting in only ten applications in total.

[0187] Optionally, the system can further perform leakage removal. For example, the system can perform leakage removal simultaneously with the final entanglement operation of each measurement qubit (e.g., simultaneously with step 1014 above). For example, the system can swap the measurement and data qubits so that each type of qubit is reset alternately. This can be achieved by applying a controlled Z-addition swapped quantum logic gate that interacts and transfers information in the computational fundamental states |0> and |1>, but does not transfer information in states |2> and higher.

[0188] In some implementations, subsequent surface code error detection loops can be performed in the reverse order of the loops described in steps 1002-1018 above. For example, instead of performing the south-west / east-north detection loop as described above, the system can perform a north-west / east-south detection loop. That is, the system can initialize multiple measurement qubits, apply a Hadamard quantum logic gate to the initialized measurement qubits, perform entanglement operations in parallel on a third subset of paired data and measurement qubits, apply a Hadamard quantum logic gate to multiple data qubits, perform entanglement operations in parallel on a second subset of paired data and measurement qubits; apply a Hadamard quantum logic gate to multiple data qubits, perform entanglement operations in parallel on a first subset of paired data and measurement qubits, apply a Hadamard quantum logic gate to multiple measurement qubits, and measure multiple measurement qubits to detect errors. Performing subsequent surface code error detection loops in this order ensures that data remains local; for example, the information read from each paired measurement qubit corresponds only to the corresponding data qubit.

[0189] Figure 11 An example implementation of surface code 1100 is shown. Example implementation 1100 shows a two-dimensional qubit array, as referenced above. Figure 1As described, each qubit in a two-dimensional qubit array is represented as a hollow circle, such as qubit 1104, or as a solid circle, such as 1106. In some embodiments, hollow circles represent data qubits, as referenced above. Figure 1 As described above. In these embodiments, solid circles represent measurement qubits, as referenced above. Figure 1 As described. For clarity, a two-dimensional qubit array comprises 5×5 qubits, but in some cases, the implementation of surface code may include a smaller or larger number of qubits.

[0190] As referenced above Figure 1 The qubits interact with each other through multiple nearest-neighbor qubit couplers; for simplicity, these couplers are not shown in example embodiment 1100. Therefore, away from the array boundary, each data qubit contacts four measurement qubits, and each measurement qubit contacts four data qubits. Thus, each measurement qubit performs four measurements. At the array boundary, a measurement qubit contacts three data qubits and performs three measurements, while a data qubit contacts two or three measurement qubits.

[0191] Example implementation 1100 includes multiple uniform stabilizers, such as stabilizer 1102. Stabilizers are used to preserve the quantum state of the qubit array. Typically, by repeatedly measuring the quantum system using the complete set of easy stabilizers, the quantum system is forced into a synchronized and unique eigenstate of all stabilizers. Stabilizers can be measured without disturbing the system. When the measurement result changes, this corresponds to one or more qubit errors, and the measurement projects the quantum state onto different stabilizer eigenstates. Surface code stabilizers are described, for example, by A. Fowler et al. in “Surface codes: Towards practical large-scale quantum computation” in Phys. Rev. A 86, 032324 (2012), the disclosure of which is incorporated herein by reference in its entirety.

[0192] Each stabilizer in example implementation 1102 includes and The product of operators. For example, stabilizer 1102 can be represented as... Where indices n, w, e, and s represent the directions north, west, east, and south relative to the stabilizer's operation on the data qubit. This is achieved by combining them in this way. and Operators can perform relative interactions synchronously (e.g., east-west interactions)—where synchronization is understood to mean synchronization to the extent allowed by the hardware used to implement the surface code—because east-west operators commute.

[0193] The digital and / or quantum themes and embodiments of digital functional operations and quantum operations described in this specification may be implemented in digital electronic circuits, suitable quantum circuits, or more generally in quantum computing systems, in tangibly embodied digital and / or quantum computer software or firmware, in digital and / or quantum computer hardware (including the structures disclosed in this specification and their structural equivalents), or combinations thereof. The term "quantum computing system" may include, but is not limited to, a quantum computer, a quantum information processing system, a quantum cryptography system, or a quantum simulator.

[0194] Embodiments of the digital and / or quantum themes described in this specification can be implemented as one or more digital and / or quantum computer programs, i.e., one or more modules of digital and / or quantum computer program instructions encoded on a tangible, non-transitory storage medium for operation by a data processing device or for controlling the operation of a data processing device. The digital and / or quantum computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubits, or a combination thereof. Alternatively or additionally, the program instructions can be encoded on artificially generated propagating signals capable of encoding digital and / or quantum information, such as machine-generated electrical, optical, or electromagnetic signals, generated to encode digital and / or quantum information for transmission to a suitable receiver device for execution by the data processing device.

[0195] The terms quantum information and quantum data refer to information or data carried, stored, or preserved in quantum systems, the smallest non-trivial system being the qubit, i.e., the system that defines the unit of quantum information. It should be understood that the term "qubit" encompasses all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems can include, for example, multi-level systems with two or more levels. For example, such systems can include atoms, electrons, photons, ions, or superconducting qubits. In many implementations, the computational fundamental state is equivalent to the ground state and the first excited state; however, it should be understood that other settings where the computational state is equivalent to a higher-level excited state are also possible.

[0196] The term "data processing device" refers to digital and / or quantum data processing hardware and encompasses all kinds of devices, apparatuses, and machines for processing digital and / or quantum data, including programmable digital processors, programmable quantum processors, digital computers, quantum computers, multiple digital and quantum processors or computers, and combinations thereof. The device may also be or include special-purpose logic circuitry, such as FPGAs (Field-Programmable Gate Arrays), ASICs (Application-Specific Integrated Circuits), or quantum simulators—that is, quantum data processing devices designed to simulate or generate information about a particular quantum system. Specifically, a quantum simulator is a special-purpose quantum computer that does not have the ability to perform general-purpose quantum computing. In addition to the hardware, the device may optionally include code that creates the operating environment for digital and / or quantum computer programs, such as code constituting processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.

[0197] Digital computer programs (which may also be referred to or described as programs, software, software applications, modules, software modules, scripts, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form, including as standalone programs or as modules, components, subroutines, or other units suitable for use in a digital computing environment. Quantum computer programs (which may also be referred to or described as programs, software, software applications, modules, software modules, scripts, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or can be written in a quantum programming language (such as QCL or Quipper).

[0198] Digital and / or quantum computer programs may, but do not need to, correspond to files in a file system. Programs may be stored as a portion of a file holding other programs or data (e.g., one or more scripts stored in a markup language document), as a single file dedicated to the program under discussion, or as multiple coordinating files (e.g., files storing one or more modules, subroutines, or code sections). Digital and / or quantum computer programs can be deployed to run on a single digital computer or a single quantum computer, or on multiple digital and / or quantum computers located at one site or distributed across multiple sites and interconnected via digital and / or quantum data communication networks. A quantum data communication network is understood as a network that can transmit quantum data using quantum systems (e.g., qubits). Typically, digital data communication networks cannot transmit quantum data; however, quantum data communication networks can transmit both quantum and digital data.

[0199] The processes and logical flows described in this specification can be executed by one or more programmable digital and / or quantum computers, which, when appropriate, operate in conjunction with one or more digital and / or quantum processors to run one or more digital and / or quantum computer programs to perform functions by manipulating input digital and quantum data and generating outputs. The processes and logical flows can also be executed by dedicated logic circuitry (e.g., FPGA or ASIC) or a quantum simulator, or a combination of dedicated logic circuitry or a quantum simulator and one or more programmable digital and / or quantum computers. Furthermore, the apparatus can also be implemented as dedicated logic circuitry or a quantum simulator, or a combination of dedicated logic circuitry or a quantum simulator and one or more programmable digital and / or quantum computers.

[0200] For a system of one or more digital and / or quantum computers, being "configured to" perform a specific operation or action means that the system has software, firmware, hardware, or a combination thereof installed thereon that causes the system to perform the operation or action during operation. For one or more digital and / or quantum computer programs, being configured to perform a specific operation or action means that the one or more programs include instructions that cause the digital and / or quantum data processing device to perform the operation or action when run. The quantum computer can receive instructions from a digital computer that, when run by the quantum computing device, cause the device to perform the operation or action.

[0201] Digital and / or quantum computers suitable for running digital and / or quantum computer programs can be based on general-purpose or special-purpose digital and / or quantum processors, or both, or any other kind of central digital and / or quantum processing unit. Typically, the central digital and / or quantum processing unit receives instructions and digital and / or quantum data from read-only memory, random access memory, or a quantum system suitable for transmitting quantum data (e.g., photons), or a combination thereof.

[0202] The fundamental components of a digital and / or quantum computer are a central processing unit (CPU) for executing or running instructions and one or more memory devices for storing instructions and digital and / or quantum data. The CPU and memory may be supplemented or incorporated therein by dedicated logic circuitry or a quantum simulator. Typically, a digital and / or quantum computer will also include one or more mass storage devices for storing digital and / or quantum data, or operatively coupled to receive digital and / or quantum data from said mass storage device, or transmit digital and / or quantum data to said mass storage device, or both, such as magneto-optical disks, magneto-optical disks, or quantum systems suitable for storing quantum information. However, digital and / or quantum computers do not require such devices.

[0203] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include all forms of non-volatile digital and / or quantum memories, media, and memory devices, such as semiconductor memory devices like EPROM, EEPROM, and flash memory devices; disks, such as internal hard disks or removable disks; magneto-optical disks; CD-ROMs and DVD-ROMs; and quantum systems, such as trapped atoms or electrons. It should be understood that quantum memory is a device capable of storing quantum data with high fidelity and efficiency for extended periods, for example, a light-matter interface in which light is used for transmission and matter is used for storage and preservation of quantum characteristics (such as superposition or quantum coherence) of the quantum data.

[0204] Control of the various systems or portions thereof described in this specification can be implemented in digital and / or quantum computer program products, including instructions stored on one or more non-transitory machine-readable storage media and executable on one or more digital and / or quantum processing devices. The systems or portions thereof described in this specification can each be implemented as an apparatus, method, or system, which may include one or more digital and / or quantum processing devices and a memory storing executable instructions to perform the operations described in this specification.

[0205] While this specification contains numerous specific implementation details, these details should not be construed as limiting the scope of possible claims, but rather as descriptions of features that may be specific to particular embodiments. Certain features described herein in the context of separate embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented separately in multiple embodiments or in any suitable sub-combination. Furthermore, although features may be described above as operating in certain combinations and even initially claimed in this manner, one or more features from a claimed combination may in some cases be removed from that combination, and the claimed combination may refer to a sub-combination or a variation of a sub-combination.

[0206] Similarly, although operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring such operations to be performed in the specific order shown or in a sequential order, or requiring all illustrated operations to be performed to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments. Rather, it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0207] Specific embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. For example, the actions recited in the claims may be performed in a different order, but still achieve the desired result. As an example, the processes depicted in the drawings do not necessarily require the specific order or sequence shown to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. A method for operating a system of qubits, wherein, The qubits are arranged in a two-dimensional grid, and the method includes: The first qubit is operated at a frequency within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; and The second qubit is operated at a second qubit frequency within a second qubit frequency region, wherein the second qubit frequency region covers a second frequency range, and the second qubit frequency and the second qubit frequency region are different from the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubit is diagonally opposite the first qubit in a two-dimensional grid.

2. The method of claim 1, wherein, i) the first qubit frequency is the first data qubit frequency, ii) the second qubit frequency is the second data qubit frequency, iii) the first qubit is the first data qubit, iv) the second qubit is the second data qubit, v) the first qubit frequency region includes the first data qubit frequency region, and vi) the second qubit frequency region includes the second data qubit frequency region.

3. The method of claim 1, further comprising: The third qubit is operated at a frequency within the second qubit frequency region, wherein the third qubit is diagonally opposite the first qubit in a two-dimensional grid.

4. The method of claim 3, further comprising: The fourth qubit is operated at a frequency derived from the frequency region of the third qubit, which differs from the frequency region of the first qubit, wherein the fourth qubit is diagonally opposite the first qubit in a two-dimensional grid; and The fifth qubit is operated at a frequency from the third qubit frequency region, wherein the fifth qubit is diagonally opposite the first qubit in a two-dimensional grid.

5. The method of claim 4, wherein, The frequency region of the third quantum bit is the same as that of the second quantum bit.

6. The method of claim 4, wherein, The frequency region of the third quantum bit is different from that of the second quantum bit.

7. The method of claim 2, wherein, The first qubit frequency differs from the second qubit frequency by 2 wherein denotes the system nonlinearity.

8. The method of claim 4, wherein, The first qubit frequency differs from any one of (i) the third qubit frequency, (ii) the fourth qubit frequency, or (iii) the fifth qubit frequency by 2 wherein, denotes the system nonlinearity.

9. The method of claim 8, wherein, = 0.2 GHz.

10. The method of claim 3, wherein, The second quantum bit frequency region has a width of 10 MHz.

11. The method of claim 10, wherein, The difference between the frequency of the second qubit and the frequency of the third qubit is greater than the next nearest neighbor coupling strength between the second qubit and the third qubit.

12. The method of claim 4, wherein, The frequency region of the third quantum bit includes a width of 10 MHz.

13. The method of claim 12, wherein, The difference between the frequency of the fourth qubit and the frequency of the fifth qubit is greater than the next nearest neighbor coupling strength between the fourth qubit and the fifth qubit.

14. The method of claim 2, wherein, The first and second qubit frequency regions include at least one of the following regions: idle frequency region Echo operating frequency range The gate frequency region of a single quantum bit, or Interaction frequency region.

15. An apparatus for operating a quantum bit, comprising: A system of qubits arranged in a two-dimensional grid, wherein the system of qubits comprises: A first qubit at a frequency within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; and A second qubit is located within a second qubit frequency region, wherein the second qubit frequency region covers a second frequency range, and the second qubit frequency and the second qubit frequency region are different from the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubit is diagonally opposite the first qubit in a two-dimensional grid.

16. The apparatus of claim 15, wherein, The apparatus further includes a qubit controller module configured to operate the qubits, wherein the qubit controller module includes an excitation pulse generator and one or more excitation drive systems, and wherein the qubit controller module controls the qubits at qubit frequencies from the qubit frequency region by controlling the qubits via excitation pulses on the excitation drive systems.

17. The apparatus of claim 16, wherein, The one or more excitation drive systems include a global excitation drive system.

18. The apparatus of claim 15, wherein, i) the first qubit frequency includes the first data qubit frequency, ii) the second qubit frequency includes the second data qubit frequency, iii) the first qubit includes the first data qubit, iv) the second qubit includes the second data qubit, and v) the first qubit frequency region includes the first data qubit frequency region.

19. The apparatus of claim 15, wherein, The system of qubits also includes a third qubit at a frequency of the third qubit within the frequency region of the second qubit, wherein the third qubit is diagonally opposite the first qubit in a two-dimensional grid.

20. The apparatus of claim 19, wherein, The system of qubits also includes: A fourth qubit at a frequency originating from the third qubit frequency region, wherein the fourth qubit is diagonally opposite the first qubit in a two-dimensional grid; and A fifth qubit at a frequency from the third qubit frequency region, wherein the fifth qubit is diagonally opposite the first qubit in a two-dimensional grid.

21. A method for operating a system of qubits, comprising: The first qubit in a system that operates a qubit at a frequency within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; A second qubit in a system that operates at a second qubit frequency within a second qubit frequency region, wherein the second qubit frequency region covers a second frequency range, and the second qubit frequency and the second qubit frequency region differ from the first qubit frequency and the first qubit frequency region, wherein the difference between the first qubit frequency and the second qubit frequency is a multiple of the nonlinearity of the qubit system; and The third qubit in a system operates at a frequency derived from the frequency region of the second qubit, wherein the frequency of the third qubit differs from the frequencies of the first and second qubits. The third quantum bit is different from the second quantum bit, and the frequency of the first quantum bit differs from the frequency of the third quantum bit by a multiple of the nonlinearity of the system.

22. The method of claim 21, wherein, The first qubit frequency differs from the second qubit frequency by 2 wherein, denotes the system nonlinearity, and The first qubit frequency differs from the third qubit frequency by 2 wherein, denotes the system nonlinearity.

23. The method of claim 21, wherein, The nonlinearity of a quantum bit system is equal to 0.2 GHz.

24. The method of claim 21, wherein, The frequency of the first quantum bit is the frequency of the first data quantum bit. The frequency of the second quantum bit is the frequency of the second data quantum bit. The first qubit is the first data qubit, and the second qubit is the second data qubit. The first quantum bit frequency region includes the first data quantum bit frequency region, and The second quantum bit frequency region includes the second data quantum bit frequency region.

25. The method of claim 21, wherein, The first and second qubit frequency regions include at least one of the following regions: idle frequency region Echo operating frequency range The gate frequency region of a single quantum bit, or Interaction frequency region.

26. The method of claim 21, wherein, The difference between the frequency of the second qubit and the frequency of the third qubit is greater than the next nearest neighbor coupling strength between the second qubit and the third qubit.

27. The method of claim 26, wherein, The next nearest neighbor coupling strength is equal to 1 MHz.

28. The method of claim 21, wherein, The second quantum bit frequency region has a width of 10 MHz.

29. An apparatus for operating a qubit, comprising: A system of qubits, wherein the system of qubits comprises: A first qubit at a frequency of a first qubit within a first qubit frequency region, wherein the first qubit frequency region covers a first frequency range; A second qubit at a second qubit frequency within a second qubit frequency region, wherein the second qubit frequency region covers a second frequency range, and the second qubit frequency and the second qubit frequency region differ from the first qubit frequency and the first qubit frequency region, wherein the difference between the first qubit frequency and the second qubit frequency is a multiple of the nonlinearity of the system in qubits; and A third qubit at a frequency of a third qubit from the frequency region of a second qubit, wherein the frequency of the third qubit is different from the frequencies of the first and second qubits, and the frequency of the first qubit differs from the frequency of the third qubit by a multiple of the nonlinearity of the system.

30. The apparatus of claim 29, wherein, The apparatus further includes a qubit controller module configured to operate the qubits, wherein the qubit controller module includes an excitation pulse generator and one or more excitation drive systems, and wherein the qubit controller module controls the qubits at qubit frequencies from the qubit frequency region by controlling the qubits via excitation pulses on the excitation drive systems.

31. The apparatus of claim 30, wherein, The one or more excitation drive systems include a global excitation drive system.

32. The apparatus of claim 29, wherein, The first qubit frequency differs from the second qubit frequency by 2 wherein, denotes the system nonlinearity, and The first qubit frequency differs from the third qubit frequency by 2 wherein, denotes the system nonlinearity.

33. The apparatus of claim 29, wherein, The nonlinearity of the quantum bit system is equal to 0.2 GHz.

34. The apparatus of claim 29, wherein, The frequency of the first quantum bit is the frequency of the first data quantum bit. The frequency of the second quantum bit is the frequency of the second data quantum bit. The first qubit is the first data qubit, and the second qubit is the second data qubit. The first quantum bit frequency region includes the first data quantum bit frequency region, and The second quantum bit frequency region includes the second data quantum bit frequency region.

35. The apparatus of claim 29, wherein, The first and second qubit frequency regions include at least one of the following regions: idle frequency region Echo operating frequency range The gate frequency region of a single quantum bit, or Interaction frequency region.

36. The apparatus of claim 29, wherein, The difference between the frequency of the second qubit and the frequency of the third qubit is greater than the next nearest neighbor coupling strength between the second qubit and the third qubit.

37. The apparatus of claim 36, wherein, The next nearest neighbor coupling strength is equal to 1 MHz.

38. The apparatus of claim 29, wherein, The second quantum bit frequency region has a width of 10 MHz.

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