Quantum bit array, quantum computer, and quantum error detection method

Abstract

This invention provides a qubit array that enables operations between multiple logical qubits with implemented quantum error correction, while securing the space for wiring and elements necessary for qubit control. [Solution] The device has a first quantum dot array in which multiple data qubits or multiple syndrome qubits are arranged to move, and a second quantum dot array in which multiple data qubits or multiple syndrome qubits are fixed, and a double ring consisting of an outer ring and an inner ring is formed by arranging the pair of first quantum dot arrays and second quantum dot arrays in a loop.

Description

Technical Field

[0001] The present invention relates to a qubit array, a quantum computer, and a quantum error detection method. Background Art

[0002] The ultimate goal of quantum computer development is a fault-tolerant quantum computer (FTQC), and various research and development activities are actively conducted aiming for this goal. There are many candidates for physical systems to be used for qubits, which are the fundamental elements of quantum computers, and each is being energetically researched. From the viewpoint of integration, a method using silicon electron spins is advantageous.

[0003] While silicon has very high integration and is advantageous for large-scale implementation, it has a problem in that sufficient space for control lines and the like cannot be secured due to its excessively high integration. Therefore, a practical solution is to reduce integration density to secure space for control lines and the like.

[0004] In a quantum computer implemented with quantum error correction codes, qubits are classified into data qubits and syndrome qubits, and redundant information is stored in the data qubits. The syndrome qubits are used for measurement for error detection, and are measured after information is transferred from a plurality of data qubits. Through analysis of the measurement results, it is estimated which qubit has what kind of error.

[0005] As a means for securing space for the aforementioned control lines and the like, it is known to arrange data qubits and syndrome qubits one-dimensionally in parallel to form a 2×N array (see Non-Patent Document 1).

[0006] Data qubits are moved in a one-dimensional direction to change the combination of adjacent data qubits and syndrome qubits, and information transfer relating to a plurality of data qubits is performed. Since qubits are only arranged in 2×N columns, sufficient space for control lines and the like can be secured.

[0007] However, if data qubits are arranged in one dimension, the logical qubits that make up that group will also be arranged in one dimension. In order to perform operations between two non-adjacent logical qubits, it is necessary to, for example, move (shuttle) the syndrome qubit that mediates between the two logical qubits over a long distance so that they interact, or swap the logical qubits so that they become adjacent, or merge a logical qubit between the two logical qubits with one of the logical qubits to make them adjacent.

[0008] This is a significant limitation: if the two logical qubits to be interacted with are separated by an array size, the operation that can be performed in one step becomes O(1) (order 1), regardless of the number of logical qubits, and a single gate operation can use almost the entire qubit array. In other words, parallel processing is generally not possible.

[0009] While slightly different in perspective, an idea has been disclosed in which each qubit is not fixed to a single point but moved around while performing the necessary actions (see Non-Patent Document 2). This expands the space. This idea expands space on a qubit-by-qubit basis, but it has also been extended to the idea of ​​expanding space by grouping multiple qubits together (see Non-Patent Document 3). Here, an idea is also shown in which grouped multiple qubits move through the space they use.

[0010] However, the disclosure in Non-Patent Document 3 is purely conceptual and does not disclose any implementation details for a device. Considering the extended functionality, the device structure and operation are likely to become complex. [Prior art documents] [Non-patent literature]

[0011] [Non-Patent Document 1] Adam Siegel et al., arXiv:2402.12599. [Non-Patent Document 2] Zhenyu Cai et al., Phys. Rev. X 4, 020345 (2023). [Non-Patent Document 3] Adam Siegel et al., arXiv:2501.02120. [Overview of the project] [Problems that the invention aims to solve]

[0012] Considering the above background technologies, the challenges are to secure space for control lines and other elements, resolve the aforementioned situation where parallel processing is not possible, and furthermore, to create a simple and simplified method that can be implemented in devices.

[0013] In particular, the above-mentioned non-patent literature implements error correction in a one-dimensional array, but it has limitations due to its one-dimensionality, such as constraints on operations between logical qubits and an increase in the shuttle distance.

[0014] The objective of the present invention is to provide a qubit array that enables operations between multiple logical qubits with implemented quantum error correction, while securing space for wiring and elements necessary for qubit control. [Means for solving the problem]

[0015] A qubit array according to one aspect of the present invention comprises a first quantum dot array in which a plurality of data qubits or a plurality of syndrome qubits are arranged to move, and a second quantum dot array in which a plurality of the data qubits or a plurality of the syndrome qubits are fixed, wherein a double ring consisting of an outer ring and an inner ring is formed by arranging a pair of the first quantum dot arrays and the second quantum dot array in a loop, and the positional relationship between the plurality of data qubits and the plurality of syndrome qubits is changed between the first quantum dot array and the second quantum dot array by moving the plurality of data qubits or a plurality of syndrome qubits along the first quantum dot array using a plurality of gate electrodes, and a 2-qubit operation is performed between the plurality of data qubits and the plurality of syndrome qubits while changing the positional relationship using a plurality of gate electrodes. [Effects of the Invention]

[0016] According to one aspect of the present invention, it is possible to provide a qubit array that enables operations between multiple logic qubits with implemented quantum error correction while securing space for wiring and elements necessary for qubit control. [Brief explanation of the drawing]

[0017] [Figure 1] This diagram shows the configuration of a logical qubit with a code distance of 3. [Figure 2] (a) is a diagram showing a quantum circuit for syndrome measurement (stabilizer measurement) responsible for bit inversion error detection, and (b) is a diagram showing a quantum circuit for syndrome measurement (stabilizer measurement) responsible for phase inversion error detection. [Figure 3] This figure shows an example implementation of a qubit array consisting of multiple logical qubits. [Figure 4] This figure shows a qubit array representing one aspect of the operation of logical qubits. [Figure 5] This figure shows a qubit array representing another example of one scenario in the operation of logical qubits. [Figure 6] (a) is a diagram showing two-dimensionally arranged logical qubits, and (b) is a diagram showing logical qubits obtained by converting (a) into a one-dimensional arrangement. [Figure 7] (a) is a diagram showing a two-dimensional arrangement of two coupled logical qubits, and (b) is a diagram obtained by converting (a) into a one-dimensional arrangement. [Figure 8] is a diagram obtained by changing the numbering in FIG. 7. [Figure 9] (a) is a diagram showing a two-dimensional array of four logical qubits, and (b) is a diagram obtained by converting the array into a one-dimensional but quadrangular (ring-shaped) arrangement. [Figure 10] (a) is a diagram showing a two-dimensional array of eight logical qubits, and (b) is a diagram showing an arrangement obtained by arranging every four logical qubits in a quadrangular (ring-shaped) form and connecting them. [Figure 11] (a) is a diagram showing a two-dimensional array of multiple logical qubits, and (b) is a diagram showing an arrangement obtained by arranging every twelve logical qubits in a ring (loop) shape and connecting them. [Figure 12] (a) is an enlarged view of block B in FIG. 11(a), and (b) is a diagram obtained by converting (a) into a one-dimensional array. [Figure 13] (a) is an enlarged view of block C in FIG. 11(a), and (b) is a diagram obtained by converting (a) into a one-dimensional array. [Figure 14] (a) is an enlarged view of block B in FIG. 11(a), and (b) is a diagram obtained by adding measurement quantum dots to FIG. 12(b). [Figure 15] (a) is an enlarged view of block B in FIG. 11(a), and (b) is a diagram obtained by shifting the syndrome qubit in FIG. 14(b) by one dot. [Figure 16] (a) is an enlarged view of block C in FIG. 11(a), and (b) is a diagram obtained by adding measurement quantum dots to FIG. 13(b). [Figure 17] (a) is an enlarged view of block C in FIG. 11(a), and (b) is a diagram obtained by shifting the syndrome qubit in FIG. 16(b) by one dot. [Figure 18](a) is an enlarged view of block B in Figure 11(a). (b) is a view of Figure 14(b) with electrodes added. (c) is a cross-sectional view of the substrate and gate electrode. [Figure 19] (a) is an enlarged view of block C in Figure 11(a), (b) is Figure 16(b) with electrodes added, and (c) is a cross-sectional view of the substrate and gate electrode. [Figure 20] This is an overall diagram of the system, including the quantum computing device. [Modes for carrying out the invention]

[0018] A fault-tolerant quantum computer (FTQC) is a quantum computer that implements quantum error correction codes. Surface codes are a well-known example of such codes. In the following embodiments, surface codes will be described as an example. As will be clear from the following description, the present invention is not limited to surface codes but is applicable to any type of code.

[0019] Before describing the embodiments in detail, we will discuss surface codes. Figure 1 shows the mounting configuration of surface codes when the code distance is 3.

[0020] Qubits are classified into data qubits and syndrome qubits. The former are placed at the vertices of a 2D lattice (○), and the latter are placed at the center of the faces (●). There are 9 data qubits and 8 syndrome qubits. Information is stored in the data qubits, and the syndrome qubits are measurement qubits for error detection. Each syndrome qubit is measured after information is transferred from the 2-4 nearest data qubits. 9-8=1 is the information content of the logical qubit.

[0021] The circuit diagram for information transfer and measurement is shown in Figure 2. Syndrome qubits are classified into two types: one responsible for bit inversion error detection and the other for phase inversion error detection, and the circuits for each are shown in Figures 2(a) and (b). The series of operations based on Figure 2 is called syndrome measurement (stabilizer measurement).

[0022] Figure 1 represents one logical qubit as a whole. Multiple logical qubits are realized by arranging multiple such qubits side by side, as shown in Figure 3. Operations on each individual logical qubit are performed on each logical qubit separately. Operations between two logical qubits are realized through operations that combine or separate the two logical qubits in question. The upper left of Figure 4 shows the combined state. Operations between non-adjacent logical qubits are realized by either reserving a region where no logical qubits are placed and moving (shutting) the entire logical qubit, as shown in Figure 4, or by swapping (SWAP) each qubit that makes up a logical qubit (called a physical qubit) to make the interacting logical qubits adjacent to each other. When constructing qubits with semiconductor electron spins, quantum dots are formed at the positions where each qubit will be placed to fix the position of each qubit.

[0023] In Figure 4, when using shuttles, quantum dots in areas where no logic qubits are placed should, in principle, be left empty. This principle is based on the fact that, as shown in Figures 4 and 5, when logic qubits are coupled, the positions of the originally empty quantum dots become the locations of the logic qubits at the time of coupling, and a qubit is required at that coupling point. When using swaps, electrons (qubits) should, in principle, be placed in quantum dots in areas where no logic qubits are placed. This principle is based on the fact that empty quantum dots are necessary when using shuttles in conjunction with swaps.

[0024] Operations between non-adjacent logical qubits can also be realized by combining multiple logical qubits sandwiched between the two target logical qubits. For example, 103 in Figure 5 is a combination of 101 and 102 in Figure 3, including the multiple logical qubits sandwiched between them. In the case of the form of 103 in Figure 5, electrons (qubits) are generally placed in the quantum dots in the region where no logical qubits are placed. The reason for this principle is that empty quantum dots are also necessary when using shuttles. [Examples]

[0025] As shown in Figure 2, surface coding performs a CNOT operation between the nearest data qubit and syndrome qubit to transfer information. Since only the nearest interaction is used, the relative positions of the data qubit and syndrome qubit can be fixed if the qubits are arranged in a two-dimensional configuration as shown in Figures 1-5. On the other hand, if the qubits can be moved, a two-dimensional configuration is not necessarily required. An example of this is shown in Figure 6(b). In Figure 6(b), the data qubits numbered 1-9 in the two-dimensional configuration of Figure 6(a) are arranged in a single row, and the syndrome qubits numbered ah are arranged parallel to them.

[0026] In Figure 6(b), for example, data qubit 1 is in nearest-neighbor state with syndrome qubit c. Moving the syndrome qubit left or right changes the nearest-neighbor combination. Therefore, if the syndrome qubit can be moved, all the necessary nearest-neighbor positions in Figure 6(a) can be realized. Since semiconductor electron spin-based qubit arrays allow for electron (qubit) movement (shutting), surface coding can be implemented in a parallel 1D configuration (2×N configuration). In Figure 6(b), no qubits are placed above the data qubit or below the syndrome qubit, providing ample space for control lines, etc. Note that while Figure 6(b) shows the syndrome qubit being moved, the data qubit could also be moved.

[0027] In Figure 6(b), gray circles are arranged in a row of syndrome qubits (black circles) (for example, 202). These represent the positions of vacant syndrome qubits. Their function will be explained using Figures 7 and 8.

[0028] Even when there are multiple logical qubits, if they are independent, they can simply be connected in a one-dimensional manner. However, it is necessary to reserve a qubit to connect adjacent logical qubits (see upper left of Figure 4). Figures 7 and 8 show the case when two logical qubits are connected. The positions that were vacant before connection become logical qubits, so the number of data qubits and syndrome qubits used increases.

[0029] Some of the circles that were gray in Figure 6(b) become black in Figures 7 and 8. The same applies to data qubits; although Figure 6 only shows data qubits currently in use, there are actually data qubits that are reserved for the coupling of logical qubits. For example, data qubits 4, 8, and 12 in Figure 7 and data qubits 4, 12, and 20 in Figure 8 are data qubits used during coupling.

[0030] When arranging multiple logic qubits in a one-dimensional array, there are several options for how to arrange the physical qubits. Figure 7(b) shows the case where individual logic qubits are used as units for the arrangement. Here, the part used during coupling is also incorporated. The dotted lines in Figure 7(a) represent the boundaries of the logic qubits before coupling. Figure 8(b) shows the case where the two coupled logic qubits are treated as one and the physical qubits are arranged accordingly. Either arrangement is acceptable. [Examples]

[0031] In Example 1, data qubits and syndrome qubits were arranged in parallel in a one-dimensional manner to secure space for control lines, etc. Since the main purpose is to secure space for control lines, etc., it is not necessary to be exactly one-dimensional. The ends of the one-dimensional arrangement can be connected to form a closed arrangement. Figure 9(b) shows an example of a closed arrangement of physical qubits equivalent to four logical qubits. By connecting the ends, the logical qubits at both ends can be placed adjacent to each other.

[0032] Furthermore, since it is basically one-dimensional, sufficient space is secured for control lines, etc. The original two-dimensional arrangement is shown in Figure 9(a). The arrangement in Figure 9(b) is geometrically a ring, and the qubits could be arranged in a circle instead of a quadrilateral, but semiconductor technology usually arranges gate electrodes in vertical and horizontal lines, so the arrangement in Figure 9(b) was chosen.

[0033] Figure 9(a) shows four logical qubits arranged. Each logical qubit consists of nine data qubits. Figure 9(b) shows the corresponding 4 × 9 = 36 data qubits. The data qubits used when logical qubits are combined are not shown. The data qubits used for combining are vacant in Figure 9(b).

[0034] Not all of the syndrome qubits shown in Figure 9(a) and the syndrome qubits used in coupling are shown in Figure 9(b). Only the syndrome qubits located in the nearest position above the data qubit in Figure 9(a) are shown in Figure 9(b). Therefore, in reality, there are more qubits or electrons that can be used as qubits than are shown in Figure 9(b).

[0035] In Figure 9(b), the unshown syndrome qubits are located at the four corners of the square. A specific example is shown enlarged within the dashed line in the lower left of Figure 9(b) (250). In addition to the unused syndrome qubits shown as solid gray circles, there are also dotted gray circles (e.g., 205). This is one method of corner handling and represents quantum dots used for moving (shutting) syndrome qubits. Unused data qubits are also shown as dotted white circles within the enlarged dashed circle 250 (e.g., 215).

[0036] The number of logical qubits can be increased by arranging multiple squares (ring arrangement) as shown in Figure 9(b). Figure 10(b) shows the case where two squares are arranged side by side. Figure 10(a) is the original 2D arrangement, which has 8 logical qubits. Unused syndrome qubits and shuttle quantum dots were placed in the dotted lines at the four corners of Figure 9(b). The same applies to Figure 10(b).

[0037] In Figure 10(b), two more rectangles are connected by dotted lines (e.g., 223). These connecting dotted lines are pathways made of quantum dots that allow syndrome qubits to move between the upper and lower rectangles. These pathways enable the coupling of logic qubits belonging to the upper rectangle with logic qubits belonging to the lower rectangle. In other words, thanks to these pathways, eight logic qubits can be directly or indirectly connected. Geometrically, this structure is like two connected rings, and considering that data qubits and syndrome qubits form a double ring, it can be described as a coupled double-ring structure.

[0038] The linked double-ring structure has the following advantages, for example. Firstly, thanks to the double-ring structure, a syndrome qubit is always located in the closest proximity to the data qubit. This means that the number of constituent qubits in each ring is kept to a minimum, and the shuttle distance required for the syndrome qubit is kept to a minimum. Shuttling can reduce fidelity, and minimizing this is a superior property. This is a property that cannot be expected in the single-ring configuration disclosed in Non-Patent Literature 2 and Non-Patent Literature 3. Secondly, in the linked double-ring structure, only the outer rings are linked, and the inner rings are simple rings. As a result, the structure is simplified, and implementation and operation are simplified and easy.

[0039] Figure 10(b) shows two rings, each consisting of 4 logical qubits, joined together. The number of rings to be joined is arbitrary, and the number of logical qubits in a single ring is also arbitrary. Figure 11 shows the case where one ring is composed of 12 logical qubits. For example, the dashed line connecting the block BCDMNOPQRSTU in Figure 11(b) represents the data qubits belonging to the block BCDMNOPQRSTU in Figure 11(a) arranged one-dimensionally to form a single ring. The solid line in Figure 11(b) represents the arrangement of syndrome qubits. The thin dotted lines drawn perpendicular to the dashed lines (e.g., 241) represent block divisions.

[0040] In Figure 11(b), the thick solid lines (e.g., 224) between A and B and between V and U represent pathways for syndrome qubits to travel between each block. Quantum bits (quantum dots) are only located along the solid lines (including the thick solid lines) and dashed lines; the remaining areas are empty space used for control lines, etc. In Figure 11(a), the gray areas represent empty space. While empty space was limited in the two-dimensional configuration, Figure 11(b) provides ample empty space.

[0041] In this invention, when realizing interaction between non-adjacent logic qubits, the concept of 103 in Figure 5 is used. Interaction between logic qubits is realized by coupling and separating two logic qubits. If the two logic qubits are far apart, coupling and separating should include the logic qubit sandwiched between them. 103 in Figure 5 represents the coupled state in that case. Let's consider this method in the case of Figures 11(a) and (b). If we want to make block A and block F interact, we should couple blocks A, B, C, D, E, and F. To do this, we make the logic qubit include the region connecting each block. That is, we should perform a syndrome measurement (stabilizer measurement) in that connecting region.

[0042] In this embodiment, the data qubits were fixed in position while the syndrome qubits were shuttled. This is because the data qubits hold the information. Generally, shuttled qubits reduce fidelity. To minimize this effect, it is advisable to fix the data qubits and shuttle the syndrome qubits. There are no particular disadvantages to fixing the data qubits, and as mentioned above, remote logic qubit interaction is possible, the linked double-ring structure functions well, and simplicity and ease of implementation and operation are guaranteed.

[0043] However, this does not negate the possibility of fixing the position of the syndrome qubit and shuttle the data qubit. Depending on the application, this option is also available. For example, it becomes possible to move logic qubits through the movement of data qubits. [Examples]

[0044] As shown in Figures 6-8, this invention is based on a one-dimensional arrangement of syndrome qubits and data qubits in parallel, and as shown in Figure 9(b), it is made into a rectangle with the two ends connected. The four corners of the rectangle are special points in terms of the device structure. Furthermore, in Figure 11(b), the structure is made to increase the number of bends. In this embodiment, the handling of the bent portion will be described.

[0045] Figures 12(a) and 12(b) show the qubits belonging to block B in Figures 11(a) and 11(b). In Figure 12(a), the qubits within the area enclosed by the dashed and dotted lines belong to block B. Here, syndrome qubits on the dashed lines belong precisely to block B, but syndrome qubits on the dotted lines actually belong to one of blocks U, T, or C (see Figure 11). However, since syndrome qubits on the dotted lines are located at the boundary between U, T, C and B, they perform CNOT operations not only with data qubits belonging to U, T, C but also with data qubits belonging to B. Figure 12(b) shows all the data qubits and syndrome qubits belonging to B, as well as the connection path (225) to block A.

[0046] In Figure 12(b), data qubits (white circles) are located on the dashed lines. The dotted white circles in the row of white circles (e.g., 213) are located on the lattice in Figure 12(a) and can become data qubits when logic qubits are combined. Syndrome qubits (black circles) are located on the solid lines in Figure 12(b), and the solid gray circles in the row of black circles can be used as syndrome qubits when logic qubits are combined (e.g., 203), and are located on the plane in Figure 12(a).

[0047] The arrangement of syndrome qubits (on the solid line) also includes dotted gray circles (e.g., 206). These are quantum dots that correspond to the 90-degree bend in the arrangement of syndrome qubits. They do not function as syndrome qubits at these positions, but rather provide pathways for shuttle operations. Dotted gray circles are also found in the upper right of Figure 12(b) (on the dotted line, e.g., 207). These are quantum dots that form a bridging pathway between block B and block A and are used for shuttle operations. These positions also do not function as syndrome qubits.

[0048] In Figure 12(b), which represents Block B, the 90-degree bend indicates that the data qubits are located on the inside. In Block C, shown in Figure 13(b), the syndrome qubits are located on the inside. Regardless of which is on the inside, the processing of the 90-degree bend is the same: quantum dots, represented by dotted gray circles (e.g., 208), are placed to form the shuttle path. [Examples]

[0049] Up to this point, we have mainly discussed the positional relationship between data qubits and syndrome qubits. Syndrome qubits are measured after a CNOT operation with data qubits. In this embodiment, we will describe the measurement process.

[0050] In qubits using semiconductor electron spins, upward spins |↑> and downward spins |↓> are associated with |0> and |1>. Directly distinguishing between |↑> and |↓> is difficult, so the spin information is converted into charge information before measurement. This conversion is achieved by installing a new measurement quantum dot containing the upward electron spin, placing a syndrome qubit close to this measurement quantum dot, and then moving the syndrome qubit to the measurement quantum dot.

[0051] If the syndrome qubit is |↑>, its spin direction matches that of the |↑> stored in the measurement quantum dot, so it cannot move according to the Pauli exclusion principle. However, if the syndrome qubit is |↓>, its spin direction does not match that of the |↑> stored in the measurement quantum dot, so it can move without the Pauli exclusion principle being in effect.

[0052] As a result, the number of electrons in the quantum dot used for measurement remains 1 in the former case, but becomes 2 in the latter. The spin information has been converted into the number of electrons (spin-charge conversion). The measurement detects this difference between 1 and 2 electrons. Here, the phenomenon where movement is not possible in the cases of |↑> and |↑> is called Pauli spin blockade.

[0053] To apply this principle, it is necessary to place measurement quantum dots, which are added to Figure 12(b) corresponding to block B, as shown in Figure 14(b). The solid line dots (e.g., 231) arranged in the dashed line sequence of data qubits are the measurement quantum dots. Each data qubit has a syndrome qubit opposite it, but the measurement quantum dots are newly added, and there are no syndrome qubits opposite them on the solid line.

[0054] During the measurement of syndrome qubits, they are moved to a position facing the measurement quantum dot, as shown in Figure 15(b). For example, qubit 201 in Figure 14(b) moves to qubit 201 in Figure 15(b). A spin-charge conversion is performed in this positional relationship, and then the charge of the measurement quantum dot is measured. After the measurement, the syndrome qubits are returned to their original positions, and the syndrome measurement (stabilizer) cycle (the process in Figure 2) is restarted.

[0055] Figures 14(b) and 15(b) are diagrams of Figure 12(b) with measurement quantum dots added. Similarly, Figures 16(b) and 17(b) are diagrams of Figure 13(b) with measurement quantum dots added. Figure 16(b) shows a diagram with measurement quantum dots added between data qubits, and Figure 17(b) shows a diagram where the syndrome qubit has been moved to a position opposite the measurement quantum dot. [Examples]

[0056] Examples 1-4 described the arrangement of electrons in quantum dots and their use as qubits or measurement electrons, as well as the immobilization of data qubits and measurement electrons and the movement (shutting) of syndrome qubits. The formation of quantum dots and the shuttle of electrons (qubits) are realized using gate electrodes formed on a semiconductor substrate.

[0057] Figure 18(b) shows an example of electrode implementation in the case of Figure 14(b) corresponding to Block B. The quantum dot is formed on the substrate at the intersection of the common gate electrode and the individual gate electrodes. In Figure 18(b), the solid line (301) is the common gate electrode for the syndrome qubit, and the gray patches (e.g., 302) are the individual gate electrodes. Figure 18(c) shows a cross-sectional view of the electrode structure. The quantum dot 351 is formed on the semiconductor substrate 350 at the intersection of 301 and 302. The syndrome qubit needs to be moved (shutled). Therefore, an AC voltage with a phase shift is applied to each individual gate electrode to modulate the depth of each quantum dot, and the positions of the deepest potentials are moved in the order of, for example, 302, 303, and 304. This causes the syndrome qubit to move.

[0058] Here, we focus on T-junction 226, which connects to the path to block A. The arrangement of gates that realizes shuttle (arrangement of gray patches) can be successfully deployed even at a T-junction, but if this were an intersection, the gray patches would overlap and implementation would not be possible. There are no intersections in the embodiment of the present invention. This is one of the consequences derived from the basic configuration of the present invention, and it means that implementation and operation are simplified.

[0059] In the data qubit arrangement, the dashed line (311) represents the common gate electrode. The individual gate electrode for the data qubit is, for example, 312. A quantum dot 352 is formed at the intersection of 311 and 312 on the semiconductor substrate 350. Since the data qubits do not need to be moved, the gate electrode corresponding to 303, which was present in the syndrome qubit arrangement, is not present in the data qubit arrangement.

[0060] Measurement quantum dots (e.g., 231 in Figures 14(b) and 15(b)) are also arranged in the data qubit array. An individual gate electrode for forming the measurement quantum dot is, for example, 314 in Figure 18(b).

[0061] A CNOT operation is performed between the data qubit and the syndrome qubit. CNOT is realized by causing the two qubits to interact. This interaction needs to be switched on and off. For example, the gate electrode 322 is used to adjust the height of the potential barrier between quantum dots 351 and 352.

[0062] When a syndrome qubit is moved to a measurement quantum dot, the potential barrier between the two must be lowered. This is done, for example, by using the gate electrode 324. After the move, the number of electrons in the quantum dot directly below 314 becomes 1 or 2, corresponding to whether the syndrome qubit was |↑> or |↓>. This difference is reflected in the impedance of the gate electrode 314. For example, if RF is input through the wire 334, the reflection characteristics change to reflect the difference in impedance. This change can be used to distinguish between the difference between 1 and 2 electrons.

[0063] The above shows an example of electrode implementation using Figure 18(b), which corresponds to Figure 14(b). Similarly, Figure 19 shows an implementation example for block C, which corresponds to Figure 16(b). [Examples]

[0064] Up to Example 5, the arrangement, movement, and operation of qubits were described from the perspective of geometric arrangement and device structure, and in relation to the operating principle of quantum error correction codes. In this example, we will describe how the quantum device is utilized when viewed as part of the entire system.

[0065] Figure 20 shows an example of the computer configuration of this embodiment. Figure 20 is similar to the configuration of a typical computer, but is characterized by the inclusion of a quantum computing device 1000. The quantum computing device 1000 is a quantum computing device consisting of the qubit array described in Examples 1 to 5. Other general operations are performed by the general computing device 2002.

[0066] The above configuration may be set up as an all-in-one computer, or any part such as the main memory 2001, general processing unit 2002, control unit 2003, auxiliary storage device 2004, input device 2005, output device 2006, etc., may be set up in other computers connected via a network.

[0067] General calculations are performed using the same procedures as a regular computer. Data is exchanged between the main memory 2001 (the memory unit) and the general arithmetic unit 2002 (the calculation unit), and calculations are carried out by repeating this process. The control unit 2003 directs the entire process. Programs executed by the general arithmetic unit 2002 are stored in the main memory 2001. If the storage capacity of the main memory 2001 is insufficient, the auxiliary memory 2004, also a memory unit, is used. Input devices 2005 are used for inputting data and programs, and output devices 2006 are used for outputting results. Input devices 2005 include manual input devices such as keyboards, as well as interfaces for network connectivity. This interface also doubles as an output device.

[0068] Quantum computation is performed using a similar procedure. Data is exchanged between the main memory 2001, which is the memory unit, and the quantum computing device 1000, which is the calculation unit, and the calculation proceeds by repeating this process. The control unit 2003 directs the entire process. The program executed by the quantum computing device 1000 is stored in the main memory 2001, which is the memory unit.

[0069] The program is converted into a language used by the quantum computing device 1000 using the general processing unit 2002 and stored in the main memory 2001. If the storage capacity is insufficient, the auxiliary memory device 2004, which is also a memory unit, is used. This language-based program is sent from the main memory 2001 to the quantum computing device 1000, and the control unit 2003 sends control signals to the quantum computing device 1000 according to the language-based program to execute the calculations. The results of the quantum computing device 1000 are sent to the main memory 2001 and processed by the general processing unit 2002 as needed.

[0070] In the above embodiment, a double-loop structure is formed in which one of the data qubits or syndrome qubits is arranged in a loop, and the other is arranged in a loop outside the first loop. The qubits belonging to both loops are positioned so that the nearest neighbors can interact with each other. Necessary information is transferred by moving (shutting) the outer qubits along the loop to change the combination of nearest neighbor qubits. The number of logical qubits belonging to the loop is approximately O(1) (order of 1), and multiple double loops are prepared and arranged two-dimensionally according to the required number of logical qubits. A bridging path is placed between adjacent double loops, allowing the outer qubits to move between the double loops. This achieves both space allocation for control lines, etc., and highly flexible logical qubit operations.

[0071] The double-ring structure in the qubit array of the above embodiment is a closed curve made of a 2×N array with a small N, and is one-dimensional, allowing for ample space to be secured for control lines and the like. While it is one-dimensional in this sense, multiple double rings are arranged two-dimensionally, enabling parallel computation. Since qubits can move between adjacent double rings, all logical qubits are directly or indirectly connected, and net, any pair of logical qubits can interact. This configuration allows for both space allocation for control lines and the like, and parallel computation.

[0072] According to the above embodiment, space for control lines and other elements is secured, and highly flexible logical qubit operations are enabled. In this way, operations between multiple logical qubits with implemented quantum error correction are realized while securing space for the wiring and elements necessary for qubit control. [Explanation of Symbols]

[0073] 101,102: Logical qubits 103: Combined logical qubits 201: Syndrome Qubit 202,203: Unused Syndrome Qubits 205, 206, 207, 208: Quantum dots for shuttle 213: Unused data qubit 215: Unused data qubit 223,224,225: Bridging routes 226:T-junction 231: Quantum dot for measurement (electrons in it) 241: Block divider line 250: Circle representing an enlarged view 301: Common gate electrode for quantum dot formation for syndrome qubits 302, 303, 304: Discrete gate electrodes for quantum dot formation for syndrome qubits 311: Common gate electrode for data qubit and measurement quantum dot formation 312: Discrete gate electrodes for quantum dot formation for data qubits 314: Discrete gate electrodes for forming quantum dots for measurement 322: Grid gate for adjusting the interaction between data qubits and syndrome qubits 324: Electrode gate for adjusting the interaction between quantum dots for measurement and quantum dots for syndrome qubits 334: Electrical wire for measuring syndrome 350: Semiconductor substrate 1000: Quantum operation device 2001: Main memory 2002:General arithmetic equipment 2003: Control device 2004: Auxiliary storage 2005: Input device 2006: Output device

Claims

1. A first array of quantum dots arranged such that multiple data qubits or multiple syndrome qubits move, It comprises a second quantum dot array on which a plurality of the data qubits or a plurality of the syndrome qubits are fixed, By arranging the pair of first quantum dot rows and the second quantum dot row in a loop, a double ring consisting of an outer ring and an inner ring is formed. By using multiple gate electrodes to move multiple data qubits or multiple syndrome qubits along the first quantum dot array, the positional relationship between the multiple data qubits and the multiple syndrome qubits between the first quantum dot array and the second quantum dot array is changed. A qubit array characterized by performing two-qubit operations between a plurality of data qubits and a plurality of syndrome qubits while changing the positional relationship using a plurality of gate electrodes.

2. By moving a plurality of the data qubits or a plurality of the syndrome qubits along the first quantum dot array, the nearest-nearest pairs in which the data qubit and the syndrome qubit are located closest to each other between the first quantum dot array and the second quantum dot array are changed over time. The qubit array according to claim 1, characterized in that the two-qubit operation is performed between the data qubit and the syndrome qubit constituting the nearest-nearest pair at the nearest-nearest position to perform the data transfer required for the quantum error correction code.

3. A first quantum dot array on which multiple data qubits or multiple syndrome qubits move is arranged on the outer ring of the double ring, The qubit array according to claim 1, characterized in that the second quantum dot array, on which a plurality of data qubits or a plurality of syndrome qubits are fixed, is arranged in the inner ring of the double ring.

4. In the first array of quantum dots arranged on the outer ring, only a plurality of the syndrome qubits are movably arranged. The qubit array according to claim 3, characterized in that only a plurality of data qubits are fixedly arranged in the second quantum dot row arranged in the inner ring.

5. The aforementioned double wheels are The qubit array according to claim 1, characterized in that it is composed of a combination of straight sections and bent sections.

6. The qubit array according to claim 5, characterized in that a shuttle quantum dot on which the data qubit or the syndrome qubit can move is arranged near the bent portion.

7. Multiple of the aforementioned double rings arranged in a loop shape are arranged, The shuttle quantum dots on which the data qubit or the syndrome qubit can move are arranged between a plurality of the double rings, The qubit array according to claim 6, characterized in that a plurality of the double rings are connected using the aforementioned shuttle quantum dots.

8. The data qubit or the syndrome qubit has a path that allows it to move across a plurality of the double rings, The qubit array according to claim 7, characterized in that a plurality of the double rings are connected via the aforementioned path.

9. The aforementioned route is The qubit array according to claim 8, characterized in that it is constructed using a T-junction.

10. The qubit array according to claim 7, characterized in that it is composed of a plurality of the aforementioned double rings and has a plurality of empty spaces arranged for use as control lines.

11. The qubit array according to claim 1, characterized in that the plurality of gate electrodes are arranged along the double ring.

12. The qubit array according to claim 9, characterized in that the plurality of gate electrodes are arranged along the T-junction.

13. The second quantum dot array includes, The qubit array according to claim 1, characterized in that measuring quantum dots for measuring the syndrome qubits arranged in the first quantum dot row are provided.

14. When measuring the aforementioned syndrome qubit, The qubit array according to claim 13, characterized in that the state of the syndrome qubit is measured by utilizing the principle that the number of electrons inside the measuring quantum dot changes according to the state of the syndrome qubit.

15. The plurality of gate electrodes consist of a common gate electrode and individual electrodes. The qubit array according to claim 14, characterized in that the data qubit, the syndrome qubit, and the measurement quantum dot are controlled using the common gate electrode and individual electrodes.

16. The qubit array according to claim 15, characterized in that the syndrome qubits are moved by controlling the individual gate electrodes using phase-shifted AC voltages.

17. The aforementioned double wheels are By constructing a logical qubit with quantum error correction implemented, The qubit array according to claim 1, characterized in that operations are performed between a plurality of logical qubits using the plurality of gate electrodes.

18. A quantum dot array having multiple data qubits and multiple syndrome qubits, A quantum computer having a control device for controlling the quantum dot array, The aforementioned quantum dot array is A first array of quantum dots arranged such that a plurality of the data qubits or a plurality of the syndrome qubits move, It comprises a second quantum dot array on which a plurality of the data qubits or a plurality of the syndrome qubits are fixed, By arranging the pair of first quantum dot rows and the second quantum dot row in a loop, a double ring consisting of an outer ring and an inner ring is formed. The control device is By using multiple gate electrodes to move multiple data qubits or multiple syndrome qubits along the first quantum dot array, the positional relationship between the multiple data qubits and the multiple syndrome qubits between the first quantum dot array and the second quantum dot array is changed. A quantum computer characterized by performing two-qubit operations between a plurality of data qubits and a plurality of syndrome qubits while changing the positional relationship using a plurality of gate electrodes.

19. By arranging a pair of first and second quantum dot rows in a loop, a double ring consisting of an outer ring and an inner ring is formed. A first step is to arrange multiple data qubits or multiple syndrome qubits so that they move along the first array of quantum dots, A second step of arranging a plurality of data qubits or a plurality of syndrome qubits in fixed positions along the second quantum dot array, A third step of changing the positional relationship between the data qubits and the syndrome qubits between the first quantum dot row and the second quantum dot row by moving the data qubits or the syndrome qubits along the first quantum dot row using a plurality of gate electrodes, A fourth step involves using a plurality of gate electrodes to perform a two-qubit operation between a plurality of data qubits and a plurality of syndrome qubits while changing the positional relationship, A quantum error detection method characterized by having the following features.

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