Operation of quantum computing elements

Abstract

A method for operating a quantum computing element (1) having a network (2) of shuttle channels (4) having a plurality of junction points (5) and a plurality of manipulation regions (7), where the method comprises, for a plurality of spin qubits (9): a) initializing the qubits (9), b) manipulating the qubits (9) in at least one of the manipulation regions (7), c) reading out the qubits (9), where the qubits (9) are each in the presence of at least one of the manipulation regions (7). At least one qubit (9) shuttles along the network (2) of shuttle channels (4) between steps a) to c) in order to pass through at least four different ones of the junction points (5).

Description

[0001] The present invention relates to a method for operating a quantum computing element and a quantum computer configured to operate according to the method.

[0002] It is well known that, in theory, quantum computers can significantly outperform conventional computers in specific applications. However, the capabilities of existing quantum computers today are limited. In particular, people would like to develop a universal quantum computer. However, according to the quantum computing concepts of the prior art, a useful universal quantum computer would require at least 10 4 Today, this seems difficult or even impossible to achieve.

[0003] From WO 2021 / 052541 A1, a quantum computing device with a network of shuttle channels is known. The elements used therein are further described in WO 2021 / 052531 A1 (shuttle channels), WO 2021 / 052539 A1 (junction points), WO 2021 / 052538 A1 (loading terminals), WO 2021 / 052537 A1 (manipulation regions) and WO 2021 / 052536 A1 (readout terminals). Although the quantum computing devices described in these documents are already promising, there is still room for improvement, especially in achieving universal quantum computing.

[0004] A major challenge of quantum computing is that qubits are unstable due to decoherence. Attempts have been made to compensate for this, in particular by introducing various error correction measures. For example, an error correction method is described in Phys. Rev. A 86, 032324 (2012) by A. G. Fowler, M. Mariatoni, J. M. Martinis, and A. N. Cleland. Hereinafter, this will be referred to as "Fowler et al." Among them, "auxiliary qubits" are used to correct errors in "data qubits." However, a universal quantum computer that realizes this concept will require a very large number of data qubits and auxiliary qubits.

[0005] The object of the present invention is to provide a quantum computing concept which is more flexible than prior art solutions.

[0006] This object is solved by a method and a quantum computer according to the independent claims. Advantageous refinements are set forth in the dependent claims. The features described in the claims and in the description can be combined with one another in any technically reasonable manner.

[0007] According to the present invention, a method for operating a quantum computing element having a shuttle channel network with a plurality of junctions and a plurality of manipulation regions is provided, wherein the method comprises, for a plurality of spin qubits, respectively:

[0008] a) initializing the qubit,

[0009] b) manipulating the qubit in at least one of the manipulation regions,

[0010] c) reading out said qubit,

[0011] Wherein, at least temporarily, the number of qubits is greater than half the number of junction points.

[0012] The method is configured to operate a quantum computing element. Specifically, this can be achieved by executing a quantum algorithm using a quantum computing element. However, the method can also be used to execute only some quantum operations that may not qualify as a complete quantum algorithm. Specifically, a quantum computing element can be used to execute only a portion of a quantum algorithm, and different quantum computing hardware can be used to execute another portion. Therefore, the method is generally directed to operating a quantum computing element.

[0013] A quantum computing element is a piece of hardware. A quantum computing element can be a quantum computer or part of a quantum computer. A quantum computing element can be connected to additional quantum computing hardware and / or additional conventional hardware. A quantum computing element can be configured for general purpose quantum computing. That is, a quantum computing element can be used for a variety of algorithms. Even if a quantum computing element is not configured for something that can qualify as general purpose quantum computing, the described methods still allow for a more flexible use of the quantum computing element than prior art concepts.

[0014] The quantum computing element uses a spin qubit. A spin qubit is a two-level quantum system. Preferably, the spin qubit is implemented as an electron spin qubit or a hole spin qubit. An electron spin qubit can be implemented with one electron. However, an electron spin qubit can also be implemented with a group of electrons (e.g., two or three electrons). In fact, the method can be performed using any conceivable type of spin qubit. If the electron spin has entered a known state, the electron can be used as a qubit. To this end, the electron can be initialized to become the implementation of a spin qubit. Typically, a qubit remains implemented by the same electron throughout the quantum algorithm. However, it is also possible that a qubit is initialized with a first electron and implemented by a second electron after the operation. There are even some operations after which it is impossible to determine whether the qubit is still implemented by the first electron or by a different second electron. This is not a problem for executing quantum algorithms, because it is sufficient to implement the qubit in some way at any time. The discussion of electrons in this paragraph also applies to holes with necessary modifications. That is, the method can be performed using any conceivable type of hole spin qubit.

[0015] The quantum computing element is preferably based on semiconductor technology. That is, the quantum computing element is preferably made of semiconductor material, particularly preferably made of silicon (Si). Preferably, the semiconductor material is silicon germanium (SiGe), in particular undoped silicon germanium. In addition to semiconductor materials, the quantum computing element may also include other materials, in particular metal contacts. The quantum computing element can be described as a semiconductor heterostructure. Preferably, the quantum computing element includes a semiconductor substrate, preferably a SiGe substrate or a Si substrate. The substrate is preferably undoped. The advantage of using semiconductor materials is that these materials are relatively easy to handle and inexpensive. This is particularly applicable to silicon. In addition, there is a mature technology for using silicon in computing hardware. Two-dimensional electron gas (2DEG) or two-dimensional hole gas (2DHG) can be confined in the substrate. The potential can be manipulated using a gate electrode to obtain a quantum well or even a quantum dot in a 2DEG or 2DHG. Among them, electrons or holes can be captured respectively so that their spins can be used as the realization of a spin qubit. Moving the potential can move quantum wells and quantum dots, which can lead to the movement of charge carriers and therefore the movement of qubits.

[0016] The quantum computing element has a network of shuttle channels. Spin qubits can shuttle, i.e. move, along the shuttle channels. This should be understood as, for example, causing electrons or holes that realize the corresponding spin qubits to shuttle along the shuttle channels. The shuttle channel is a path configured to actively move the spin qubits. Specifically, a plurality of gate electrodes can be used to realize the shuttle channel. By changing the potential of the gate, the electron or hole can be moved. If the potential of the gate along the shuttle channel changes in a continuous manner, the electron or hole can move along the shuttle channel. Preferably, the shuttle channel is arranged on the surface of the substrate of the quantum computing element. The shuttle channel is preferably straight. That is, the electrons or holes moving along the shuttle channel do not have to follow a winding or curved path, and following a winding or curved path will be more difficult to achieve.

[0017] The shuttle channel network includes a plurality of junctions. The junction is preferably a T-junction. That is, the end of the first shuttle channel is connected to the second shuttle channel at a point spaced apart from the end of the second shuttle channel. In addition, an X-junction is also conceivable. Among them, the two shuttle channels meet at a point spaced apart from the ends of the two shuttle channels. For practical reasons, the X-junction can be more easily realized by a pair of T-junctions. Unless the two shuttle channels intersect each other so that both form a straight line at least near the X-junction, the X-junction is considered to be realized by a pair of T-junctions. However, if one of the two intersecting shuttle channels is offset at the junction, it is considered that the junction is realized by a pair of T-junctions.

[0018] Furthermore, the quantum computing element comprises a manipulation region. In the manipulation region, the state of the spin qubit can be changed. Thus, a quantum operation can be performed. In the manipulation region, a single qubit can be manipulated. The corresponding operation can be referred to as a single-qubit operation. Furthermore, multiple qubits can be manipulated together in the same manipulation region. Specifically, this can be done with two qubits. The corresponding operation can be referred to as a multi-qubit operation, in particular a double-qubit operation.

[0019] For a plurality of qubits, the method comprises steps a) to c). That is, for each qubit, steps a) to c) are respectively performed. For each qubit, the corresponding steps a) to c) are preferably performed in the order described.

[0020] During steps a) to c), the spin qubit should remain stable. That is, the qubit state should not be changed unintentionally or in an arbitrary way. However, in particular due to decoherence, the spin qubit may lose its state. This unavoidable effect leads to errors, which can be handled by error correction. In addition, decoherence losses can be minimized by making the distance traveled by the spin qubit as short as possible. The coherence time of the spin qubit implemented in a semiconductor depends on the temperature. Therefore, it is preferred to place the quantum computing element in a refrigerator at a temperature below 4K, preferably below 1K to perform the method. In experiments, particularly good results were achieved at 30mK.

[0021] Below, steps a) to c) are described for one of the qubits. As an example, consider an electron spin qubit. In step a), the qubit is initialized. This can be achieved by loading the corresponding electron into the shuttle channel network in a manner where the spin state of the electron is known. Therefore, the spin state can be implemented as a qubit. Preferably, the quantum computing element includes at least one loading terminal. Using the loading terminal, electrons can be loaded into the shuttle channel network. If the quantum computing element includes several loading terminals, each qubit can be loaded using one of the loading terminals. Several qubits can be loaded one by one using the same loading terminal. Alternatively, the qubit can be loaded into the shuttle channel network by moving the qubit from outside the shuttle channel network into the shuttle channel network. This is particularly possible when the quantum computing element is connected to another quantum computing hardware that is not considered to be part of the quantum computing element. However, it is not necessary to perform initialization according to step a) by loading the qubit into the shuttle channel network. Alternatively, the qubit can be initialized in step a) by manipulating the electrons already present in the shuttle channel network so that their spin states become known. For example, electrons that have already been loaded into the shuttle channel network for a previous execution of a quantum algorithm can be used. Electrons that are already present in the shuttle channel network can be initialized in any way that leads to knowledge of the spin state of the electrons. For example, a qubit can be read out at the end of a previous quantum algorithm. As a result of the readout, the qubit can be in a known state. For this reason, the qubit can be used for a subsequent quantum algorithm. That is, the readout step of the first quantum algorithm can be the initialization step of the subsequent quantum algorithm. In addition, the spin qubit can be relaxed to its ground state by waiting for a sufficient amount of time. This is the simplest but also quite slow way to initialize a qubit.

[0022] In step b), a qubit is manipulated in at least one manipulation region. In this case, single-qubit operations or multi-qubit operations, in particular double-qubit operations, can be performed. Single-qubit operations can in particular be spin flips. Double-qubit operations can in particular be entanglement of two qubits. In the case of multi-qubit operations, the qubits involved are jointly manipulated in their respective manipulation regions. To this end, step b) can be performed jointly for a plurality of qubits). By manipulating qubits in the manipulation region, a quantum algorithm can be implemented. In this case, the quantum algorithm determines how many qubits are involved and which qubit is manipulated at which time, in which manipulation region, and by which operation. Since the quantum computing element is preferably configured for universal quantum computing, all potential combinations of manipulation operations are generally conceivable.

[0023] In step c), the qubit is read out. That is, the state of the qubit is determined by measurement. Since the qubit is a spin qubit, this means measuring the spin of the qubit. By measuring, the state of the qubit is lost, so that the quantum operation is terminated by this measurement. The results of the respective step c) for each qubit involved can be further processed using conventional computer hardware.

[0024] Step a) is preferably performed using a load terminal. Step c) is preferably performed using a read terminal. The load terminal and the read terminal may be implemented using the same element, which may be referred to as a load and read terminal. In this case, steps a) and c) may be performed using the load and read terminals.

[0025] Between steps a) to c), the qubit may be shuttled along one or more shuttle channels. For example, the qubit may be loaded into the shuttle channel using a loading terminal (step a)), shuttled from the loading terminal to a manipulation region where it is manipulated (step b)), shuttled from the manipulation region to a readout terminal where it is read out (step c)). In step b), the qubit may also be shuttled from the manipulation region to another manipulation region where it is manipulated a second time. This may be repeated for even more manipulation regions.

[0026] The shuttle channel network is preferably configured to have a pattern that repeats itself. Preferably, the shuttle channel network is configured as a grid. Adjacent rows of the grid are preferably offset from each other so that the grid only involves T-junctions and not X-junctions, which would be more difficult to achieve. However, the network unit does not necessarily have to have a rectangular shape. The network unit may also have, for example, a hexagonal shape.

[0027] If the network of shuttle channels is configured to have a pattern that repeats itself, a unitary cell can be identified. The network may include multiple copies of the unit cell, which are arranged next to each other in rows and columns. In this way, a two-dimensional network of shuttle channels can be obtained. At its edges, the network may deviate from the described structure based on the unit cell. That is, at its edges, the network may have incomplete copies of the unit cell, or just shuttle channels that are not part of the copies of the unit cell.

[0028] Preferably, the unit cell is defined only with respect to the shuttle channel. That is, each copy of the unit cell has the same arrangement of the shuttle channel. This includes that each copy of the unit cell has the same number and arrangement of junctions. However, elements such as loading terminals, manipulation areas, and readout terminals may be arranged independently of the definition of the unit cell. That is, the copies of the unit cells may differ in the number and arrangement of these elements. Nevertheless, it is preferred that each copy of the unit cell has the same number and arrangement of loading terminals, manipulation areas, and readout terminals. That is, the copies of the unit cell are identical to each other not only in the arrangement of the shuttle channel, but also in other elements. Preferably, each copy of the unit cell has exactly one loading terminal, exactly one manipulation area, and exactly one readout terminal.

[0029] It is preferred that not every copy of the unit cell has a corresponding loading terminal. It is sufficient for the network to have only one loading terminal. A small number of loading terminals can facilitate manufacturing. In addition, spacing the loading terminal from the qubit during operation can improve performance. However, providing more loading terminals can improve loading efficiency and reduce the distance that the qubit must travel. In view of this, it is reasonable to find that the network has one loading terminal for every 5 to 20 junctions. This is a reasonable definition because the number of junctions is a measure of the number of copies of the unit cell. The junctions can in particular be T-junctions or X-junctions. A T-junction counts as one junction and an X-junction counts as one junction. However, if an X-junction is implemented by a pair of T-junctions, such an X-junction counts as two junctions. However, it is also conceivable that each copy of the unit cell includes a corresponding loading terminal. In any case, it is sufficient if each copy of the unit cell has at most one loading terminal.

[0030] Furthermore, it is preferred that not every copy of the unit cell has a corresponding readout terminal. It may be sufficient for the network to have even just one readout terminal. A small number of readout terminals may facilitate manufacturing. Furthermore, spacing one or more readout terminals from the qubit during operation may improve performance. However, providing more readout terminals may improve readout efficiency and reduce the distance that the qubit must travel. In view of this, it is found reasonable that the network has one readout terminal for every 5 to 20 junctions.

[0031] It is particularly preferred to have as few loading terminals and readout terminals as possible. This is because both the loading terminals and the readout terminals cause heat to enter the quantum computing element, which reduces the coherence time of the qubits. Ideally, the quantum computing element has only one loading and readout terminal for loading and reading out all qubits. However, it is already advantageous if the number of loading terminals, the number of readout terminals and the sum of the number of loading and readout terminals are smaller than the number of network units, in particular at least 10 times smaller, more particularly even at least 100 times smaller. Since the number of junctions is a measure of the number of network units, it is preferred that the number of loading terminals, the number of readout terminals and the sum of the number of loading and readout terminals are smaller than the number of junctions, in particular at least 10 times smaller, more particularly even at least 100 times smaller.

[0032] It is conceivable that the number of load terminals is equal to the number of read terminals. For example, the ratio of the number of load terminals to the number of read terminals may be in the range of 0.5 to 2. However, it is also conceivable that each copy of the unit cell includes a corresponding read terminal. In any case, it is sufficient if each copy of the unit cell has at most one read terminal.

[0033] It is further preferred that each copy of the unit cell has a corresponding manipulation area.

[0034] The concept of a unit cell cannot be used only to describe the arrangement of a shuttle channel and the elements connected to it. The number of copies of a unit cell can also be associated with the number of qubits used in the method. Each copy of a unit cell can use one qubit. In this case, each qubit has its own copy of the unit cell and each unit cell has one and only one qubit. In a particularly simple case, each qubit will be loaded into the shuttle channel of this copy of the unit cell using the loading terminals of its copy of the unit cell, shuttled to the manipulation region of this copy of the unit cell, manipulated therein, shuttled to the readout terminals of this copy of the unit cell and read out therein. For this purpose, the qubit does not have to leave its copy of the unit cell. Since this can be applied to all qubits, no interference between qubits occurs, since no qubit will enter a copy of a unit cell assigned to a different qubit.

[0035] However, it was found that it is not necessary to make such restrictions in terms of the number of qubits and the locations where the qubits can be shuttled. In fact, it was found that it is not even necessary to assign qubits to copies of the unit cell and vice versa. Therefore, the described method can involve an arbitrary number of qubits, regardless of the extent of the shuttle channel network, in particular, regardless of the number of copies of the unit cell. In addition, the qubits can move freely through the entire network of shuttle channels, where only decoherence losses may limit the distance that the qubits can be shuttled. That is, it is preferred that between steps a) to c), at least one qubit moves through multiple copies of the unit cell. This definition naturally only applies to the case where the unit cell can be identified. However, this concept can also be transferred to arbitrary shuttle channel networks. Even in this case, the insight can be used that the number of qubits and the area where they can move can be selected independently of the configuration of the shuttle channel network. According to the generally applicable definition of this insight, the number of qubits is at least temporarily higher than half of the number of junctions. It was found that this is the key idea of ​​the concept. In particular, the junction can be a T-junction or an X-junction. A T-junction counts as one junction and an X-junction counts as one junction. However, if an X-junction is implemented by a pair of T-junctions, such an X-junction is counted as two junctions.

[0036] This means that the number of qubits is not limited by the number of network units. Since the number of network units is usually related to the number of junctions, this means that the number of qubits is not limited by the number of junctions. This is expressed as the number of qubits being at least temporarily higher than half the number of junctions. Preferably, the number of qubits is at least temporarily higher than the number of junctions, in particular higher than twice the number of junctions. Theoretically, there is no upper limit to the number of qubits. However, it has been found that for practical reasons it is advantageous if the number of qubits does not exceed twenty times the number of junctions, in particular if the number of qubits does not exceed ten times the number of junctions.

[0037] In the case where the number of qubits is high as described above, it is preferred that at least one manipulation region is configured to perform at least a SWAP operation. That is, the manipulation region is used as an implementation of a SWAP gate and possibly as an implementation of one or more other gates. In this case, the qubits can be arranged in groups, where the qubits in the group shuttle together through the shuttle channel. Among them, the qubits in the group can form a line in the shuttle channel so that the qubits in the group are arranged one after another. Since the shuttle channel can be considered to be one-dimensional, the qubits in the group usually have a fixed order. However, by the SWAP operation, the order of the qubits within a certain group can be changed. To this end, for example, two qubits in the group can be entangled with each other, even if these qubits are not originally arranged next to each other. It is particularly preferred that entanglement and SWAP operations are performed using the same manipulation region. Even a group of qubits can be assigned to a certain manipulation region, where all operations on these qubits are performed using only this manipulation region. That is, the group of qubits can shuttle back and forth in the manipulation region, where the qubits exchange positions when necessary. In theory, the entire quantum algorithm can therefore be performed using a group of qubits and a single manipulation region.

[0038] Additionally, it is preferred that the number of qubits is at least temporarily higher than the number of manipulation regions. This is another way of expressing that there is no strict assignment between qubits and network units in the method. The shuttle channel can be configured as described in the published document WO 2021 / 052531 A1, which is hereby incorporated by reference in its entirety as part of the present invention. The junction point can be configured as described in the published document WO 2021 / 052539 A1, which is hereby incorporated by reference in its entirety as part of the present invention. The loading terminal can be configured as described in the published document WO 2021 / 052538 A1, which is hereby incorporated by reference in its entirety as part of the present invention. The manipulation region can be configured as described in the published document WO 2021 / 052537 A1, which is hereby incorporated by reference in its entirety as part of the present invention. The readout terminal can be configured as described in the published document WO 2021 / 052536 A1, which is hereby incorporated by reference in its entirety as part of the present invention. The shuttle channel network can be configured as described in the published document WO 2021 / 052541A1, which is hereby incorporated by reference in its entirety as a part of the present invention.

[0039] In a preferred embodiment of the method, steps a) to c) are performed simultaneously for at least some of the qubits.

[0040] Steps a) to c) are performed separately for each qubit involved in the method. If step b) is implemented as a multi-qubit operation, step b) is performed jointly for the corresponding qubits. In addition, steps a) to c) can be performed independently for each qubit. For this reason, it is relatively free to choose when to perform the corresponding steps a) to c) for each qubit. However, it is found that performing steps a) to c) simultaneously for at least some qubits is not only advantageous in terms of computing time. More importantly, it is found that if steps a) to c) are performed simultaneously for at least some qubits, decoherence losses can be reduced. Ideally, steps a) to c) are performed simultaneously for all qubits.

[0041] In another preferred embodiment, the method comprises a plurality of adjacent time intervals, and wherein in each of said time intervals, steps a) to c) are performed for a respective set of qubits.

[0042] Steps a) to c) can be performed multiple times for one, some or all qubits, wherein dividing the method into time intervals facilitates the interaction between the qubits. At certain points in time, i.e. the beginning and the end of a time interval, steps a) to c) have been completed for all qubits. Thus, the next cycle can be started without waiting for a certain qubit.

[0043] In another preferred embodiment of the method, between steps a) to c), at least one qubit is shuttled along the network of shuttling channels to pass through at least four different ones of the junctions.

[0044] The key concept is to move qubits freely through the shuttle channel network, i.e., without any strict assignment between qubits and network units. This also means that qubits can shuttle through multiple junctions. Before a certain point, the more junctions passed, the more obvious the advantage is generally. The optimal number of junctions passed can depend on the details of the quantum algorithm and / or the coherence time. Therefore, it is preferred that at least one qubit shuttles along the shuttle channel network between steps a) to c) so as to pass through at least five, in particular at least ten different junctions. It is particularly preferred that at least one qubit shuttles along the shuttle channel network between steps a) to c) so as to pass through four to ten different junctions. The more qubits that meet the requirements of the number of junctions passed, the more obvious the advantage is generally. Therefore, it is preferred that at least half of the qubits shuttle along the shuttle channel network between the corresponding steps a) to c) so as to pass through at least four different junctions, in particular at least five, in particular at least ten different junctions, in particular four to ten different junctions. It is also possible that all qubits meet this requirement.

[0045] The junction may in particular be a T-junction or an X-junction. Passing through a T-junction counts as passing through one junction, and passing through an X-junction counts as passing through one junction. However, if an X-junction is realized by a pair of T-junctions, passing through such an X-junction counts as passing through two junctions.

[0046] Passing through at least four different junctions between steps a) to c) can be achieved in various ways. In a first example, in step a), the qubit is initialized by loading charge carriers into the network, such as to have a known spin state. This can be done using a loading terminal. The loading terminal can be arranged at the end of a dead-end shuttle channel branching from another shuttle channel. To this end, the qubit can pass through the first junction immediately after moving out of the loading terminal. In step c), the qubit can be read out using a readout terminal. The readout terminal can be arranged at the end of a dead-end shuttle channel branching from another shuttle channel. To this end, the qubit can pass through another junction immediately before moving into the readout terminal. That is, in the first example, the qubit can pass through at least four different junctions between steps a) to c), because it passes through at least two different junctions in addition to the two junctions assigned to the loading terminal and the readout terminal.

[0047] In a second example, all qubits are initialized in step a) by loading the corresponding charge carriers into the network, such as to have a known spin state. Therein, for all qubits, the same loading terminal arranged at the edge of the network is used. After being loaded, the qubits are shuttled to the location in the network where they should be used. Since the loading terminals are arranged at the edge of the network, this usually involves passing through multiple junctions. In a variant of the second example, there are more than one loading terminals and / or one or more loading terminals are not arranged at the edge of the network. Therein, between steps a) to c), it is still possible to shuttle at least one qubit along the shuttle channel network so as to pass through at least four different junctions.

[0048] In a third example, electrons already present in the shuttle channel network are used to initialize the qubit in step a). That is, the qubit is not initialized by loading charge carriers into the network. The qubit can be shuttled along the shuttle channel network between steps a) to c) so as to pass through at least four different junctions, none of which are assigned to a load terminal or a readout terminal. In another preferred embodiment of the method, at least some of the qubits are shuttled past at least one manipulation region in which they are manipulated in step b).

[0049] In this embodiment, a qubit is moved into a corresponding manipulation region from a first side thereof, manipulated in the manipulation region, and moved out of the manipulation region at a second side thereof. To this end, the qubit does not change its shuttling direction for the manipulation.

[0050] When the first qubit is shuttled through the manipulation region, the first qubit may encounter the second qubit. The second qubit may be stationary in the manipulation region or may shuttle through the manipulation region in a direction opposite to that of the first qubit. This can be achieved by configuring the manipulation region to perform at least a SWAP operation. That is, the manipulation region serves as an implementation of a SWAP gate and may serve as an implementation of one or more other gates. Therein, the charge carriers used to implement the first qubit before the exchange can be used to implement the second qubit after the exchange, and vice versa. It is even possible that, after the exchange, it is impossible to determine whether the first qubit is implemented by the same charge carrier before and after the exchange, and whether the second qubit is implemented by the same charge carrier before and after the exchange. This is acceptable because the qubit, i.e., the representation of a certain quantum state, should be moved and not strictly bound to a certain charge carrier.

[0051] In another preferred embodiment of the method, at least some of the qubits have a shuttling direction which is reversed at at least one manipulation region where they are manipulated in step b).

[0052] In this embodiment, a qubit is moved from a first side of a corresponding manipulation region into the manipulation region, manipulated in the manipulation region, and moved out of the manipulation region at the first side of the manipulation region. To this end, the shuttling direction of the qubit is reversed at the manipulation region.

[0053] Depending on the operations to be performed using the method, in particular depending on the quantum algorithm to be performed, it can be selected which qubits should be shuttled through which manipulation regions and which qubits should reverse their shuttling direction in which manipulation region. Since the quantum computing element is preferably configured for universal quantum computing, the selection between these options is preferably performed by software rather than a fixed hardware configuration.

[0054] In another preferred embodiment of the method, at least some of the qubits are manipulated sequentially in a plurality of manipulation regions, and wherein individual qubits are shuttled between these manipulation regions.

[0055] In this embodiment, for example, the method may include, for a plurality of spin qubits, respectively:

[0056] a) initializing the qubits, in particular by loading the qubits into the shuttle channel network using the load terminal,

[0057] shuttling the qubit to a first manipulation region, in particular from a loading terminal to the first manipulation region,

[0058] b) manipulating the qubit in the first manipulation region,

[0059] Shuttle qubits from the first manipulation region to the second manipulation region,

[0060] manipulating the qubit in a second manipulation region,

[0061] shuttling qubits from the second manipulation region to, in particular, the readout terminal,

[0062] c) Reading out the qubits, in particular using a readout terminal to read out the qubits.

[0063] For qubits manipulated in three or more manipulation regions in step b), this can be easily extended by also involving corresponding shuttling and manipulation sub-steps in step b).

[0064] Manipulating one, some, or all qubits in more than one manipulation region can improve efficiency. This is because it eliminates the need to load and read out the qubits before and after each manipulation. In addition, this makes it possible to execute multi-operation quantum algorithms.

[0065] In a further preferred embodiment of the method, for at least some of the qubits, the manipulation in the respective step b) is entanglement with at least one other qubit.

[0066] The mutual entanglement of two qubits is an example of a two-qubit operation. Most practically useful quantum algorithms involve the entanglement of qubits. Entanglement is possible if both involved qubits are shuttled to the same manipulation region, so that eventually both qubits are in the manipulation region at the same time. The method was found to be particularly suitable for entangled qubits. This is due to the fact that with the method there is no strict assignment between network units and qubits. Thus, two qubits can be shuttled from anywhere in the network and meet in a certain manipulation region to be entangled. For this reason, the method is particularly flexible, since any qubit can be entangled with each other. This helps to achieve universal quantum computing. If there is a strict assignment between qubits and network units, then at most two qubits from adjacent network units can be entangled with each other.

[0067] In another preferred embodiment, the method is an implementation of a surface code.

[0068] Surface codes are implementations of quantum algorithms involving the movement of qubits on a surface. Examples of surface codes involving error correction have been described by Fowler et al. However, there, the number of qubits is limited compared to the described methods.

[0069] In general, the method may be an implementation of any QEC code, in particular a 2D code, a 3D code, a color code or a stabilizer code.

[0070] As another aspect of the present invention, there is provided a quantum computer, comprising:

[0071] - a quantum computing element having a shuttle channel network having a plurality of junctions and a plurality of manipulation regions,

[0072] - Control means connected to the quantum computing element and configured to perform a method according to any of the preceding claims.

[0073] The advantages and features of the method are transferable to a quantum computer and vice versa. The quantum computer is preferably configured to be used according to the method. The method is preferably performed using a quantum computer.

[0074] The present invention will be described below in conjunction with the accompanying drawings. The accompanying drawings show preferred embodiments, but the present invention is not limited thereto. The accompanying drawings and the dimensions shown therein are only schematic. The accompanying drawings show:

[0075] Figure 1 : According to the quantum computing element of the present invention,

[0076] Figure 2 : According to the quantum computer of the present invention,

[0077] Figure 3 : Figure 1 The quantum computing element is part of the shuttle channel,

[0078] Figure 4 : Figure 3 The cross section of the shuttle channel,

[0079] Figure 5 : Figure 1 The T-junction of the quantum computing element,

[0080] Figure 6 : Figure 5 A cross section of a T-junction, where the sequence shows the potential development within the T-junction,

[0081] Figure 7 : Figure 1 The manipulation area of ​​the quantum computing element,

[0082] Figure 8 : Figure 7 A cross section of the manipulation region of FIG. 1 , wherein the sequence shows the potential development in the manipulation region during single-qubit operation,

[0083] Fig. 9 : Figure 7A cross section of the manipulation region, where the sequence shows the potential development in the manipulation region during a two-qubit operation,

[0084] Fig.10 : Figure 1 The loading terminal of the quantum computing element,

[0085] Fig.11 : Fig.10 A cross section of a loading terminal, wherein the sequence shows the development of the potential within the loading terminal during loading,

[0086] Fig.12 : Figure 1 The readout terminal of the quantum computing element,

[0087] Fig.13 : Fig.12 A cross section of a readout terminal, wherein the sequence shows the development of the potential within the readout terminal during readout,

[0088] Figure 1 A quantum computing element 1 is shown with a network 2 of shuttle channels 4 having four network units 3. The network 2 is implemented on a surface 19 of a substrate 10. The extension of the network units 3 is in the order of 10 μm [micrometers]. The shuttle channels 4 are interconnected by junctions 5. Each network unit 3 has a respective loading terminal 6, a respective manipulation region 7 and a respective readout terminal 8. The quantum computing element 1 is configured for a method comprising, respectively, for a plurality of spin qubits 9 (indicated only by the reference numerals assigned to the shuttle channels 4, since the qubits 9 can be at any position in the shuttle channels 4):

[0089] a) initializing the qubit 9 by loading the corresponding electron or hole into the network 2 of the shuttle channel 4 using one of the loading terminals 6,

[0090] b) manipulating a qubit 9 in at least one manipulation region 7,

[0091] c) reading out the qubit 9 using one of the readout terminals 8,

[0092] Therein, at least one qubit 9 is shuttled along the network 2 of the shuttle channel 4 between steps a) to c) so as to pass through at least four different junctions 5. In particular, these qubits 9 are not bound to one of the network units 3. Instead, these qubits 9 can move across multiple network units 3. Furthermore, at least temporarily, the number of qubits 9 can be higher than half the number of junctions 5. Furthermore, the number of qubits 9 can be higher than the number of network units 3.

[0093] Steps a) to c) may be performed simultaneously for at least some of the qubits 9. In particular, the method may comprise a plurality of adjacent time intervals, wherein in each time interval steps a) to c) are performed for a respective group of qubits 9.

[0094] The qubits 9 may be manipulated in various ways in the respective manipulation regions 7. For example, at least some of the qubits 9 may be shuttled through the respective manipulation regions 7 at which they were manipulated in step b), and / or at least some of the qubits 9 may have a shuttling direction that is reversed at the respective manipulation regions 7 at which they were manipulated in step b).

[0095] Some or all qubits 9 may be manipulated successively in a plurality of manipulation regions 7. The qubits 9 are shuttled between the manipulation regions 7. For at least some qubits 9, the manipulation in the respective step b) may be entanglement with at least one further qubit 9.

[0096] This method can be an implementation of the surface code.

[0097] Figure 2 A quantum computer 11 is shown, which includes a quantum computing element 1 having a network 2 of shuttle channels 4, the network 2 of shuttle channels 4 having a plurality of junctions 5 and a plurality of manipulation regions 7. The quantum computing element 1 can be Figure 1 Furthermore, the quantum computer 11 includes a control device 12 connected to the quantum computing element 1. The control device 12 may be configured to execute Figure 1 Describe the method.

[0098] Figure 3 and Figure 4 Shows how this can be achieved Figure 1 The shuttle channel 4 of the quantum computing element 1. Therefore, Figure 3 Schematically shows Figure 1 FIG. 1 is a top view of a portion of a semiconductor substrate 10 of a quantum computing element 1. Figure 3 The portion of the semiconductor substrate 10 shown in FIG. 1 comprises one of the shuttle channels 4 extending between the first side 100 and the second side 101. Thus, three layers of gate electrode arrays 102, 103, 104 are provided, which are separated from each other by insulating layers 108, 109. One or more voltage sources (not shown) may be used to apply corresponding voltages to the gate electrode arrays 102, 103, 104. Thus, the gate electrode arrays 102, 103, 104 have corresponding electrical terminals 105, 106, 107.

[0099] The first gate electrode array 102 is located on the surface 19 of the substrate 10. Behind the first gate electrode array 102 is an insulating layer 108, on which the second gate electrode array 103 is arranged. An insulating layer 109 is arranged on top of the second gate electrode array 103, and the insulating layer 109 electrically isolates the second gate electrode array 103 from the third and uppermost gate electrode array 104.

[0100] Figure 4 Shows Figure 3 1 is a cross-section of a portion of the substrate 10 shown in . Therein, the gate electrode 115 of the first gate electrode array 102 can be seen. The gate electrode 115 extends longitudinally on the surface 19 of the substrate 10 and is separated from the second gate electrode array 103 by the first insulating layer 108. The electrode fingers 110, 111 of the second gate electrode array 103 are partially shown. The second gate electrode array 103 is separated from the third gate electrode array 104 by the second insulating layer 109. Only the electrode fingers 112, 113 of the third gate electrode array 104 are shown. In this view, it can be clearly seen how the electrode fingers 110, 111, 112, 113 alternate.

[0101] A potential well 116 is created by applying a sinusoidal voltage to the gate electrode array 102, 103, 104. A quantum dot 117 trapped in this potential well 116 can move through the substrate 10. The potential well 116 is moved longitudinally through the substrate 10 by driving the electrode fingers 110, 111, 112, 113 with a sinusoidal voltage without changing the quantum mechanical properties of the quantum dot 117. The movement of the quantum dot 117 in the direction of the arrow 118 is indicated by the dashed line 119. The quantum mechanical state is indicated by the small arrow 114 of the quantum dot 117.

[0102] Voltage is applied to the gate electrode arrays 102, 103, 104 so that the electrode fingers 110, 111, 112, 113 form a movable potential well 116 in the substrate 10. By controlling the gate electrode arrays 102, 103, 104, the potential well 116 can be moved through the substrate 10 along the shuttle channel 4. The second gate electrode array 103 and the third gate electrode array 104 are provided with a sinusoidal voltage.

[0103] Figure 5 and Figure 6 Shows Figure 1 How can the junction 5 of the quantum computing element 1 be realized? Figure 5 Shows Figure 1 A portion of a semiconductor substrate 10 of a quantum computing element 1. Figure 5 The portion of the semiconductor substrate 10 shown in FIG. 1 includes one of the T-junctions 5 .

[0104] The quantum computing element 1 is configured such that a two-dimensional electron gas (2DEG) is contained within the substrate 10. Gate electrode arrays 201, 202, 203 are disposed on the surface 19 of the substrate 10. The gate electrode arrays 201, 202, 203 help define the shuttle channel 4 because the gate electrode arrays 201, 202, 203 manipulate the potential within the substrate 10 so that electrons of the 2DEG can move in a controlled manner.

[0105] The gate electrode arrays 201, 202, 203 each include two corresponding gate electrodes 204, 205, 206, 207. The gate electrodes 204, 205, 206, 207 are electrically separated from each other by an insulating layer 208. To this end, the gate electrode arrays 201, 202, 203 are constructed in the form of layers, and the insulating layer 208 is arranged between the gate electrodes 204, 205, 206, 207. The gate electrodes 204, 205, 206, 207 also include electrode fingers 209, 210, 211, 212. The electrode fingers 209, 210, 211, 212 of a certain gate electrode 204, 205, 206, 207 are arranged parallel to each other on the surface 19 of the substrate 10.

[0106] The gate electrode arrays 201, 202, 203 can be supplied with voltage via electrical connections (not shown in detail). By applying a sinusoidal voltage to the gate electrodes 204, 205, 206, 207 of the gate electrode arrays 201, 202, a potential well can be generated in the substrate 10. Thus, quantum dots trapped in the potential well can move through the substrate 10. By applying a sinusoidal voltage to the electrode fingers 209, 210, 211, 212, the potential well can be moved longitudinally through the substrate 10.

[0107] In a quantum dot, a single electron can be trapped. If the quantum dot is moved, the electron will move with it. The spin of this trapped electron can be used as a spin qubit 9. For this purpose, the qubit 9 can be shuttled through a shuttle channel 4 with a junction 5. Therein, the electron moves together with the quantum dot in which the electron is trapped. The process is continuous because the electron stays in the same quantum dot throughout the journey through the junction 5. The electron does not have to tunnel into a different quantum dot to change direction at the junction 5.

[0108] The gate electrode array 202 branches from the gate electrode array 201 in the intersection region 213. The gate electrode arrangement 203 is arranged in the intersection region 213. The gate electrode array 203 includes two barrier gate electrodes 214, 215. When the moving potential well with quantum dots is located in the intersection region 213, the barrier gate electrodes 214, 215 can be turned on. By turning on the barrier gate electrodes 214, 215, the potential well with quantum dots is maintained in the intersection region 213. The pump gate electrode 216 of the gate electrode array 203 can cause the potential well with quantum dots to change direction toward the gate electrode array 202.

[0109] Assuming that the potential well with the quantum dot does not change direction, the barrier gate electrode 217 of the gate electrode array 203 is activated. The other two barrier gate electrodes 214, 215 are turned off. Therefore, the barrier gate electrode 217 blocks access to the gate electrode array 202. Therefore, there is no reason for the quantum dot in the mobile potential well to change direction. For this reason, a T-junction 5 is realized through which the qubit 9 can move. Depending on the applied voltage, it can be determined through which branch of the junction 5 the qubit 9 leaves the junction 5.

[0110] Figure 6 Shows Figure 5 1 is a cross section of a portion of a semiconductor substrate 10. For clarity, only electrode fingers 211, 212, barrier gate electrode 217 and pump gate electrode 216 are shown. A sequence A to C is shown below, which illustrates the movement of a potential well 218 with a quantum dot 219.

[0111] The electrode fingers 211, 212 of the gate electrode array 202 form a moving potential well 218. The movement of the potential well 218 is achieved by interconnecting the electrode fingers 211, 212. To this end, the electrode fingers 211, 212 of the gate electrode array 201 are periodically interconnected in an alternating manner, which causes the potential well 218 to move almost continuously through the substrate 10. Figure 6 2, it is shown how a potential well 218 with a quantum dot 219 branches out from the intersection region 213. The moving potential well 218 is located in the direction of the gate electrode array 202. An arrow 220 indicates the moving direction 219 of the potential well 218 with the quantum dot.

[0112] exist Figure 7 It is shown in Figure 1 The gate electrode arrays 300, 301, 314 are arranged on the surface 19 of the substrate 10. The gate electrode arrays 300, 301 each include two gate electrodes 302, 303, 304, 305. The respective gate electrodes 302, 303, 304, 305 are electrically isolated from each other by an insulating layer 306. The gate electrode arrays 300, 301 are provided in the form of layers, wherein an insulating layer 306 is provided between each gate electrode 302, 303, 304, 305 of the gate electrode arrays 300, 301. The gate electrodes 302, 303, 304, 305 also include electrode fingers 307, 308, 309, 310 arranged parallel to each other on the surface 19 of the substrate 10.

[0113] The manipulation region 7 is formed in a region 311 in which the gate electrode arrays 300, 301 are adjacent to each other. A manipulator 313 including a gate electrode array 314 is located in the manipulation region 7. The gate electrode array 314 includes barrier gate electrodes 315, 316, 317 forming at least one static potential well. The gate electrode array 314 also includes pump gate electrodes 318, 319, each of which can cause the quantum dots or charge carriers to move or oscillate.

[0114] Voltage is applied to the gate electrode arrays 300, 301, 314 through electrical connections. By applying a sinusoidal voltage to the gate electrodes 302, 303, 304, 305 of the gate electrode arrays 300, 301, a potential well is created in the substrate 10. Quantum dots or charge carriers trapped in this potential well can move through the substrate 10. By appropriately driving the electrode fingers 307, 308, 309, 310 with a sinusoidal voltage, the potential well moves longitudinally through the substrate 10.

[0115] Figure 8 The sequence of manipulating the charge carriers in the quantum dots 320, 321 in the manipulation region 7 for single qubit operation is shown. Therefore, a cross-sectional view of the manipulation region 7 is shown, in which only the electrode fingers 307, 308, 309, 310, the barrier gate electrodes 315, 316, 317 and the pump gate electrodes 318, 319 are shown. Below is the sequence A to F of the propagation of the potential wells 322, 323 in the substrate 10. Although Figure 8 A single qubit operation is shown, but two quantum dots 320, 321 are shown trapped in quantum wells 322, 323. The single qubit operation is performed using quantum dot 321 within the manipulation region 7, while the other quantum dot 320 "wait" outside the manipulation region 7. This is useful because after the single qubit operation, a two qubit operation involving the two quantum dots 320, 321 can be performed.

[0116] The electrode fingers 307, 30, 32, 34 of the gate electrode arrays 300, 301 form potential wells 322 and 323. The movement of the potential wells 322, 323 is achieved by appropriately interconnecting the electrode fingers 307, 308, 309, 310. To this end, the electrode fingers 307, 308, 309, 310 of the gate electrode arrays 300, 301 are periodically interconnected in an alternating manner, which results in the potential wells 322, 323 moving almost continuously through the substrate 10.

[0117] A static double well 324 is formed in the manipulation region 7. The static double well 324 is created by barrier gate electrodes 315, 316, 317. First, the quantum dot 321 is brought into the static double potential well 324 in the manipulation region 7 together with the movable potential well 323. This is indicated by a horizontal arrow 325. The manipulator 313, such as a gradient magnetic field, allows the quantum dot 321 to assume a defined quantum mechanical state. Another quantum dot 320 is waiting outside the manipulation region 7. By moving in the magnetic field gradient of the manipulator 313, the defined quantum state of the quantum dot 321 is achieved. Now, the quantum dot 321 can assume a defined quantum state by delocalizing in the double well (E) or moving quickly back and forth in the magnetic field gradient (F). When guided out of the manipulation region 7, the quantum dot 321 therefore has a defined quantum mechanical state.

[0118] Fig. 9 The sequence of manipulation in the manipulation region 7 of the two-qubit operation is shown. In which, a static double well 324 is formed in the manipulation region 7 by barrier gate electrodes 315, 316, 317, and quantum dots 320, 321 are moved to the static double potential well 324 in the manipulation region 7 by movable potential wells 322, 323, and are each introduced into the double potential well 324. The manipulator 313, such as a gradient magnetic field, allows the quantum dots 320, 321 to assume a defined quantum mechanical state. Two-qubit operations can be performed between the quantum dots 320, 321 through exchange interaction, as indicated by the horizontal double arrow 326. Therefore, the quantum dots 320, 321 that move out of the manipulation region 312 obtain a defined quantum mechanical state.

[0119] exist Fig.10 It is shown in Figure 1 The gate electrode array 400 and 401 are arranged on the surface 19 of the substrate 10. The gate electrode array 400 has two gate electrodes 402 and 403. The respective gate electrodes 402 and 403 are electrically isolated from each other by an insulating layer 404. To this end, the gate electrodes 402 and 403 of the gate electrode array 400 are provided in the form of a layer, and the insulating layer 404 is arranged between each gate electrode 402 and 403 of the gate electrode array 400. The gate electrodes 402 and 403 also include electrode fingers 405 and 406 arranged parallel to each other on the surface 19 of the substrate 10.

[0120] Voltage is applied to the gate electrode arrays 400, 401 through electrical connections. By applying a sinusoidal voltage to the gate electrodes 402, 403 of the gate electrode array 400, a movable potential well is created in the substrate 10. Thus, quantum dots 408 or charge carriers trapped in the potential well can move through the substrate 10. By driving the electrode fingers 405, 406 of the gate electrodes 402, 403 with a sinusoidal voltage, the potential well moves longitudinally through the substrate 10.

[0121] The gate electrode array 401 forms a static double potential well. To this end, the gate electrode array 401 includes barrier gate electrodes 410, 412, 414, a pump gate electrode 416 and another pump gate electrode 418, which can make the quantum dots or charge carriers move or oscillate. The pump gate electrodes 416, 418 are alternately arranged between the barrier gate electrodes 410, 412 and 414. The gate electrodes 410, 412, 414, 416, 418 each have an electrode finger 411, 413, 415, 417, 419 (in Fig.11 Connected to the barrier gate electrodes 410, 412, 414 of the gate electrode array 401 is a storage 422 for introducing a charge change.

[0122] Fig.11 A sequence A to F of charging charge carriers is shown. The electrode fingers 405, 406 of the gate electrode array 400 form a potential well 407, which can move through the substrate 10. The movement of the potential well 407 is thereby achieved by appropriate interconnection of the electrode fingers 405, 406. To this end, the electrode fingers 405, 406 of the gate electrode array 400 are interconnected periodically in an alternating manner, which results in an almost continuous movement of the potential well 407 through the substrate 10.

[0123] The loading terminal 6 is based on the Pauli principle, according to which an electron energy level is never occupied by electrons of the same spin. On the one hand, a static double potential well 409 is generated by gate electrodes 410, 412, 414 and 416, 418, and on the other hand, a movable potential well 407 is generated by gate electrodes 402, 403. Two charge carriers 421 from a reservoir 422 are introduced into a first potential well 420 in the static double potential well 409. The charge carriers 421 are separated and aligned with an actuator 424, for example using a gradient magnetic field and pump gate electrodes 416, 418. The separated charge carriers 423 tunnel into the second static potential well 425 of the double potential well 409, which is indicated by arrows 426. Only one charge carrier 427 remains in the first static potential well 420. The quantum states of the quantum dots 423, 427 in the potential wells 420, 421 can be known by the orientation of the applied gradient magnetic field.

[0124] Through the movable potential well 407, another quantum dot 408 is brought to the second static potential well 425 in the double potential well 409 at the same energy level. The quantum mechanical state of the quantum dot 408 is unknown. Arrow 428 indicates the translation direction of the quantum dot 408 along the moving potential well 407. Through the tunneling effect, the quantum dot 423 of the second static potential well 425 is exchanged with the quantum dot 408 of the moving potential well 407. The known quantum mechanical state of the quantum dot 423 is now located in the moving potential well 407 and initializes, for example, a qubit.

[0125] If the quantum dot 408 has the same spin as the quantum dot 423 that has now moved away to initialize, the quantum dot 408 tunnels back into the first static potential well 420 in the double potential well 409. Therefore, the sensor element not shown here does not detect any charge change. If the quantum mechanical states of the quantum dots 423 and 408 are different, a charge change can be detected. The exchange by tunneling is represented by arrow 429.

[0126] exist Fig.12 It is shown in Figure 1 The readout terminal 8 of the quantum computing element 1 is shown. Therein, gate electrode arrays 500, 501 are shown, each of which includes two gate electrodes 502, 503. The respective gate electrodes 502, 503 are electrically isolated from each other by an insulating layer 504. To this end, the gate electrode arrays 500, 501 are provided in the form of layers, and the insulating layer 504 is arranged between each gate electrode 502, 503. The gate electrodes 502, 503 also include electrode fingers 505, 506 arranged parallel to each other on the surface 19 of the substrate 10.

[0127] A suitable voltage is applied to the gate electrode arrays 500, 501 through electrical connections. By applying a sinusoidal voltage to the gate electrodes 502, 503 of the gate electrode array 500, a potential well is formed in the substrate 10. Thus, quantum dots or charge carriers trapped in the potential well can move through the substrate 10. By driving the electrode fingers 505, 506 with a sinusoidal voltage, the potential well moves longitudinally through the substrate 10.

[0128] The gate electrode array 500 forms an area in which the quantum dots can move through the potential well. In contrast, the gate electrode array 501 forms a static potential well. To this end, the gate electrode array 501 includes barrier gate electrodes 507, 508 and pump gate electrodes 509, which can make the quantum dots or charge carriers move or oscillate. The pump gate electrode 509 is arranged between the barrier gate electrodes 507, 508. The gate electrodes 507, 508 and 509 are also each separated by an insulating layer 504.

[0129] Connected to the barrier gate electrode array 501 is a sensor element 510 for detecting charge changes. The sensor element 510 detects the charge present in the static potential well. The potential well is generated by the gate electrode array 501.

[0130] Fig.13 A sequence for reading out the quantum state of a qubit in a quantum dot 513 is shown. The figure shows the readout terminal 8 in a simplified manner so that only the electrode fingers 505, 506, the barrier gate electrodes 507, 508 and the pump gate electrode 509 are visible. A sequence from A to C of the routes of the potential wells 515, 516 is shown below. The electrode fingers 505, 506 of the gate electrode array 500 form a mobile potential well 515. Thus, the movement of the quantum dot 513 in the potential well 515 is achieved by suitable interconnection of the electrode fingers 505, 506. To this end, the electrode fingers 505, 506 of the gate electrode array 500 are periodically interconnected in an alternating manner, which causes the quantum dot 513 in the potential well 515 to move almost continuously through the substrate 10.

[0131] The readout terminal is based on the Pauli principle. On the one hand, a static potential well 516 is generated with the help of gate electrodes 507, 508, and on the other hand, a movable potential well 515 is generated with the help of gate electrodes 505, 506. A quantum dot 513 is introduced into the static potential well 516, and the quantum mechanical state of the quantum dot 513 at an energy level (spin in the case of electrons) is known. The quantum dot 513 is aligned with the pump gate electrode 508, for example, with the spin up, as shown in the figure. With the help of the movable potential well 515, another quantum dot 514 is brought to the static potential well 516 at the same energy level. Arrow 517 indicates the direction of movement of the quantum dot 514 with the movable potential well 515. If the quantum mechanical states are different, the energy level is now filled. The filling can be done by tunneling, represented by arrow 518.

[0132] With the addition of the quantum dot, the sensor element 510 detects a change in charge at this energy level. If the quantum mechanical states of the quantum dots 513, 514 are the same, this energy level cannot accept another charge carrier. Therefore, the quantum mechanical state does not change at this energy level. Therefore, it is possible to determine which quantum mechanical state the approaching quantum dot 513 has.

[0133] Reference numerals list

[0134] 1 Quantum computing element 115 gate electrode (first layer)

[0135] 2 Network 116 Potential Well

[0136] 3 Network Unit 117 Quantum Dots

[0137] 4 Shuttle channel 118 Arrow direction

[0138] 5 Junction 119 Dashed Line

[0139] 6 Loading terminal

[0140] 7 control area 201 gate electrode array

[0141] 8 readout terminals 202 gate electrode array

[0142] 9-spin qubit 203-gate array

[0143] 10 substrate 204 gate electrode

[0144] 11 Quantum Computer 205 Gate Electrodes

[0145] 12 control device 206 gate electrode 19 surface 207 gate electrode

[0146] 208 insulation layer

[0147] 100 first side 209 electrode finger

[0148] 101 second side 210 electrode finger

[0149] 102 first gate electrode array 211 electrode finger

[0150] 103 second gate electrode array 212 electrode fingers

[0151] 104 The third gate electrode array 213 cross region

[0152] 105 electrical terminal 214 barrier gate electrode 106 electrical terminal 215 barrier gate electrode 107 electrical terminal 216 pump gate electrode

[0153] 108 first isolation layer 217 barrier gate electrode 109 second isolation layer 218 mobile potential well

[0154] 110 electrode fingers (second layer) 219 quantum dots 111 electrode finger (second layer) 220 arrow 112 electrode finger (third layer)

[0155] 113 electrode fingers (third layer) 300 gate electrode array 114 arrow 301 gate electrode array 302 gate electrode 408 quantum dot

[0156] 303 gate electrode 409 static double potential well 304 gate electrode 410 barrier gate electrode 305 gate electrode 411 electrode finger

[0157] 306 insulating layer 412 barrier gate electrode 307 electrode fingers 413 electrode fingers

[0158] 308 electrode finger 414 barrier gate electrode 309 electrode fingers 415 electrode fingers

[0159] 310 electrode finger 416 pump gate electrode

[0160] 311 area 417 electrode fingers

[0161] 313 manipulator 418 pump gate electrode

[0162] 314 gate electrode array 419 electrode finger

[0163] 315 potential barrier gate electrode 420 first static potential well 316 barrier gate electrode 421 charge carrier 317 barrier gate electrode 422 storage

[0164] 318 Pump gate electrode 423 Separated quantum dots

[0165] 319 pump gate electrode 424 actuator

[0166] 320 quantum dots 425 second static potential well

[0167] 321 quantum dots 426 arrows (tunneling)

[0168] 322 mobile potential well 427 remaining quantum dots

[0169] 323 moving potential well 428 arrow (translation)

[0170] 324 static double well 429 arrows (exchange interaction)

[0171] 325 horizontal arrow

[0172] 326 horizontal double arrows 500 gate electrode array

[0173] 400 gate electrode array 501 gate electrode array

[0174] 401 gate electrode array 502 gate electrode

[0175] 402 gate electrode 503 gate electrode

[0176] 403 gate electrode 504 insulation layer

[0177] 404 insulation layer 505 electrode finger

[0178] 405 electrode finger 506 electrode finger

[0179] 406 electrode finger 507 barrier gate electrode

[0180] 407 potential well 508 potential barrier gate electrode

[0181] 508 Pump Gate Electrode

[0182] 510 sensor element

[0183] 513 quantum dots

[0184] 514 quantum dots

[0185] 515 Moving Potential Well

[0186] 516 Static Potential Well

[0187] 517 Arrow (Translation)

[0188] 518 Arrow (tunneling).

Claims

1. A method for operating a quantum computing element (1), the quantum computing element (1) having a network (2) of shuttle channels (4), the network (2) of shuttle channels (4) having a plurality of junctions (5) and a plurality of manipulation regions (7), wherein the method comprises, for a plurality of spin qubits (9), respectively: a) Initialize the qubit (9), b) manipulating the qubit (9) in at least one of the manipulation regions (7), c) reading out the qubit (9), The number of quantum bits (9) is at least temporarily greater than half the number of junction points (5).

2. The method according to claim 1, wherein steps a) to c) are performed simultaneously for at least some of the qubits (9).

3. The method according to any of the preceding claims, wherein the method comprises a plurality of adjacent time intervals, and wherein in each of the time intervals, steps a) to c) are performed for a corresponding set of qubits (9).

4. A method according to any one of the preceding claims, wherein between steps a) to c), at least one of the qubits (9) is shuttled along the network (2) of shuttling channels (4) so ​​as to pass through at least four different ones of the junctions (5).

5. A method according to any of the preceding claims, wherein at least some of the qubits (9) are shuttled through the at least one manipulation region (7) in which they are manipulated in step b).

6. A method according to any of the preceding claims, wherein the shuttling direction of at least some of the qubits (9) is reversed at the at least one manipulation region (7) in which they are manipulated in step b).

7. A method according to any of the preceding claims, wherein at least some of the qubits (9) are manipulated successively in a plurality of the manipulation regions (7) of the manipulation region (7), and wherein the respective qubits (9) are shuttled between these manipulation regions (7).

8. The method according to any of the preceding claims, wherein for at least some of the qubits (9), the manipulation in the respective step b) is entanglement with at least one further qubit (9) of the qubits (9).

9. The method according to any of the preceding claims, wherein the method is an implementation of a surface code.

10. Quantum computers (11), including: - a quantum computing element (1) having a network (2) of shuttle channels (4), the network (2) of shuttle channels (4) having a plurality of junctions (5) and a plurality of manipulation regions (7), - a control device (12) connected to the quantum computing element (1) and configured to perform the method according to any of the preceding claims.

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