Quantum computing apparatus and quantum computing method

Abstract

To efficiently perform error-tolerant quantum computations. [Solution] A quantum computing device according to one aspect of the present disclosure is a quantum computing device that realizes error-tolerant quantum computing by combining surface codes and HGP codes, and comprises: a conversion unit that converts a first quantum program expressed in a predetermined format into a second quantum program expressed in π / 8 rotation format; a conversion unit that converts the first instruction into a second instruction that can be executed with the logical qubits of the HGP code, based on a first instruction included in the second quantum program, logical qubits encoded by the surface codes, and logical qubits encoded by the HGP codes; and a quantum computing unit that realizes the quantum computing represented by the second instruction using shuttle.

Description

[Technical Field]

[0001] The present disclosure relates to a quantum computing device and a quantum computing method. [Background Art]

[0002] In recent years, an approach has been proposed for performing error-tolerant quantum computation with a smaller total number of physical qubits in quantum computers by combining a surface code and a code that is more efficient than the surface code but has constraints on its operations. For example, Non-Patent Document 1 proposes an approach combining a surface code and a code called an HGP (hypergraph product) code. [Prior Art Documents] [Non-Patent Documents]

[0003] [Non-Patent Document 1] Xu, Qian, et al.,"Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays.", Nature Physics (2024): 1-7. [Summary of Invention] [Problem to be Solved by Invention]

[0004] However, conventional techniques have not been able to efficiently perform error-tolerant quantum computation. For example, in the case of the approach combining a surface code and an HGP code, there is overhead in computation time because it is necessary to move data to the surface code each time to execute an instruction.

[0005] The present disclosure has been made in view of the above points, and an object of the present disclosure is to efficiently perform error-tolerant quantum computation. [Means for Solving Problem]

[0006] A quantum computing apparatus according to one aspect of the present disclosure is a quantum computing apparatus that realizes error-tolerant quantum computation by combining surface codes and HGP codes, and comprises: a conversion unit that converts a first quantum program expressed in a predetermined format into a second quantum program expressed in π / 8 rotation format; a conversion unit that converts the first instruction into a second instruction executable by the logical qubits of the HGP code, based on a first instruction included in the second quantum program, logical qubits encoded by the surface codes, and logical qubits encoded by the HGP codes; and a quantum computing unit that realizes the quantum computation represented by the second instruction using shuttlering. [Effects of the Invention]

[0007] This enables efficient execution of error-tolerant quantum computation. [Brief explanation of the drawing]

[0008] [Figure 1] This figure shows an example of the configuration of a quantum computing device according to one embodiment. [Figure 2] This figure shows an example of the hardware configuration of a control device according to one embodiment. [Figure 3] This figure shows an example of the functional configuration of a control device according to one embodiment. [Figure 4] This diagram schematically shows an example of an atomic arrangement. [Figure 5] This diagram schematically shows an example of transformation 1. [Figure 6] This diagram schematically illustrates an example of transformation 2. [Figure 7] This diagram schematically illustrates an example of transformation 3. [Figure 8] This diagram schematically illustrates an example of transformation 4-1. [Figure 9] This diagram schematically illustrates an example of transformation 4-2. [Figure 10] This diagram schematically illustrates an example of decomposition by repeatedly applying transformation 4. [Figure 11]This flowchart shows an example of the operation of a control device according to one embodiment. [Modes for carrying out the invention]

[0009] One embodiment of the present invention will be described in detail below with reference to the drawings.

[0010] <Background and Conventional Technology> ≪Quantum calculation≫ A quantum computer is a technology that performs calculations (called "quantum computation") by utilizing the superposition principle of quantum mechanics. Quantum computation is performed using information called qubits as data. In addition to the 0 and 1 states represented by ordinary bits, qubits can also represent superposition states as computer states. Large-scale quantum computers are expected to solve problems such as prime factorization and quantum chemical calculations much faster than ordinary computers, and their development is progressing rapidly worldwide. Note that quantum computers may also be called quantum computers or quantum processors.

[0011] ≪Representation of Quantum Programs≫ In a typical form of quantum computing, operational instructions for qubits are classified into three types: initialization, unitary operations, and measurement.

[0012] One type of unitary operation is the Pauli rotation operation. A Pauli rotation operation on n qubits is represented by a Pauli operator consisting of n of one of four letters (I, X, Y, or Z) and a rotation angle between 0 and 2π (inclusive). Another type of measurement is the Pauli measurement. An n-qubit Pauli measurement is defined by an n-qubit Pauli operator.

[0013] One typical form for representing a program that implements quantum computing (also called a quantum program or quantum computing program) is the Clifford+T form. In this form, the quantum program is represented by a sequence of one qubit initialization, two qubit control, and one qubit measurement (References 1, 2).

[0014] According to Reference 3, any arbitrary quantum computation can also be represented in the π / 8 rotation format. Therefore, any arbitrary quantum program can be represented as a sequence of Pauli rotation operations with a rotation angle of π / 8 acting on n qubits and Pauli measurements acting on n qubits. Further, according to Reference 3, there exists an efficient method for converting any quantum program in the Clifford+T form into the π / 8 rotation format.

[0015] <<Qubits Using Neutral Atoms>> Devices that store and control qubit data are called quantum devices. The superposition state of qubits is sensitive to noise, and the data retention lifetime in typical physical systems is extremely short. For this reason, various quantum devices that can retain long-lifetime qubits and are easy to control have been proposed. Quantum devices that implement qubits using neutral atoms are one of the candidates for highly practical quantum devices (Reference 4). Note that although the quantum computing apparatus 10 described later assumes implementation of qubits using neutral atoms, this is merely an example, and the method for implementing qubits is not limited to the method using neutral atoms. The quantum computing apparatus 10 described later can be similarly applied to all qubit implementation methods using a technique called shuttling.

[0016] In a method for implementing qubits using neutral atoms, one qubit is realized by setting the two eigenstates of electrons of a single atom trapped by light and a magnetic field in vacuum as 0 and 1. When retaining a plurality of qubits, a plurality of light spots are formed using a device called Spatial Light Modulator (SLM), and a state where at most one atom is trapped in each spot can be created. This is realized by the mechanism in which an atom experiences an attractive force corresponding to the intensity of light irradiated at an appropriate frequency.

[0017] The information of the captured neutral atom's qubits, i.e., its electronic state, can be controlled by irradiating it with light having a frequency that resonates with the transition of a given atom for a fixed period of time. Through this, it becomes possible to initialize any single qubit and perform a single Pauli measurement on any qubit realized in a neutral atom. It is also possible to perform unitary operations on two captured qubits in close proximity. On the other hand, the SLM's light is designed to have a frequency sufficiently far removed from the atomic transition so as not to affect the electronic state.

[0018] One technique that can be used when constructing a quantum computer using neutral atoms is called shuttleping. Shuttling is a technique that moves the position of neutral atoms at high speed during computation without affecting their electronic state. Shuttling is achieved using two acousto-optic deflectors (AODs), which can split a beam into spots arranged in a two-dimensional grid. The number and spacing of the grids can be controlled continuously and rapidly by electrical signals input to the acousto-optic deflectors. Similar to spatial light modulators, by designing the beam at an appropriate frequency, it is possible to create a state where atoms feel an attractive force to the relevant spots with little effect on the electron state of the atoms. Therefore, by making the attractive force of the spots created by the acousto-optic deflectors greater than that of the spots created by the spatial light modulator, the position of atoms trapped on a two-dimensional plane can be moved.

[0019] In a fixed spot configuration using a spatial light modulator, two-qubit unitary operations can only be performed between qubits in adjacent spots. However, by using shuttles in conjunction, two-qubit unitary operations can be applied to atoms that are far apart. For this reason, shuttles are a particularly useful technique when implementing quantum error correction, which will be discussed later.

[0020] ≪Quantum Error Correction≫ The superposition state of qubits is sensitive to environmental noise. While typical quantum devices, such as those using neutral atoms, have longer lifetimes than conventional physical systems, their lifetimes are typically short compared to the required operating time of quantum computers. Therefore, naive calculations often fail because the superposition state is destroyed during the computation, preventing meaningful calculations. To solve this problem, the framework of fault-tolerant quantum computing is frequently used.

[0021] In error-tolerant quantum computing, information from a quantum bit is represented using a more redundant number of qubits, based on a framework called quantum error correction codes. In this case, the represented qubits are called logical qubits, and the redundant qubits actually provided by atoms, etc., are called physical qubits.

[0022] In quantum error correction codes, Pauli measurements for parity checking are repeatedly performed on the physical qubits during computation. This measurement is called a stabilizer measurement, and the resulting value is called a syndrome value. By implementing appropriate redundancy, errors that occur during computation can be detected and corrected from the syndrome value.

[0023] The integer d is called the code distance when any error less than d / 2 that changes the state of a physical qubit can be corrected. The larger the code distance, the more errors can be corrected even if many errors occur simultaneously during stabilizer measurements, and the longer the effective lifetime of the logical qubit. However, the larger the code distance, the more physical qubits are required per logical qubit. Therefore, to perform reliable large-scale quantum computation on the smallest possible quantum computer, it is preferable to use a quantum error correction code that represents the required number of logical qubits with the fewest possible number of physical qubits at the required code distance.

[0024] Furthermore, it is not obvious whether a given arithmetic instruction can be executed on a logical qubit encoded with a quantum error-correction code while maintaining an error-tolerant state. Therefore, to realize error-tolerant quantum computing, it is preferable to use a code that can efficiently execute a wide range of arithmetic instructions in an error-tolerant manner.

[0025] Typical quantum error correction codes To date, various quantum error correction codes have been sought that offer high encoding efficiency and enable a wide range of operations. Surface codes are one such quantum error correction code that possesses these characteristics (References 1, 2).

[0026] The surface code is a grid of qubits arranged in a 2D plane with side length d. 2 A surface code is a code that uses n qubits to represent one logical qubit, with a code distance of d. Surface codes allow for efficient execution of various basic operations on encoded logical qubits by switching parity check patterns. Furthermore, because surface codes can perform stabilizer measurements using only Pauli measurements on spatially adjacent qubits in a two-dimensional arrangement, they can be efficiently implemented even in quantum devices where operations can only be performed between spatially adjacent qubits. For this reason, many quantum computer proposals propose designs based on surface codes (Reference 4).

[0027] In recent years, HGP codes have been proposed as a framework for quantum error correction codes distinct from surface codes (Reference 5). HGP codes are a general framework for designing codes, including surface codes, and with an appropriate configuration, logical qubits with a given code distance can be constructed with fewer physical qubits than surface codes. HGP codes generally require parity checks between distant qubits, which makes them difficult to implement in quantum devices where interaction is limited to adjacent qubits. Another drawback of HGP codes is that they generally cannot efficiently perform arbitrary calculations while remaining encoded. Of these, the former drawback can be solved by using shuttles in neutral atom-based methods.

[0028] <<Operations on encoded logical qubits>> In general, it is not obvious what operations can be performed on encoded logical qubits. According to Reference 2, it is known that for surface codes, any operation can be performed with a small amount of auxiliary space. For general codes, although no efficient method for performing any operation is known, some operations are known to be efficient. A typical example of this is an operation called lattice surgery.

[0029] Lattice surgery is a framework for performing Pauli measurements on encoded logical qubits. Reference 6 presents a framework for performing Pauli measurements on arbitrary logical qubits using general codes via lattice surgery. This framework implements Pauli measurements on logical qubits as follows:

[0030] Consider a code that encodes k logical qubits with n physical qubits, and we want to perform a Pauli measurement on some of the k logical qubits. In this case, a string of Pauli operators corresponding to the Pauli measurement and a subset of physical qubits corresponding to the set of logical qubits being measured can be defined by the properties of the code. This set (i.e., the subset of physical qubits) will be called the support for the Pauli operator corresponding to the Pauli measurement. Reference 7 shows that the Pauli measurement can be implemented in an error-tolerant manner by modifying the parity check involved in the physical qubits that support the Pauli operator using a predetermined procedure and adding an additional auxiliary physical qubit (also called an auxiliary qubit). This enables the implementation of a Pauli measurement on any qubit.

[0031] A surface code is a code that encodes a single logical qubit using a two-dimensional grid of physical qubits. In this case, the support for a Pauli operation corresponding to a Pauli measurement represented by X is a set of physical qubits arranged in a vertical column. Similarly, the support for a Pauli operation corresponding to a Pauli measurement represented by Z is a set of physical qubits arranged in a horizontal column.

[0032] According to Reference 7, by arranging HGP codes in a two-dimensional grid according to certain rules, a logical qubit support can be constructed that satisfies the following conditions:

[0033] (1) The support for Pauli operators corresponding to a Pauli measurement in which one character is represented by X and the remaining characters by I is a subset of physical qubits arranged in a particular row. The support for Pauli operators when performing a Pauli measurement in which two or more X characters are represented by a string can be defined as the exclusive OR of the support for Pauli operators corresponding to Pauli measurements in which one character is represented by X and the remaining characters by I.

[0034] (2) The support for Pauli operators corresponding to a Pauli measurement where one character is Z and the remaining characters are I is a subset of physical qubits arranged in a particular sequence. The support for Pauli operators when performing a Pauli measurement where two or more Zs are represented by a string can be defined as the exclusive OR of the support for Pauli operators corresponding to Pauli measurements where one character is Z and the remaining characters are I.

[0035] ≪Error-tolerant quantum computation using two signs≫ While HGP codes can hold data, they struggle to perform arbitrary operations on logical qubits quickly and error-tolerantly. Therefore, surface codes have typically been used in the design of conventional quantum computers. On the other hand, in recent years, approaches have been proposed that combine surface codes with codes that are more efficient than surface codes but have limitations on operations, in order to perform error-tolerant quantum computation with a smaller overall number of physical qubits. For example, Non-Patent Document 1 proposes an approach that combines HGP codes and surface codes as follows.

[0036] The approach proposed in Non-Patent Document 1 is a framework that uses surface codes as a processor and HGP codes as memory. When performing calculations, the quantum program is represented in Clifford+T form. All data necessary during the calculation is held in HGP codes. The region using surface codes does not hold data in its initial state, but it reserves enough space to perform any basic operations required by Clifford+T. If it becomes necessary to perform an operation belonging to Clifford+T on some of the data held in HGP codes, the data held in HGP codes is moved to the surface codes to perform the operation, and then the data is returned to the HGP codes. By repeating this process, the instruction sequence of the quantum program represented in Clifford+T form can be processed.

[0037] To perform the above procedure, a method is needed to transfer logical qubit data between HGP codes and surface codes in an error-tolerant manner. This can be achieved by constructing a protocol called quantum teleportation using the lattice surgery described above, thereby transferring qubit information between the two codes. Non-patent document 1 proposes a method for transferring data between surface codes and HGP codes based on this method.

[0038] <Challenges of conventional technology> The method of combining two codes proposed in Non-Patent Document 1 achieves both efficient data retention using HGP codes and arbitrary operations using surface codes, making it a promising approach for performing large-scale quantum computations on small quantum devices. On the other hand, this method has computational overhead because it requires moving data to the surface code each time an instruction of the quantum program is executed.

[0039] Therefore, the following describes a quantum computing device 10 that can perform more efficient quantum computation than conventional methods when combining HGP codes and surface codes to realize error-tolerant quantum computation with a smaller overall number of physical qubits. According to the quantum computing device 10 described below, for example, it becomes possible to achieve high-speed quantum computation while efficiently storing a large amount of data in an error-tolerant manner using a small quantum device.

[0040] <Example configuration of quantum computing device 10> Figure 1 shows an example of the configuration of a quantum computing device 10 according to one embodiment. As shown in Figure 1, the quantum computing device 10 according to one embodiment includes a control device 100 and a quantum processor 200.

[0041] The control device 100 controls the calculations performed by the quantum processor 200 and acquires the calculation results (measurement results) to realize quantum computing. The control device 100 is implemented, for example, by a classical computer.

[0042] The quantum processor 200 is a quantum device that realizes qubits using neutral atoms. However, the quantum processor 200 is not limited to quantum devices that realize qubits using neutral atoms, but may be any quantum device that utilizes shuttles.

[0043] Furthermore, the control device 100 and the quantum processor 200 may be able to communicate with each other via any communication network, including, for example, the Internet.

[0044] <Example of hardware configuration of control device 100> Figure 2 shows an example of the hardware configuration of a control device 100 according to one embodiment. As shown in Figure 2, the control device 100 according to one embodiment includes an input device 101, a display device 102, an external interface 103, a communication interface 104, a RAM (Random Access Memory) 105, a ROM (Read Only Memory) 106, an auxiliary storage device 107, and a processor 108. Each of these hardware components is connected to communicate via a bus 109.

[0045] The input device 101 is, for example, a keyboard, mouse, touch panel, or physical button. The display device 102 is, for example, a display or display panel. The control device 100 does not necessarily have to have at least one of the input device 101 and the display device 102.

[0046] External I / F 103 is an interface with external devices such as recording media 103a. Examples of recording media 103a include CD (Compact Disc), DVD (Digital Versatile Disk), SD memory card (Secure Digital memory card), and USB (Universal Serial Bus) memory card.

[0047] The communication interface 104 is an interface for sending and receiving various signals with the quantum processor 200. The RAM 105 is a volatile semiconductor memory (storage device) that temporarily holds programs and data. The ROM 106 is a non-volatile semiconductor memory (storage device) that can retain programs and data even when the power is turned off. The auxiliary storage device 107 is a non-volatile storage device (storage device) such as an HDD (Hard Disk Drive), SSD (Solid State Drive), or flash memory. The processor 108 is an arithmetic unit such as a CPU (Central Processing Unit).

[0048] Note that the hardware configuration shown in Figure 2 is just one example, and the hardware configuration of the control device 100 is not limited to this. For example, the control device 100 may have multiple auxiliary storage devices 107 or multiple processors 108, it may not have some of the hardware shown, or it may have various other hardware components besides the hardware shown.

[0049] <Example of the functional configuration of the control device 100> Figure 3 shows an example of the functional configuration of a control device 100 according to one embodiment. As shown in Figure 3, the control device 100 according to one embodiment includes a π / 8 rotation form conversion unit 110, a π / 8 rotation form decomposition unit 111, an X / Z-Pauli measurement decomposition unit 112, a K-basic Pauli X measurement extraction unit 113, a K-basic Pauli X measurement decomposition unit 114, a K-basic Pauli Z measurement extraction unit 115, a K-basic Pauli Z measurement decomposition unit 116, and an instruction processing unit 117. Each of these units is realized, for example, by a process in which one or more programs installed in the control device 100 are executed by a processor 108 or the like. Here, the control device 100 is given a quantum program in Clifford+T form and an integer K. Furthermore, when the instructions of the quantum program (more precisely, the instructions of the quantum program converted by the π / 8 rotation form conversion unit 110, which will be described later) are executed, the control device 100 is provided with information about the HGP code implemented on the quantum processor 200 (i.e., information about the logical qubits encoded with the HGP code) each time.

[0050] Examples of atomic configurations Figure 4 shows an example of the arrangement of a group of neutral atoms (atomic group) on the quantum processor 200. As shown in Figure 4, there is a region 1 which is the HGP coding region, a region 2 which is the X measurement region, a region 3 which is the Z measurement region, and a region 4 which is the surface coding operation region. The movement of neutral atoms from region 2 to region 4 is realized by instruction type 1, which will be described later, the movement of neutral atoms from region 3 to region 4 is realized by instruction type 2, which will be described later, the movement of neutral atoms from region 1 to region 2 and the movement of neutral atoms from region 4 to region 2 are realized by instruction type 3, which will be described later, and the movement of neutral atoms from region 1 to region 3 and the movement of neutral atoms from region 4 to region 1 are realized by instruction type 4, which will be described later.

[0051] Here, Region 1 holds the data for the n qubits used in the calculation. In Region 2, the qubits added by the decomposition related to the X measurement (transformation 4-1 described later) (auxiliary qubits) are encoded in the form of surface codes. Region 2 contains as many auxiliary qubits as are necessary for the K-basic Pauli X measurement with the auxiliary region described later, using the method described in Reference 6. In Region 3, the qubits added by the decomposition related to the Z measurement (transformation 4-2 described later) (auxiliary qubits) are encoded in the form of surface codes. Region 3 contains as many auxiliary qubits as are necessary for the K-basic Pauli Z measurement with the auxiliary region described later, using the method described in Reference 6. Region 4 contains the additional qubits necessary for the basic operations of the surface codes of the X / Z regions (qubits added by transformations 1, 2, and 3 described later).

[0052] In accordance with instructions from the instruction processing unit 117, the quantum processor 200 outputs a light irradiation pattern, which allows for the movement of physical qubits located in regions 1 to 4, calculations performed by the physical qubits, and their measurement.

[0053] ≪π / 8 rotation format conversion unit 110≫ The π / 8 rotation format conversion unit 110 converts a given Clifford+T form quantum program into a π / 8 rotation format. The π / 8 rotation format conversion unit 110 can perform this conversion using the same method as described in Reference 3. As a result, the Clifford+T form quantum program is represented as a sequence of Pauli rotation operations with a rotation angle of π / 8 acting on n qubits (also called n-body Pauli rotation operations with an angle of π / 8) and Pauli measurements acting on n qubits (also called n-body Pauli measurements), where n represents the number of qubits.

[0054] ≪π / 8 rotation type decomposition section 111≫ The π / 8 rotational decomposition unit 111, upon receiving an n-body Pauli rotation operation of angle π / 8, decomposes it into an n+1-body Pauli measurement and at most 2-body Pauli measurements on the added qubits, by adding two temporarily used qubits. In other words, the π / 8 rotational decomposition unit 111 converts an n-body Pauli rotation operation of angle π / 8 into an n+1-body Pauli measurement and at most 2-body Pauli measurements on the added qubits. Hereafter, this conversion will be referred to as "Conversion 1". The π / 8 rotational decomposition unit 111 can perform Conversion 1 using the same method as described in Reference 3. Figure 5 shows the above Conversion 1. In Figure 5, P is a Pauli operation using four types of letters: I, X, Y, and Z, and X, Y, and Z are the Pauli operations corresponding to those letters. Also, symbols like meters represent measurements. Furthermore, |A〉 is a state called a Magic state, which is a state that can be obtained, for example, through the procedure described in Reference 2.

[0055] On the other hand, the π / 8 rotation decomposition unit 111 outputs the n-body Pauli measurement as is when the n-body Pauli measurement is input.

[0056] Furthermore, the Pauli measurements of n+1 bodies or n bodies are output to the X / Z-Pauli measurement decomposition unit 112, and the Pauli measurements of at most two bodies for the added qubits are output to the instruction processing unit 117.

[0057] ≪X / Z-Pauli measurement disassembly section 112≫ The X / Z-Pauli measurement decomposition unit 112 decomposes an n-body Pauli measurement into an n+2-body Pauli measurement consisting only of the letters I and Z, an n+2-body Pauli measurement consisting only of the letters I and X, and at most two-body Pauli measurements for the added qubits. In other words, the X / Z-Pauli measurement decomposition unit 112 converts an n-body Pauli measurement into an n+2-body Pauli measurement consisting only of the letters I and Z, an n+2-body Pauli measurement consisting only of the letters I and X, and at most two-body Pauli measurements for the added qubits.

[0058] The above transformation can be performed by combining the following two transformations, 2 and 3. The correctness of these two transformations, 2 and 3, can be verified through a simple calculation.

[0059] Transformation 2: An n-body Pauli measurement with an odd number of letters in Y is transformed (decomposed) into an n+1-body Pauli measurement with an even number of letters in Y and at most two Pauli measurements for the added qubits by adding two temporary qubits. This transformation is shown in Figure 6. Note that this transformation is unnecessary if the number of letters in Y is originally even.

[0060] Transformation 3: The n-body Pauli measurement with an even number of Y characters is transformed (decomposed) into an n+1-body Pauli measurement consisting only of I and Z characters, and an n+1-body Pauli measurement consisting only of I and X characters, by adding two temporarily used qubits. Figure 7 shows how this transformation works.

[0061] Furthermore, the Pauli measurements of n+2 bodies consisting only of the letters I and Z are output to the K-basic Pauli Z measurement decomposition unit 116, the Pauli measurements of n+2 bodies consisting only of the letters I and X are output to the K-basic Pauli X measurement decomposition unit 114, and the Pauli measurements of at most two bodies for the added qubits are output to the instruction processing unit 117.

[0062] ≪K-Basic Pauli X measurement extraction section 113≫ We consider determining the arrangement of HGP codes based on the method described in Reference 7. In this case, among Pauli measurements consisting only of the strings I and X for the logical qubits encoded by the HGP code, if the physical qubits that support the Pauli operator corresponding to that Pauli measurement can be moved in a single neutral atom shuttle, and the number of physical qubits included in that support is less than an integer K, then such a Pauli measurement will be called a "K-basic Pauli X measurement".

[0063] The K-basic Pauli X measurement extraction unit 113 extracts (enumerates) K-basic Pauli X measurements based on information about the HGP code and an integer K.

[0064] Here, the K-basic Pauli X measurement has the following properties: If we define a Pauli measurement where one character in the string is X and the remaining characters are I as a single Pauli X measurement, then the support for the Pauli operator corresponding to a single Pauli X measurement is guaranteed to always be movable with a single neutral atom shuttle, provided that the arrangement of the HGP code is determined based on the method described in Reference 7. Therefore, if we choose a sufficiently large K, it is guaranteed that all single Pauli X measurements are K-basic Pauli X measurements. Below, we assume a K such that at least a single Pauli X measurement is a K-basic Pauli X measurement.

[0065] The K-basic Pauli X measurement results are output to the K-basic Pauli X measurement decomposition unit 114.

[0066] ≪K-Basic Pauli X measurement decomposition part 114≫ A K-basic Pauli X measurement is a set of Pauli measurements consisting only of support bits that can be moved in a single shuttle for logical qubits encoded with HGP codes. In this case, if a string of Pauli measurements that includes the qubits added in previous decompositions is included in a K-basic Pauli X measurement, then a set of Pauli measurements that includes such auxiliary regions is called a "K-basic Pauli X measurement with auxiliary regions." For example, if the first five characters correspond to the HGP code region and the last three characters correspond to the region of the added qubits, and IXXIX is a K-basic Pauli X measurement, then IXXIXIII, IXIXXII, IXIXXIX, etc., are all K-basic Pauli X measurements with auxiliary regions.

[0067] The K-basic Pauli X measurement decomposition unit 114 decomposes (transforms) an n-body Pauli measurement from only the letters I and X into the fewest possible repetitions of a K-basic Pauli X measurement with an auxiliary region, by adding at most two temporarily used qubits. This can be done using the following transformation 4-1.

[0068] Transformation 4-1: An n+m-body Pauli measurement consisting only of the letters I and X is decomposed (transformed) by adding two temporarily used qubits into an n+1-body Pauli measurement consisting only of the letters I and X, an m+1-body Pauli measurement consisting only of the letters I and X, and at most two-body Pauli measurements on the added qubits. Figure 8 shows this transformation 4-1. In Figure 8, Q represents a Pauli operation. Since a single Pauli X measurement is a K-basic Pauli X measurement, the above transformation is at least possible.

[0069] The K-basic Pauli X measurement with auxiliary region is output to the instruction processing unit 117.

[0070] ≪K-Basic Pauli Z measurement extraction section 115≫ By replacing X with Z, a K-basic Pauli Z measurement can be defined in the same way as a K-basic Pauli X measurement. The K-basic Pauli Z measurement extraction unit 115 extracts (enumerates) K-basic Pauli Z measurements based on information about the HGP code and an integer K.

[0071] The K-basic Pauli Z measurement results are output to the K-basic Pauli Z measurement decomposition unit 116.

[0072] ≪K-Basic Pauli Z measurement decomposition part 116≫ By substituting X with Z, a K-basic Pauli Z measurement with an auxiliary region can be defined, similar to a K-basic Pauli X measurement with an auxiliary region. The K-basic Pauli Z measurement decomposition unit 116 decomposes (transforms) an n-body Pauli measurement from only the letters I and Z into the fewest possible iterations of a K-basic Pauli Z measurement with an auxiliary region, by adding at most two temporarily used qubits. This can be done using the following transformation 4-2.

[0073] Transformation 4-2: An n+m-body Pauli measurement consisting only of the letters I and Z is decomposed (transformed) by adding two temporarily used qubits into an n+1-body Pauli measurement consisting only of the letters I and Z, an m+1-body Pauli measurement consisting only of the letters I and Z, and at most two-body Pauli measurements on the added qubits. Figure 9 shows the process of this transformation 4-2. Note that the above transformation is possible because a single Pauli Z measurement is a K-basic Pauli Z measurement.

[0074] The K-basic Pauli Z measurement with the auxiliary region is output to the instruction processing unit 117.

[0075] Here, regarding the above transformations 4-1 and 4-2, the number of measurements after decomposition depends on the decomposition algorithm, and the fewer the number, the faster the final calculation is completed, so it is preferable to decompose into as few parts as possible. This decomposition can be performed by minimizing using brute force search or by using a method that quickly finds an approximate solution using a greedy method, and is not limited to a specific algorithm. If the above decomposition is applied naively, an additional number of qubits equal to the number of decomposed parts × 2 will be required. However, by reusing auxiliary qubits that have been used once, the number of additional qubits required can be limited to 2, regardless of the number of decompositions. An example demonstrating this is shown in Figure 10. In the example shown in Figure 10, as an example, when transformation 4-2 is repeatedly applied, at most 2 auxiliary qubits are reused.

[0076] <<Instruction Processing Unit 117>> The instruction processing unit 117 executes the input instructions representing Pauli measurements (Pauli measurement for a qubit with added region 2 or region 3, K-basic Pauli X measurement with auxiliary region, K-basic Pauli Z measurement with auxiliary region) in the highest possible degree of parallelism. There are four types of Pauli measurement instructions input to the instruction processing unit 117, and each is processed as follows. Note that each arrow shown in Figure 2 represents the shuttle pattern required by each instruction type.

[0077] Instruction type 1: A Pauli measurement instruction of at most 2 qubits for logical qubits in region 2. This instruction type 1 can be implemented for surface codes using regions 2 and 4, according to the method described in Reference 2.

[0078] Instruction type 2: A Pauli measurement instruction of at most 2 qubits for logical qubits in region 3. This instruction type 2 can be implemented for surface codes using regions 3 and 4, according to the method described in Reference 2.

[0079] Instruction Type 3: K-Basic Pauli X Measurement Instruction with Auxiliary Area This instruction type 3 (a) moves the corresponding HGP code support in region 1 and the logical qubit of the associated surface code in region 4 to region 2 by shuttle. (b) Then, a Pauli measurement is performed on the surface code in region 2 in the manner described in reference 6. (c) After that, the qubit is returned. Steps (a) to (c) are repeated as many times as needed.

[0080] Instruction type 4: K-basic Pauli Z measurement instruction with auxiliary area This instruction type 4 (a) moves the corresponding HGP code support in region 1 and the logical qubit of the associated surface code in region 4 to region 3 by shuttle. (b) Then, a Pauli measurement is performed on the surface code in region 3 in the manner described in reference 6. (c) After that, the qubit is returned. Steps (a) to (c) are repeated as many times as needed.

[0081] The measurements obtained as a result of the Pauli measurements using the above instruction types 1-4 are used to determine subsequent operations and the final calculation results.

[0082] <Example of operation of control device 100> Figure 11 is a flowchart showing an example of the operation of a control device according to one embodiment.

[0083] The control device 100 converts a given quantum program in Clifford+T format into a π / 8 rotation format (step S101). That is, the control device 100 converts a quantum program in Clifford+T format into a π / 8 rotation format by performing a conversion using the π / 8 rotation format conversion unit 110.

[0084] The control device 100 executes the first instruction of the quantum program converted in step S101 (step S102). Specifically, the control device 100 performs decomposition by the π / 8 rotation form decomposition unit 111, decomposition by the X / Z-Pauli measurement decomposition unit 112, extraction of K-basic Pauli X measurement by the K-basic Pauli X measurement extraction unit 113, decomposition by the K-basic Pauli X measurement decomposition unit 114, extraction of K-basic Pauli Z measurement by the K-basic Pauli Z measurement extraction unit 115, and decomposition by the K-basic Pauli Z measurement decomposition unit 116, and then executes the instruction by the instruction processing unit 117.

[0085] The control device 100 determines whether or not to terminate (step S103). That is, the control device 100 determines, for example, whether or not all instructions of the quantum program have been executed.

[0086] If it is not determined that the process will terminate in step S103, the control device 100 executes the next instruction of the quantum program (step S104). On the other hand, if it is determined that the process will terminate in step S103, the control device 100 outputs the execution result of the quantum program to a predetermined output destination (e.g., a display device 102 such as a display, or another device that is connected to the control device 100 in a communicative manner) (step S105).

[0087] In steps S102 and S104 described above, the control device 100 executes multiple instructions sequentially with the highest possible degree of parallelism.

[0088] <Summary> As described above, in the quantum computing device 10 according to one embodiment, the quantum program is expressed in π / 8 rotation form rather than in a form that includes conventional unitary operations. Furthermore, in the quantum computing device 10 according to one embodiment, Pauli measurements to logical qubits by lattice surgery, an efficient method, are realized using shuttles on neutral atoms in HGP codes. Moreover, in the quantum computing device 10 according to one embodiment, instructions that act on many qubits generated in π / 8 rotation form are decomposed into instructions that can be executed with HGP codes. As a result, the quantum computing device 10 according to one embodiment realizes error-tolerant quantum computing that can perform arbitrary operations on logical qubits of HGP codes without moving data to surface codes, and it is possible to achieve both data retention efficiency and high computation speed.

[0089] The present invention is not limited to the embodiments specifically disclosed above, and various modifications, changes, and combinations with known technologies are possible as long as they do not deviate from the spirit described in the claims.

[0090] [References] Reference 1: Fowler, Austin G., et al. "Surface codes: Towards practical large-scale quantum computation." Phys. Rev. A 86, 032324 (2012). Reference 2: Fowler, Austin G., and Craig Gidney. "Low overhead quantum computation using lattice surgery." arXiv preprint arXiv:1808.06709 (2018). Reference 3: Litinski, Daniel. "A game of surface codes: Large-scale quantum computing with lattice surgery." Quantum 3 (2019): 128. Reference 4: Bluvstein, Dolev, et al. "Logical quantum processor based on reconfigurable atom arrays." Nature 626.7997 (2024): 58-65. Reference 5: Tillich, Jean-Pierre, and Gilles Zemor. "Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength." IEEE Transactions on Information Theory 60.2 (2013): 1193-1202. Reference 6: Cohen, Lawrence Z., et al. "Low-overhead fault-tolerant quantum computing using long-range connectivity." Science Advances 8.20 (2022): eabn1717. Reference 7: Quintavalle, Armanda O., and Earl T. Campbell. "Reshape: A decoder for hypergraph product codes." IEEE Transactions on Information Theory 68.10 (2022): 6569-6584. [Explanation of symbols]

[0091] 10 Quantum computing device 100 Control device 101 Input Device 102 Display device 103 External I / F 103a Recording medium 104 Communication I / F 105 RAM 106 ROM 107 Auxiliary storage 108 processors 109 Bus 110 π / 8 rotation format conversion unit 111 π / 8 rotation type decomposition section 112 X / Z-Pauli Measurement Decomposition Unit 113 K-Basic Pauli X measurement extraction part 114 K-Basic Pauli X measurement decomposition part 115 K-Basic Pauli Z measurement extraction part 116 K-Basic Pauli Z measurement decomposition part 117 Instruction Processing Unit 200 Quantum Processors

Claims

1. A quantum computing device that combines surface codes and HGP codes to achieve error-tolerant quantum computation, A conversion unit that converts a first quantum program expressed in a predetermined format into a second quantum program expressed in π / 8 rotation format, A conversion unit that converts the first instruction into a second instruction executable with the logic qubits of the HGP code, based on the first instruction included in the second quantum program, the logic qubits encoded by the surface code, and the logic qubits encoded by the HGP code, A quantum computing unit that realizes the quantum computation represented by the second instruction using shuttle, A quantum computing device having the following features.

2. The conversion unit is The quantum computing apparatus according to claim 1, which converts the first instruction into the second instruction representing a Pauli measurement executable with the logical qubits of the HGP code.

3. The second instruction is, The quantum computing apparatus according to claim 2, which is an instruction that represents shutting the physical qubits constituting the logical qubits encoded by the surface code and the physical qubits constituting the logical qubits encoded by the HGP code to a region different from the computational region used for the surface code, and performing the Pauli measurement.

4. A quantum computing method that combines surface codes and HGP codes to achieve error-tolerant quantum computation, A transformation procedure for converting a first quantum program expressed in a predetermined format into a second quantum program expressed in π / 8 rotation format, A conversion procedure for converting the first instruction into a second instruction executable by the logic qubit of the HGP code, based on the first instruction included in the second quantum program, the logic qubit encoded by the surface code, and the logic qubit encoded by the HGP code, A quantum computation procedure that realizes the quantum computation represented by the second instruction using shuttle, A quantum computing method performed by a computer.

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