Quantum computing method and apparatus for physically implementing quantum algorithms

Abstract

A quantum computing method is provided. The quantum computing method includes providing a physical quantum system (1) comprising components (2). The quantum computing method includes performing an encoded quantum computation (7) on the physical quantum system (1), including: preparing at least a portion of the physical quantum system (1) in an initial quantum state; evolving the physical quantum system (1) to a final quantum state; measuring at least a portion of the physical quantum system (1) to provide a readout value; and determining the output of the encoded quantum computation (7) based on the readout value. During at least a portion of the encoded quantum computation (7), the quantum state of at least a subset of the components (2) is an encoded quantum state according to the encoding. Evolving the physical quantum system (1) to the final quantum state includes performing: a plurality of encoded evolution steps (105) for changing the encoding of the components (2), and a plurality of algorithmic evolution steps (106) for at least a portion of the action of at least one of a plurality of instructions (61, 62) for physically implementing a quantum algorithm (6) under the current encoding. At least some of the multiple coding evolution steps (105) and at least some of the multiple algorithm evolution steps (106) are performed according to an alternation sequence, which alternates between the coding evolution steps (105) and the algorithm evolution steps (106). At least one coding evolution step (105) in the alternation sequence includes performing a set of parity coding operations (75). Each parity coding operation (75) in the set of parity coding operations (75) is performed on a corresponding subset comprising at least two components (2). Each parity coding operation (75) in the set of parity coding operations (75) encodes the parity of all components (2) in the corresponding subset comprising at least two components (2) into at least one component (2) of the subset. At least one algorithmic evolution step (106) in the alternating sequence includes performing at least one algorithmic action operation (74) on at least one component (2), wherein the at least one algorithmic action operation (74) physically implements at least a portion of the action of at least one of the multiple instructions (61, 62) of the quantum algorithm (6) under the current encoding of the component (2).

Description

Technical Field

[0001] The embodiments described herein relate to quantum computing methods and apparatuses, the apparatus including a physical quantum system comprising components for physically implementing a quantum algorithm, the quantum algorithm including a plurality of instructions associated with logical qubits. Background Technology

[0002] Quantum computing utilizes quantum mechanical effects to solve computational problems. Quantum computing is performed on physical quantum systems that consist of constituent parts. Each constituent part of a physical quantum system can carry one unit of quantum information. Typically, the constituent parts include physical qubits (hereinafter referred to as "qubits"). A qubit can exist in two basis states |0| ... and |1 Defined in the computational basis. The two basis states of a qubit are called computational states.

[0003] In gate-based quantum computing, the quantum state of a component is evolved by performing a series of quantum operations on the component. Quantum operations can be quantum gates (i.e., unitary operations) on qubits, measurements, initializations, and so on.

[0004] Gate-based quantum computing can be described by quantum algorithms. A quantum algorithm is a sequence of instructions associated with (abstract) logical qubits. These instructions can be representations of quantum operations, which can be represented by the operation name (e.g., a controlled-NOT gate), its associated logical qubit, and one or more optional parameters.

[0005] One important quantum algorithm is the Quantum Fourier Transform (QFT). The importance of QFT stems primarily from its role as a crucial subroutine in many quantum algorithms, such as Shor's algorithm, which solves the integer factorization problem in polynomial time. Another important algorithm incorporating quantum subroutines is the Quantum Approximate Optimization Algorithm (QAOA), a variational quantum algorithm used to find approximate values ​​of the ground state of the Ising spin model. Many real-world optimization problems (e.g., the Traveling Salesman Problem) can be mapped to the ground state of the classical Ising spin model and solved using QAOA.

[0006] To run a quantum algorithm, it needs to be physically implemented in a physical quantum system, enabling the physical execution of quantum computations based on that algorithm. A straightforward way to physically implement a quantum algorithm is to assign each logical qubit of the algorithm to a corresponding (physical) component of the physical quantum system. The instructions for the quantum algorithm can be implemented by (physically) performing the corresponding quantum operations. In this way, quantum computation can be performed where the quantum states of the physical quantum system evolve to a final state, which is then measured to obtain a readout value, i.e., the output or solution.

[0007] However, typical quantum algorithms (such as QFT or QAOA) include instructions to perform quantum operations on several logical qubit pairs or even subsets of more than two logical qubits. For example, a quantum algorithm might include instructions to perform corresponding quantum operations (such as QFT, or QAOA for some problems) on almost all logical qubit pairs or larger subsets of logical qubits. If a quantum algorithm is implemented in the direct manner described above (assigning each logical qubit to a corresponding component of the physical quantum system), the physical quantum system needs to be able to perform quantum operations between several component pairs (in the worst case, all component pairs) or larger subsets of components. This would require long-range interactions between several component pairs (in the worst case, all component pairs) or larger subsets of components.

[0008] Many physical quantum systems may only be able to perform quantum operations on two or more adjacent or at least close to each other components, because only short-range interactions can be well controlled without disturbing other components. More generally, many physical quantum systems offer only limited connectivity between components. For example, in a one-dimensional (e.g., linear) chain of components, each component of the quantum system can interact with at most two other components, or in other words, each component of the quantum system is “connected” to at most two other components.

[0009] It is known in the prior art to swap the quantum states of at least two components, thereby modifying (especially permuting) the mapping of logical qubits to components of a physical quantum system. The quantum states of components can be swapped by performing swap gates on pairs of components. It is possible to physically perform bi-qubit quantum operations on two components when the instructions of a quantum algorithm instruct the execution of bi-qubit gates on two logical qubits, and the modified mapping such that the two components to which the two logical qubits are assigned are connected. Typically, for the purpose of "connection," the two components are arranged adjacently or at least close to each other, which allows for the performance of bi-body quantum operations on these two components. Typically, during the execution of quantum computation implementing a quantum algorithm, multiple swap gates are required to assign different pairs of logical qubits (to which bi-body quantum operations should be performed according to the instructions of the quantum algorithm) to the connected components.

[0010] The drawback of permuting the mapping of logical qubits to physical system components by executing swapping gates is that swapping gates are relatively inefficient in many physical quantum systems. For example, a swapping gate can be implemented by sequentially applying three CNOT gates. Therefore, the physical implementation of quantum algorithms significantly increases circuit depth (i.e., the total number of non-parallel quantum operations) and the number of gates (i.e., the total number of quantum operations). This results in longer runtimes for quantum computing and the need to implement more complex, potentially faulty, sequences of quantum operations. Furthermore, components are susceptible to errors, and longer runtimes or the application of faulty quantum operations can increase the error rate. Reducing runtime will reduce the error rate caused by errors due to idle time. Reducing the number of physical quantum operations will further reduce the error rate caused by errors due to faulty quantum operations.

[0011] Purpose of the invention The purpose of this invention is to provide a quantum computing method and apparatus that, compared with the prior art, requires fewer physical quantum operations and has a shorter running time for the physical implementation of a quantum algorithm comprising multiple instructions.

[0012] Other objects and advantages of the present invention will be apparent in part from the description and drawings. Summary of the Invention

[0013] The above objective is achieved by the quantum computing method according to claim 1 and the apparatus according to claim 17.

[0014] According to the present invention, the quantum computing method includes the following steps: - Provides physical quantum systems including their components; - Performing encoded quantum computations on physical quantum systems, including: o Prepare at least a portion of a physical quantum system in its initial quantum state; o To evolve physical quantum systems to their final quantum state; o Measure at least a portion of a physical quantum system to provide readouts; and o The output of the encoded quantum computation is determined based on the readout value.

[0015] During at least a portion of the encoded quantum computing, the quantum states of at least a subset of the constituent parts are based on the encoded quantum states.

[0016] Further according to the present invention, evolving a physical quantum system to a final quantum state includes: performing a plurality of encoding evolution steps for changing the encoding of the components, and a plurality of algorithm evolution steps for at least a portion of the action of at least one of a plurality of instructions for physically implementing a quantum algorithm under the current encoding.

[0017] At least some of the multiple coding evolution steps and at least some of the multiple algorithm evolution steps are performed according to an alternating sequence, which alternates between the coding evolution steps and the algorithm evolution steps.

[0018] Further according to the invention, at least one coding evolution step of the alternating sequence includes performing a set of parity coding operations, wherein each parity coding operation in the set of parity coding operations is performed on a corresponding subset comprising at least two components, wherein each parity coding operation in the set of parity coding operations encodes the parity of all components of the corresponding subset of at least two components into at least one component of the subset.

[0019] According to the present invention, at least one algorithmic evolution step of the alternating sequence includes performing at least one algorithmic action operation on at least one component, wherein the at least one algorithmic action operation physically implements at least a portion of the action of at least one instruction of a plurality of instructions of a quantum algorithm under the current encoding of the component.

[0020] Another embodiment of the present invention includes an apparatus comprising a physical quantum system that can be configured to perform the quantum computing method described above.

[0021] In this invention, instead of exchanging the quantum states of at least two components, the quantum states of at least a subset of components are based on the encoded quantum states, and the encoding is changed in the encoding evolution step by performing a parity check encoding operation on at least a subset of components.

[0022] Parity checking operations can be implemented efficiently on many physical quantum systems. In particular, on many physical quantum systems, parity checking operations can be implemented more efficiently than swapping gates. This reduces runtime and circuit depth.

[0023] The physical implementation of the action of at least one of the multiple instructions must respect the current encoding; that is, the action of at least one algorithmic action of the action of at least one of the multiple instructions that implement the quantum algorithm depends on the current encoding.

[0024] Other advantages, features, aspects, and details that can be combined with the embodiments described herein will become apparent from the dependent claims, the specification, and the drawings. Attached Figure Description

[0025] For those skilled in the art, the complete and feasible disclosure is set forth in more detail in the remainder of the specification (including with reference to the accompanying drawings), wherein: Figures 1a to 1e A schematic diagram of physical quantum systems with different finite connectivity is shown.

[0026] Figure 2a A circuit diagram of an exemplary quantum algorithm with single-body and two-body instructions is shown.

[0027] Figure 2b This demonstrates a physical implementation on a physical quantum system with finite connectivity, based on existing techniques. Figure 2a Circuit diagram of quantum computing using quantum algorithms.

[0028] Figure 2c The circuit diagram is shown as a switching gate decomposed into a controlled NOT gate.

[0029] Figure 3 A schematic diagram of a device for performing quantum computing methods is shown.

[0030] Figure 4 A flowchart of coded quantum computing is shown for a quantum computing method used to physically implement quantum algorithms.

[0031] Figure 5a A circuit diagram depicting the evolution of a physical quantum system is shown, which includes an encoding evolution step and an algorithm evolution step, each comprising a parity check encoding operation and an algorithm action operation, respectively.

[0032] Figure 5b and Figure 5c The circuit diagram is shown, which decomposes the parity check encoding operation into a controlled NOT gate.

[0033] Figure 6 A flowchart of the quantum approximation optimization algorithm is shown.

[0034] Figure 7 A circuit diagram is shown depicting a quantum algorithm for a single iteration of a quantum approximation optimization algorithm for a fully connected Ising Hamiltonian.

[0035] Figure 8a , Figure 8b This illustrates the physical implementation depicted on a one-dimensional component chain. Figure 7 The circuit diagram of the quantum operation sequence of a one-iteration quantum algorithm for quantum approximation optimization.

[0036] Figure 9a , Figure 9b A network of fictitious qubits is shown, from which the following can be derived: Figure 8b The physical implementation of parity check coding operation.

[0037] Figure 9c A circuit diagram depicting the parity check encoding operation is shown.

[0038] Figure 10a The coded evolution steps of the quantum approximation optimization algorithm are shown for physical implementation on a physical system with trapezoidal connectivity and additional diagonal connections.

[0039] Figure 10b , Figure 10c The algorithmic evolution steps for physically implementing a quantum approximation optimization algorithm on a physical system with trapezoidal connectivity and additional diagonal connections are shown.

[0040] Figure 11 A network of fictitious qubits is shown, from which the following can be derived: Figure 10a The physical implementation of parity check coding operation.

[0041] Figure 12a It shows that for from Figure 11 The exported specific encoding, corresponding to Figure 10a The coding evolution steps.

[0042] Figure 12b , Figure 12c It shows that for Figure 12a Specific encoding, corresponding to Figure 10b The algorithm evolution steps.

[0043] Figure 13 A circuit diagram depicting a quantum algorithm for quantum Fourier transform is shown.

[0044] Figure 14 A circuit diagram is shown depicting a sequence of quantum operations that physically realize a quantum Fourier transform on a one-dimensional chain of components. Detailed Implementation

[0045] Reference will now be made in detail to various exemplary embodiments, one or more examples of which are illustrated in each of the accompanying drawings. Each example is provided in an illustrative manner and is not intended to be limiting. For example, features illustrated or described as part of one embodiment may be used in or combined with other embodiments to produce further embodiments. This disclosure is intended to include such modifications and variations.

[0046] In the description of the accompanying drawings, the same reference numerals refer to the same or similar parts. Generally, only differences with respect to the various embodiments are described. The structures shown in the drawings are not necessarily drawn to scale and may contain exaggerated details to allow for a better understanding of the embodiments.

[0047] Some embodiments described herein relate to quantum computing methods and apparatuses designed to implement quantum algorithms comprising multiple instructions.

[0048] Physical quantum systems and connectivity The quantum computing method aimed at physically implementing quantum algorithm 6 can be executed on device 4, which includes physical quantum system 1. Quantum algorithm 6 includes multiple instructions 61, 62 associated with logical qubits 5.

[0049] A quantum physical system 1 includes a component 2, which can carry one unit of quantum information. Specifically, component 2 can be a physical qubit. A qubit can be generated by two state vectors |0, 1, ..., 2. and |1 Defined in the computational basis. The two ground states of a qubit are called computational states. The ground states can be Pauli... Operator (Pauli) The eigenstates of (-operator) and satisfy the relation and Component 2 as a whole can be configured in an entangled quantum state.

[0050] Component 2 can be a superconducting quantum bit, quantum dot, atom, ion, photon, or any other physical system that can encode a quantum bit.

[0051] The components 2 of the physical quantum system 1 can be arranged in a fixed configuration relative to each other. In particular, the components 2 can be arranged in a two-dimensional plane, such as on a circuit board. Alternatively, at least some of the components 2 can be movable during the operation of the quantum computing 7.

[0052] During quantum computing 7, the quantum state of the components evolves by performing a series of quantum operations 71, 72 on the components. Quantum operations 71, 72 can be quantum gates (i.e., unitary operations), measurements, or initializations of qubits, etc. Single-unit quantum operations 71 (especially single-qubit operations) are performed on a single component 2. Many-unit quantum operations 72 (especially two-qubit or multi-qubit operations) are performed on at least two components 2.

[0053] Performing a many-body quantum operation 72 requires that at least two components for performing the quantum operation 72 be "connected". In other words, two or more components being "connected" means that many-body quantum operations 72 can be performed on those components. Specifically, this may require that the components 2 be arranged physically close to each other, that the physical quantum system 1 provides an electrical connection between the components 2, or in general, that physical interactions can be realized between the components 2.

[0054] The overall connectivity between component 2 is referred to as the “connectivity” of quantum physical system 1. For quantum physical system 1, connectivity can be fixed, particularly when component 2 is fixedly arranged. Alternatively, connectivity can be variable during the operation of quantum computing 7, particularly when at least some component 2 is movable. In the latter case, the total connectivity may only be reached at different time steps.

[0055] Most physical quantum systems 1 have finite connectivity. This means that many-body quantum operations 72 cannot be performed between some subsets of component 2 (especially pairs of component 2). In other words, all-to-all connectivity does not exist in most physical quantum systems 1.

[0056] Figures 1a to 1e A schematic diagram of a physical quantum system 1 with different finite connectivity is shown. Connectivity 3 can be a physical connection such as an electrical connection. Connectivity 3 can more generally indicate that the components 2 connected to each other can interact, for example, through electromagnetic fields propagating in free space.

[0057] Figure 1a A one-dimensional chain of components 2 is shown, which are connected to their nearest neighbors only through connection 3 (often referred to as "linear nearest neighbor" or LNN connectivity). Component 2 is connected to at most two other components 2. In particular, two components 2 on the boundary are connected to one other component 2, while other components 2 are connected to two other components 2. Thus, connectivity is strongly restricted. Component 2 can be arranged on a straight line or, more generally, on a curve ("linear" can mean a straight line or a curve, referring to "one dimension"). Many quantum physical systems 1 (e.g., ions in a linear ion trap) may be restricted to this kind of connectivity.

[0058] Figure 1b A physical quantum system 1 with nearest-neighbor ring connectivity is shown. All components 2 are connected to two other components 2.

[0059] Figure 1c A physical quantum system 1 with trapezoidal connectivity is illustrated. Components 2 (the upper rails of the trapezoid) in a first subset are connected to at most two other components 2 in the first subset, and components 2 (the lower rails of the trapezoid) in a second subset are connected to at most two other components 2 in the second subset, wherein the first and second subsets do not intersect. Furthermore, at least one component 2 in the first subset is connected to at least one component 2 (a rung of the trapezoid) in the second subset. Preferably, each component 2 in the first subset is connected to exactly one component 2 in the second subset, and each component 2 in the second subset is connected to exactly one component 2 in the first subset. Preferably, the connections 3 do not overlap.

[0060] Figure 1d It shows Figure 1c The physical quantum system 1 in the middle has trapezoidal connectivity and additional connections 3 between components 2 in two different subsets (i.e., between different side rails of the trapezoid), such that each component 2 of the first subset is connected to three components of the second subset 2, and vice versa.

[0061] Figure 1e A physical quantum system 1 with “broken” trapezoidal connectivity is shown. “Broken” means that at least one connection 3 along at least one side rail of the trapezoid is interrupted, or at least one crossbar is missing.

[0062] Quantum Algorithm The (gate-based) quantum computing 7 can be described by a quantum algorithm 6. The quantum algorithm 6 is a sequence of instructions 61, 62 associated with (typically abstract) logical qubits 5. Instructions 61, 62 can be representations of quantum operations 71, 72, which can be specified by the name of the operation (e.g., a controlled NOT gate), its associated logical qubit 5, and one or more optional parameters. The sequence length of instructions 61, 62 can be one, meaning the quantum algorithm 6 can consist of only one instruction 61, 62. Preferably, the quantum algorithm 6 includes multiple instructions 61, 62.

[0063] The “instructions” of quantum algorithm 6 convey information about what quantum algorithm 6 does. Furthermore, they also convey information about how to physically implement quantum algorithm 6 through direct physical implementation. Direct physical implementation could be assigning logical qubits 5 to each component 2 of the physical quantum system 1. However, the “instructions” of quantum algorithm 6 do not need to be read or stored during the operation of quantum computing. They do not need to be read or stored by a computer at all.

[0064] "Physical implementation of a quantum algorithm" can mean that the quantum algorithm is executed by a physical quantum system, in a sense its instructions are read into the machine, and actions are performed based on the read instructions, but it doesn't necessarily have this meaning. More generally, "physical implementation of a quantum algorithm" can mean performing quantum computation on a physical quantum system 1, which implements the actions of a specific quantum algorithm 6. In particular, the quantum algorithm does not need to be provided as input during the execution of the quantum computation, nor does it need to be physically stored.

[0065] In the direct physical implementation of quantum algorithm 6, instructions 61 and 62 “associated” with one or more logical qubits 5 mean that instructions 61 and 62 instruct the execution of quantum operations 71 and 72, which act on one or more components 2 corresponding to the logical qubit 5. The relationship to the logical qubit 5 is represented by the index of the logical qubit 5 as a superscript or subscript. For example, the controlled NOT gate associated with logical qubits one and two can be represented as CNOT. 12 The parameters for instructions 61 and 62 can, for example, specify the angle of rotation of the qubit. For example, a command named "R" could... x The single-unit instruction 61 (rotation about the x-axis) can have parameters. 5 logical qubits - rotation angle It can be represented as .

[0066] Single-body instruction 61 relates to a single logical qubit 5 and instructs the execution of a single-body quantum operation 71 acting on one component 2 (in a direct physical implementation). Multi-body instruction 21 relates to multiple logical qubits 5 and instructs the execution of a multi-body quantum operation 72 acting on multiple components 2 (in a direct physical implementation). Two-body instruction 62 is a special form of multi-body instruction 62. It relates to two logical qubits 5 and instructs the execution of a two-body quantum operation 72 acting on two components 2.

[0067] The problem to be solved by the present invention is in a physical quantum system 1 with finite connectivity (e.g., in accordance with...) Figures 1a to 1e One of the physical quantum systems 1) Physical implementation of quantum algorithms 6.

[0068] As an illustrative example, Figure 2aA circuit diagram of a simple quantum algorithm 6 associated with five logical qubits 5 is shown. This algorithm comprises a single-body instruction 61 and three two-body instructions 62 associated with pairs of logical qubits 5. The logical qubits 5 can be indexed using an ascending index from top to bottom. The topmost qubit is indexed at 0, and the bottommost at 4. Logical indices are depicted using italicized numbers. Typically, instruction 62 can be a multi-body instruction associated with a subset of logical qubits greater than a pair.

[0069] Because of the existence of two-body instructions 62 associated with different logical qubit pairs 5, not all of these pairs are mapped to nearest neighbor component 2 under direct mapping. Therefore, in Figure 1a The physical implementation of component 2 on a one-dimensional chain. Figure 2a Quantum algorithm 6 cannot be directly implemented.

[0070] The known solution in the prior art is to apply a swapping gate 73 during quantum computing 7. Figure 2b Describes the physical realization Figure 2a The circuit diagram of quantum computation 7 of quantum algorithm 6 is depicted. The physical quantum system 1 includes components 2 with linear nearest-neighbor connectivity, meaning that the two-body quantum operation 72 can only be performed on adjacent components 2. Component 2 can be represented by unique identifiers from zero to four, where the top component 2 has a unique identifier of zero, and the identifiers increment to four for the bottom component 2. The unique identifier of component 2 is not in... Figure 2b Instead of showing them in the diagram, their logical indices are shown in italics. The logical indices indicate which logical qubit 5 is assigned to the corresponding component 2 (see [reference]). Figure 2a A one-bit logical index indicates that the state of a logical qubit 5 with that index is encoded into component 2. A two-bit logical index indicates that the parity of two logical qubits 5 (indexed to the first and second bits respectively) is encoded into component 2.

[0071] In the first step, an initial state (not shown) is prepared according to Quantum Algorithm 6. The logical index of Component 2 is the same as that in Quantum Algorithm 6.

[0072] In the second step, evolutionary physics quantum system 1 is used to achieve Figure 2aThe operation of the circuit diagram. The first two-body instruction 62 of quantum algorithm 6 can be directly implemented because it only involves adjacent logical qubits 5, which correspond to adjacent component 2 when directly implemented in physical quantum system 1. Conversely, the second and third two-body instructions 72 cannot be directly implemented on physical quantum system 1 with linear nearest neighbor connectivity because they involve non-adjacent logical qubits 5, specifically logical qubits 5 zero and two, and zero and three. To solve this problem, in the prior art, a swap gate 73 is executed to swap the quantum states of the two component 2, thereby permuting the mapping from logical qubits 5 to component 2. This is in Figure 2b This is depicted by component 2, which has a permuted logical index. Importantly, during quantum computing, component 2 does not need to be physically permuted (i.e., moved).

[0073] After the quantum states of component 2 (zero and one, the topmost and next component) are swapped, the quantum states cause logical qubits 5 (zero and two) to be assigned to adjacent components. Thus, the second instruction 62 related to logical qubits 5 (zero and two) in quantum algorithm 6 can be physically implemented by performing a two-body quantum operation 72 on components 2 (one and two). Similarly, before the third two-body instruction 62 of quantum algorithm 6 can be physically implemented, the quantum states of components 2 (one and two) are swapped by executing another swap gate 73. Afterward, logical qubits 5 (zero and three) are assigned to adjacent components 2 (two and three). Thus, the third instruction 72 related to logical qubits 5 (zero and three) in quantum algorithm 7 can be physically implemented by performing a two-body quantum operation 72 on components 2 (two and three). The single-unit instruction 61 related to logical qubit 5 (four) can be executed by performing a single-unit quantum operation 71 on component 2 (four).

[0074] In the third step, the system can be read out, and the final state can be determined by considering the permutation mapping from logical qubit 5 to component 2.

[0075] A swapping gate 73 can be physically implemented using basic quantum operations. In many physical quantum systems, executing the swapping gate 73 can be achieved by executing a sequence of three controlled NOT gates, such as... Figure 2c As shown.

[0076] Therefore, the additional swapping gate 73 introduced in the physical implementation of quantum algorithm 6 increases the circuit depth by six (2 x 3) controlled NOT gates. In this example, the circuit depth caused by the quantum operations 71, 72 (hereinafter referred to as algorithm action operation 74) of the actions of instructions 61, 62 in the physical implementation of quantum algorithm 6 remains unchanged.

[0077] Compared to existing technologies using a swapped gate 73, the quantum computing method and apparatus according to the present invention aim to reduce circuit depth and gate count. The method and apparatus according to the present invention are described below.

[0078] Device for performing quantum computing methods Figure 3 An embodiment of a device 4 for quantum computing according to the present invention is shown. Device 4 includes a physical quantum system 1 (including components 2), a control unit 41 for evolving and measuring at least some of the components 2, and a logic unit 42 connected to the control unit 41. The physical quantum system 1 may have finite connectivity, particularly as... Figures 1a to 1e One of the connectivity aspects.

[0079] The physical quantum system 1 can be evolved and measured by the control unit 41. The control unit 41 can be configured to perform quantum operations 71, 72 on the physical quantum system 1. The quantum operations 71, 72 can typically include quantum gates (i.e., unitary operations), quantum measurements, and the preparation of quantum states.

[0080] Control unit 41 can prepare at least a portion of the physical quantum system 1 in an initial quantum state. Control unit 41 can evolve the physical quantum system 1 to a final quantum state. Control unit 41 can measure at least a portion of the physical quantum system 1 to provide readout values. Figure 3 In the diagram, the dashed boxes surrounding all components of the physical quantum system 1 indicate that measurements involving all components 2 were performed in this embodiment, but measurements could also involve fewer components 2.

[0081] Control unit 41 can input signals to or receive output signals from the physical quantum system 1. Physically, the signal can be current, voltage, electromagnetic field, or any other physical data carrier. Control unit 41 can be a classical computer, i.e., a computer that operates using classical bits. Control unit 41 can be distributed across multiple devices.

[0082] The logic unit 42 can establish a bidirectional data connection with the control unit 41 to send control data to the control unit 41 and receive measurement data from the control unit 41.

[0083] Logic unit 42 can determine the output 73 of the encoded quantum computation 7 performed by physical quantum system 1, i.e., decode information about the final quantum state obtained from the readout value. The final quantum state can be an encoded quantum state. Typical classical decoding steps can obtain at least a part of the plaintext quantum state or some information about at least a part of the plaintext quantum state from the readout value of at least a part of the encoded quantum state.

[0084] The logic unit 42 can receive at least one instruction 61, 62 of the quantum algorithm 6. The at least one instruction 61, 62 of the quantum algorithm 6 can be stored in a storage device. The logic unit 42 can convert the input quantum algorithm 6 into a series of quantum operations 71, 72 to be performed on the physical quantum system 1.

[0085] Alternatively, the sequence of quantum operations 71 and 72 can be predetermined given quantum algorithm 6 and can be stored in a storage device when quantum computation 7 is performed. In this case, quantum algorithm 6 does not need to be stored and does not need to be the actual input to logic unit 42.

[0086] Logic unit 42 can be a classic computer, that is, a computer that operates using classic bits. Logic unit 42 can also be distributed across multiple devices. Logic unit 42 and control unit 41 can be a single device.

[0087] Logic unit 42 can, for example, output the output 104 of quantum computing 7 to the user interface.

[0088] Encoding quantum computing Figure 4 A flowchart of coded quantum computing 7 of quantum computing method 10 according to an embodiment of the present invention is shown.

[0089] In the first step 100, at least a portion of the physical quantum system 1 is prepared in an initial quantum state. In the second step 101, the physical quantum system 1 is evolved to a final quantum state. The initial and / or final quantum state can be an encoded quantum state or a plaintext (unencoded) quantum state. In the third step 102, at least a portion of the physical quantum system 1 can be measured to provide a readout value. In the fourth step 103, the output 104 of the encoded quantum computation 7 can be determined based on the readout value.

[0090] During at least a portion of the encoded quantum computation 7, the quantum states of at least a subset of component 2 are encoded quantum states according to the encoding. "Encoding" refers to the relationship between the quantum state of logical qubit 5 and physical component 2. Under a selected basis, the encoding can be represented by a two-ray mapping between the eigenstates of component 2 and the eigenstates of logical qubit 5. The basis can be chosen as a Pauli... The eigenbase of the operator, which will be referred to as the standard basis below.

[0091] In other words, through this mapping, each logical qubit 5 is assigned to at least one component 2.

[0092] When a subset of logical qubit 5 is assigned to component 2, the following two correspond to each other: the component's Eigenvalues, logical qubit 5 in this subset The product of eigenvalues ​​(when there is only one logical qubit 5 in the subset, then it is...) (The eigenvalue itself). The components The eigenvalue uniquely corresponds to Eigenstate, i.e. or , because of the state of The eigenvalue is +1, and the state is... The eigenvalue is -1 (due to...) and ).

[0093] When a single logical qubit 5 is assigned to component 2 The correspondence of eigenvalues ​​leads to a "direct" mapping, which can be summarized as follows: Where L represents logical qubit 5. In this case, component 2 can be represented by the index (“logical index”) of logical qubit 5.

[0094] When at least two logical qubits 5 are assigned to component 2 The correspondence of eigenvalues ​​leads to a "parity check" mapping. When the eigenvalues ​​of logical qubit 5 have an even parity check, component 2 is in... The state (i.e., the eigenvalues ​​of the component are positive). When the eigenvalues ​​of logical qubit 5 have odd parity, component 2 is in a state where... The state (i.e., the eigenvalue of the component is negative). Therefore, the parity check of at least two logical qubits 5 is encoded into said component 2.

[0095] Considering only two logical qubits 5, the parity mapping from the two logical qubits 5 to component 2 can be written as: Where the subscript L represents logical qubit 5. The parity mapping of m logical qubits 5 to a component 2 can be written as: in Or 1, and It is modulo 2 addition.

[0096] In this case, component 2 can be represented by a tuple (or concatenation) of all indices of the logical qubit 5 assigned to component 2.

[0097] When a logical qubit 5 is represented by a one-bit index, a component 2 that has a single logical qubit 5 assigned to it can be represented by a one-bit index, while a component 2 that has several (especially two) logical qubits 5 assigned to it can be represented by a multi-bit index. In the following text, these one-bit or multi-bit indices are referred to as the “logical index” of component 2.

[0098] When the encoding changes, the logical index of component 2 also changes. Component 2 can also be represented by a unique identifier that remains unchanged when the encoding changes.

[0099] refer to Figure 4 In the first step 100, the initial quantum state can be determined by quantum algorithm 6. Alternatively, the initial quantum state can be the output state of a previously performed quantum computation, or it can depend on the output of a previous classical computation, particularly when quantum algorithm 6 is a subroutine. The initial quantum state can be an encoded quantum state or a plaintext quantum state. Preparation can be implemented by control unit 42.

[0100] Referring to step 101, evolving the physical quantum system 1 to the final quantum state includes: executing a plurality of encoding evolution steps 105 for changing the encoding of component 2, and a plurality of actions for physically implementing at least one of a plurality of instructions 61, 62 of quantum algorithm 6 under the current encoding. At least some of the plurality of encoding evolution steps 105 and at least some of the plurality of algorithm evolution steps 106 are executed according to an alternating sequence, which alternates between encoding evolution steps 105 and algorithm evolution steps 106.

[0101] Figure 5a A circuit diagram depicting an exemplary evolution of a physical quantum system 1 is shown, the evolution including an encoding evolution step 105 and an algorithm evolution step 106, the encoding evolution step 105 and the algorithm evolution step 106 respectively including a parity check encoding operation 75 and an algorithm action operation 74. Figure 5a An alternating sequence of steps between encoding evolution step 105 and algorithm evolution step 106 is depicted, with the steps separated by dashed lines.

[0102] Alternating sequences are five components 2 (e.g., linear nearest neighbor connectivity) that have linear nearest neighbor connectivity. Figure 1a(As shown) is executed. Component 2 is represented by unique identifiers from zero to four, where the top component 2 has a unique identifier of zero, and the identifiers increment to four for the bottom component 2. Only components 2 with adjacent unique identifiers are connected to each other (nearest neighbor connectivity). The unique identifier of component 2 can be inferred from the arrangement of component 2 and is not in... Figure 5a The diagram shows the logical index of component 2. Instead, the logical index is shown in italics. The logical index indicates which logical qubit 5 is assigned to the corresponding component 2.

[0103] Encoding Evolution Steps At least one coding evolution step 105 in the alternating sequence (in Figure 5a In the example, both depicted coding evolution steps 105 include performing a set of parity coding operations 75. Each of the parity coding operations 75 in the set is performed on a corresponding subset comprising at least two components 2, wherein each of the parity coding operations 75 in the set encodes the parity of all components 2 in the corresponding subset of at least two components 2 into at least one component 2 of the subset.

[0104] Figure 5a The first encoding evolution step 105 includes a parity coding operation 75 (a set of parity coding operations 75 in this step has one element). The parity coding operation 75 is performed on a pair of components 2 including components 2 zero and one. The effect of the parity coding operation 75 is that the parity of components 2 zero and one is encoded into components 2 zero, while components 2 one remain unchanged.

[0105] Encoding the parity check of a subset of component 2 into component 2 can be described in the same way as encoding the parity check of a subset of logical qubit 5 into component 2: when the parity check of a subset of component 2 is encoded into component 2, the following two correspond to each other: the component's Eigenvalues, component 2 of the subset The product of eigenvalues. Unlike the encoding from logical qubit 5 to component 2, encoding the parity of a subset of component 2 into component 2 is a physical operation, not an abstract mapping.

[0106] Before parity coding operation 75, component 2 is in an uncoded state, meaning logical qubit 5-0 is assigned to component 2-0 and logical qubit 5-1 is assigned to component 2-1. The coding changes upon performing parity coding operation 2. After parity coding operation 75, the parity of logical qubits 5-0 and 5-1 is encoded into component 2-0 (i.e., logical qubits 5-0 and 5-1 are assigned to component 2-0). The coding of the other components of component 2 remains unchanged.

[0107] Figure 5a The second coding evolution step 105 includes a set of parity coding operations 75 with two elements. The first parity coding operation 75 is performed on the three components 2 zero, one, and two, and the second parity coding operation 75 is performed on the two components 2 three and four. In the second coding evolution step 105 of the alternating sequence, the parity coding operations 75 in the set of parity coding operations 75 are executed in parallel.

[0108] Similarly, parity encoding operation 75 changes the current encoding. The parity encoding operation 75 above encodes the parity of component 2 (zero, one, and two) into component 2-1. Since component 2 is already encoded according to the previous encoding, the resulting logical index of component 2-1 becomes 02. By collecting the logical indices of all components 2 in a set of components 2 and removing numbers that appear an even number of times, the logical index of component 2 into which the parity of that set of components 2 is encoded can be obtained. For example, when determining the logical index of component 2-1 after applying the parity encoding operation 75 above, the number one in the logical index appears in component 2 (zero and one, even number of times) under the previous encoding, thus canceling out. The numbers one and two appear only once (odd number of times), so the logical index of component 2 becomes 02. For encoding, this means that after performing the parity encoding operation 75 above, the parity of logical qubits 5 (zero and two) is encoded into component 2-1.

[0109] Therefore, the parity coding operation 75 changes the coding.

[0110] The parity coding operation 75 can be performed by applying a sequence of basic quantum operations to component 2. This sequence can include one or more basic quantum operations. At least one (preferably each) basic quantum operation is a controlled NOT gate 77, or a gate obtained by performing a single-qubit basis transformation on both components 2 from the controlled NOT gate 77.

[0111] A fundamental quantum operation can be a primitive operation of a physical quantum system 1. A primitive operation can be a quantum operation implemented by a single physical action (e.g., a single pulse that cannot be broken down into smaller pulses). Alternatively, a fundamental quantum operation can be a primitive operation. A primitive operation can be a standard sequence of primitive gates that can be efficiently implemented on a particular physical quantum system 1.

[0112] In particular, Figure 5a The two parity check encoding operations 75 involving only two components 2 can be performed by a single controlled NOT gate 77, such as Figure 5b As shown. Figure 5a The parity check encoding operation 75, involving three components 2, can be performed through two sequential controlled NOT gates 77, as follows: Figure 5c As shown. Alternatively, other decompositions of the basic quantum operations can be used, particularly those dependent on the native gates provided by the physical quantum system 1.

[0113] Advantageously, the depth of the basic quantum operation sequence can be less than five, preferably less than three. In particular, the depth of the basic quantum operation sequence can be less than two swapping gates (a controlled NOT gate with a depth of six) or one swapping gate (a controlled NOT gate with a depth of three) (see...). Figure 2c The depth of the basic quantum operation sequence. This feature allows for a reduction in circuit depth.

[0114] In some embodiments, the basic quantum operation sequence may include subsequences of many-body quantum operations 72 (basic quantum operations performed on at least two components 2), wherein the depth of said subsequence is less than five, preferably three. In other words, the many-body circuit depth is less than three. Individual quantum operations 71 may be additionally applied, but these operations are generally less error-prone and have shorter execution times.

[0115] Preferably, the depth of the basic quantum operation sequence or the many-body quantum operation 72 sub-sequence of the entire encoding evolution step 105 is less than five, and more preferably less than three.

[0116] At least one (preferably each) basic quantum operation in the basic quantum operation sequence is performed on at most four (preferably at most two) component 2.

[0117] Algorithm evolution steps At least one algorithmic evolution step 106 in the alternating sequence includes performing at least one algorithmic action operation 74 on at least one component 2. The at least one algorithmic action operation 74 physically implements the action of at least one of the multiple instructions 61, 62 of the quantum algorithm 6 under the current encoding of component 2.

[0118] exist Figure 5aIn the first algorithmic evolution step 106, three algorithmic action operations 74 are executed. Two of these are single-body quantum operations 71, and one is a two-body quantum operation 72. The algorithmic action operations 74 physically implement the actions of instructions 61 and 62 of the quantum algorithm 6. Which algorithmic action operation 74 is executed depends on instructions 61 and 62 and the current encoding.

[0119] For a specific encoding, instructions 61 and 62 of quantum algorithm 6 can be converted into quantum operations 71 and 72 (i.e., quantum action operation 74) to be performed on component 2. The inventors discovered the following conversion. For the following discussion, the encoding basis is chosen as Pauli. Operator.

[0120] With base( The action of the single-unit instruction 61 associated with the logical qubit 5 diagonally below (-basis) can be achieved by performing an algorithmic action operation 74 based on instruction 61 on the component 2 that is assigned the logical qubit 5. For example, the rotation angle around the z-axis associated with logical qubit 5. Actions (represented as) ) can be done in Figure 5a In the first algorithmic evolution step 106, the corresponding rotation around the z-axis is physically performed on component 2 (i.e., component 2 that is only assigned to logical qubit 5). Figure 5a In the second algorithm step 106, there is no component 2 that is merely assigned logical qubit 5, therefore, under the current encoding of the second algorithm step 106, there is no simple quantum action operation 74 for implementing the rotation.

[0121] With The actions of some dual-body instructions 62 related to the two logical qubits 5 diagonally opposite to the base can be achieved by performing an algorithmic action operation 74 according to the instructions 62 on the component 2 that is assigned the two logical qubits 5.

[0122] For example, the bibody rotation angle around the z-axis associated with the 5 zeros and 1s of the logical qubit. (represented as) ) can be done in Figure 5a In the first or second algorithmic evolution step 106, a single-unit rotation about the z-axis is physically implemented by performing a single-unit rotation on component 2 (i.e., component 2 that is assigned logical qubits 5 zero and one, thereby encoding the parity of logical qubits 5 zero and one). Advantageously, the two-body instruction 62 can be physically implemented by performing a single-unit quantum operation 71, as it further reduces the two-body circuit depth (i.e., fewer two-body quantum operations 72 need to be performed).

[0123] Other two-body gates (such as controlled phase gates) can be implemented in a similarly simple way. Controlled phase gates can be implemented through relationships. = It is decomposed into two single-body rotations and one double-body rotation. These can be physically implemented by performing three single-body algorithmic action operations 74 on component 2 under appropriate encoding. These three single-body algorithmic action operations 74 can be performed under different encodings, i.e., in different algorithmic evolution steps 106 in the alternating sequence (not depicted here).

[0124] With The action of the single-unit instruction 61 associated with the asymmetrical logical qubit 5 can be achieved by performing an algorithmic action operation 74 according to instruction 61 on the component 2 assigned to the logical qubit 5, and performing additional controlled NOT gates 77 on all other components 2 assigned to the logical qubit 5 (e.g., those encoding the parity of the logical qubit 5 and other logical qubit 5). If no other components 2 are assigned to the logical qubit 5 in the encoding, a single-unit operation 71 is sufficient. An example of such a quantum operation is a rotation angle about the x-axis associated with the logical qubit 5. (represented as) Another example is that it can be broken down into... General unitary operations (e.g., Hadamard gates).

[0125] For the latter off-diagonal operation, the circuit depth for implementing instructions 61 and 62 depends critically on the current encoding.

[0126] In a particular embodiment, each logical qubit 5 can be assigned to at most two components 2 via a mapping representing the encoding. Thus, instructions 61 and 62 (which instruct execution in Pauli...) Basis (when the chosen basis is Pauli) Off-diagonal quantum operations 71, 72 under the eigenbase of the operator can be physically implemented by performing quantum operations 71, 72 on at most two components 61, 62.

[0127] Specifically, the encoding can be represented by the following mapping: this mapping assigns logical qubit 5 to component 2 in a connected subset of component 2. Thus, instructions 61 and 62 (which instruct execution in Pauli) Base (when the selected base is Pauli) The off-diagonal quantum operations 71, 72 under the eigenbase of the operator can be physically implemented under this encoding because the component 2 of the quantum operations 71, 72 that need to be performed on them is connected.

[0128] The following examples illustrate the physical implementation of two important quantum algorithms: the Quantum Approximate Optimization Algorithm (QAOA) and the Quantum Fourier Transform (QFT). For both examples, a reduction in circuit depth and gate number is achieved compared to prior art switch-gate-based implementations.

[0129] Quantum Approximation Optimization Algorithm (QAOA) QAOA is a well-known quantum algorithm for finding approximate ground states of the Ising Hamiltonian 200. It was proposed by E. Farhi in the scientific article "A quantum approximate optimization algorithm" (published as arXiv:1411.4028 [quant-ph]). It represents a hybrid quantum-classical heuristic for solving combinatorial optimization problems encoded in the Ising Hamiltonian 200 (hereinafter also referred to as the "problem Hamiltonian"), which acts on n qubits: in It is the coupling strength between qubits. It represents a local field.

[0130] In short, QAOA evolves quantum systems to candidate states. The Hamiltonian of the driver is Then, in the quantum-classical feedback loop, by changing 2p parameters and Optimize candidate states by finding the candidate state with the minimum energy. The candidate state with the minimum energy is approximated as the ground state of the Ising Hamiltonian 200. The quantum-classical feedback loop involves multiple iterations, each iteration including a subroutine quantum algorithm 6.

[0131] By selecting appropriate coupling strengths and local fields, the classical combinatorial optimization problem can be encoded into the Ising Hamiltonian 200. Finding the ground state of the Ising Hamiltonian 200 then yields the solution to the combinatorial optimization problem.

[0132] A more detailed description of QAOA is as follows: Figure 6 The flowchart is shown. Initially, the Ising Hamiltonian 200 is provided. The Ising Hamiltonian 200 can be described by the coupling strength and the local field. The coupling strength and the local field can be stored in a storage device or provided as input.

[0133] The QAOA iteration includes step 201: determining the initial parameters. and The initial parameters can be determined based on pre-defined stored values. Alternatively, they can be determined based on empirical values.

[0134] Subsequently, quantum algorithm step 202 includes running subroutine quantum algorithm 6, which includes instructions 61 and 62, to perform quantum operations in an alternating manner. and This involves a total of p alternations. Parameters and This can change in each iteration. Physically implementing and running this quantum algorithm 6 evolves quantum physical system 1 to its final quantum state. (i.e., candidate state), which depends on the parameters. and .

[0135] Next, in energy readout step 203, the final quantum state is measured, and the energy of the quantum state is determined. Energy can be read out by measuring an individual's energy level. or Operator, and according to Calculate energy. Alternatively, energy can be read from any (e.g., macroscopic) observable, from which energy can be inferred.

[0136] Next, in the termination check step 204, QAOA checks whether the energy meets the termination criteria. The termination criteria are considered met when the energy is lower than a predetermined energy value or when the energy difference compared to the energy of the previous iteration is less than a predetermined energy difference value.

[0137] Any other suitable termination condition can be used in the termination check step 204. The termination condition can be that the minimum number of iterations already performed has been reached, and QAOA can terminate after a certain number of iterations has been reached.

[0138] If the termination condition ("Yes") is met, QAOA terminates, and the quantum state can be at least partially read out in state readout step 205. It is not necessary to completely determine the quantum state, but it is possible to focus on all components 2. or The expectation value of the operator. Quantum states can be measured by individual... or The operator is used to read out the quantum state. The quantum state should then be approximated as the ground state 206 of the Ising Hamiltonian 200.

[0139] If the termination condition ("No") is not met, proceed to the next QAOA iteration and start again from another parameter determination step 201. This step may include the classic optimization step, in which new parameters are determined. and The parameters can depend on the energy or energy difference that may have been determined in step 203 from the energy readout of one or more previous iterations, for example, by using a gradient descent optimization algorithm. Subsequently, another subroutine quantum algorithm 6 with new parameters is executed in step 202.

[0140] Repeat this process until the termination condition is met in the termination check step 204 of a certain iteration.

[0141] This invention focuses on the physical implementation of a quantum algorithm 6 on a quantum physical system 1 with finite connectivity (particularly on a one-dimensional chain or a trapezoid of component 2). In embodiments of QAOA, the quantum algorithm 6 to be physically implemented can be a subroutine quantum algorithm 6, which involves performing quantum operations in an alternating manner. and Instructions 61 and 62 are executed a total of p times in alternation.

[0142] The connectivity of quantum algorithm 6 depends on the input Ising Hamiltonian 200, specifically which parameters Non-zero. Particularly difficult optimization problems can often be mapped to problems with only a few non-zero parameters. The Ising Hamiltonian is 200, which leads to the quantum algorithm 6 containing two-body instructions 62 between almost all logical qubit pairs 5.

[0143] For n=5, the quantum algorithm 6 for a subroutine of a single QAOA iteration for a fully connected Ising Hamiltonian 200 can be described as follows: Figure 7 The quantum circuit shown. Figure 7 The quantum circuit shown depicts one of the p iterations of the quantum algorithm 6 subroutine in step 202, i.e., in one QAOA iteration, Figure 7 The quantum circuit is repeated p times, where instructions 61 and 62 remain unchanged in each iteration except for the parameters (which may depend on the index k).

[0144] Quantum Algorithm 6 instructs that the state of each qubit be prepared as a plus state. This makes the state of all n logical qubits 5 be... And corresponding to the Hamiltonian The ground state. Figure 7 The initialization part of quantum algorithm 6, which is not described in the text, may include preparing the states of all n logical qubits 5 as follows: The state is then instructed to perform an Adama gate on each logical qubit 5 to obtain state.

[0145] Figure 7The first part of quantum algorithm 6 (represented by vertical dashed lines) includes... The relevant two-body instruction 62 and single-body instruction 61. Two-body instruction 62 relates to the Ising Hamiltonian 200. The term causes time evolution and instructs the execution of two-body rotations over all 5 pairs of logical qubits (indexed as i and j). The single-unit instruction 61 involves... The time evolution caused by the term, and indicates the time evolution for all terms with non-zero values. Logical qubit 5 (all logical qubit 5 here) performs a single-unit spin. .

[0146] Figure 7 The second part of quantum algorithm 6 includes... The relevant single-unit instruction 61. Single-unit instructions involve the driver Hamiltonian. of The term causes time evolution and instructs the execution of a single-unit rotation over all logical qubits 5. .

[0147] implement Instruction 61 can be directly implemented on a quantum physical system 1 with arbitrary connectivity because Includes only individual items Due to the two-body instructions between all 5 pairs of logical qubits, execution... Instructions 61 and 62 cannot typically be implemented directly on a physical quantum system 1 with finite connectivity.

[0148] Therefore, it is not possible to directly physically implement the iterative subroutine quantum algorithm 6 of QAOA by assigning the components 2 of the physical quantum system 1 to each logical qubit 5.

[0149] To physically implement the QAOA subroutine quantum algorithm 6 on a chain of component 2 with linear nearest neighbor (LNN) connectivity, prior art typically uses a swap network to provide connectivity between all component 2 that must interact due to the two-body instructions 62 of the quantum algorithm 6. Crooks, in his scientific article “Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem” published on arXiv:1811.08419 [quant-ph], provides an exemplary implementation using a swap network. The authors find that the overhead of controlled NOT gates (a swap gate consisting of three controlled NOT gates) makes the preceding step require… A controlled NOT gate. The circuit depth required for the switching network scales linearly with the number of qubits n.

[0150] In one embodiment of the present invention, the QAOA subroutine quantum algorithm 6 is physically implemented by performing coded quantum computation 7 on the physical quantum system 1.

[0151] Encoding quantum computing 7 involves preparing at least a portion of the physical quantum system 1 in an initial quantum state, in particular The quantum computation 7 further includes evolving the physical quantum system 1 to a final quantum state. The evolution of the quantum state can include any combination of an initial encoding step, an encoding evolution step 105, and an algorithmic evolution step 106. Finally, the encoding quantum computation 7 involves: measuring at least a portion of the physical quantum system 1 to provide a readout value; and determining the output of the encoding quantum computation 7 based on the readout. The output of the encoding quantum computation 7 can be energy, which can be used to terminate the check step 204. The readout value can be additionally or alternatively used to obtain at least partial information about the quantum state of the physical system 1 to obtain an approximate ground state of the Ising Hamiltonian 200. The approximate ground state of the Ising Hamiltonian 200 can be read directly from the quantum state. An approximate solution to the Ising Hamiltonian 200 can be obtained through classical decoding of the Ising Hamiltonian 200, depending on the encoding of component 2 at the time of measurement.

[0152] Quantum Approximation Optimization Algorithm (QAOA) on Linear Chains Figure 8a , Figure 8b A circuit diagram depicting the sequence of quantum operations 71 and 72 is shown, which has the following characteristics: Figure 1a The one-dimensional component of nearest neighbor connectivity shown is physically implemented on the chain. Figure 7 A quantum algorithm 6 for one iteration of a quantum approximation optimization algorithm. The physical arrangement of component 2 has the same characteristics as... Figure 8a and Figure 8b The order of the lines depicted corresponds to a fixed order. Figure 8a and Figure 8b The circuits are applied sequentially. Figure 8b The uplink and downlink of the circuit each correspond to one of the p iterations of the quantum algorithm 6 subroutine from QAOA (step k and step k+1, respectively). A total of p iterations are performed. Figure 8a The initialization is applied only once.

[0153] The circuit diagram depicts the encoded quantum computation 7 of the physical quantum system 1 to the final quantum state, which is in Figure 8bThe part includes the execution of: multiple encoding evolution steps 105 for changing the encoding of component 2, and multiple algorithm evolution steps 106 for the action of at least one of multiple instructions 61, 62 for physically implementing quantum algorithm 6 under the current encoding. The multiple encoding evolution steps 105 and the multiple algorithm evolution steps 106 are executed according to an alternating sequence that alternates between the encoding evolution steps 105 and the algorithm evolution steps 106.

[0154] Before this, such as Figure 8a As shown, step 100 is performed to prepare the encoded quantum state, including the Adama gate H and the controlled NOT gate 77. Component 2 is prepared in State (all components 2 are in state) Furthermore, logical qubit 5 is defined to map to component 2 in a permutation order, meaning each logical qubit 5 in quantum algorithm 6 corresponds to one of component 2, but the order of the logical indices does not correspond to the order of component 2 in the linear chain. Therefore, the logical state of logical qubit 5 is also... State. First, perform the Adama gate H (single-unit quantum operation 71) on each component 2, changing the quantum state of component 2 from Convert to As required by quantum algorithm 6. Secondly, in the initial encoding evolution step, parity-check encoding operations 75 in the form of four controlled NOT gates are applied to put the physical quantum system into an encoded quantum state. The state at the end of step 100 is the logical encoding under the current encoding. The current encoding is the status. Figure 8a The italicized logical index is given at the end of the step. Physically, the state at the end of step 100 is a complex entangled state.

[0155] Specifically, Figure 8a In the embodiments, the initial encoding is represented by the following mapping: logical qubits 52 and 53 are mapped to component 24 (top component), logical qubits 51 and 53 are mapped to component 23, logical qubits 51 and 54 are mapped to component 22, logical qubits 50 and 54 are mapped to component 21, and logical qubit 50 is mapped to component 20 (bottom component). That is, the parity check of logical qubits 52 and 53 is encoded in component 24, and so on.

[0156] Algorithm evolution step 106 includes algorithmic action operation 74 that implements the actions of instructions 61 and 62 of quantum algorithm 6. Quantum algorithm 6 (see...) Figure 7 This includes two-body instructions 62 between all logical qubits, which instruct the execution of two-body rotations. As mentioned earlier, a two-body rotation can be performed on component 2 of logical qubit 5, which is assigned indices i and j according to the current encoding, by performing a single-body rotation. To achieve this. In Figure 8b In the text, parameter abbreviations are used. and These include the variational and problem parameters defined above.

[0157] In the first algorithm evolution step 106, the encoding enables the action of the two-body instruction 62 associated with the logical qubit 5 pair to be realized by performing a single-body rotation (algorithm action operation 74) on the component 2 of the parity check of the logical qubit 5 pair (indexed as 23, 13, 14 and 04), and the action of the single-body instruction 61 associated with the logical qubit 5 to be realized by performing a single-body rotation (algorithm action operation 74) on the component 2 of the logical qubit 5 on which only the logical qubit 5 with index zero is assigned.

[0158] In the subsequent first encoding evolution step 105, the encoding is changed by performing a parity check encoding operation 75. In the embodiment given here, the parity check encoding operation 75 is performed by a sequence of basic quantum operations, wherein the basic quantum operations are controlled NOT gates.

[0159] In the second algorithm evolution step 106, there is a changed current encoding relative to the first algorithm evolution step 106, so different instructions 61 and 62 of the quantum algorithm 6 can be effectively physically implemented.

[0160] The second encoding evolution step 105 and subsequent encoding evolution steps 105 include the same parity coding operation 75. Therefore, the coding is changed in the same relative manner in each step.

[0161] from Figure 8b It can be seen that the alternating sequence of encoding evolution step 105 and algorithm evolution step 106 ensures that at least one algorithm evolution step 106 in one of the p iterations of the quantum algorithm 6 subroutine (i.e., respectively in...) Figure 8b During the uplink or downlink algorithm evolution step 106 of the circuit diagram, parity checking of each pair of logical qubits 5 is encoded into at least one component 2. Therefore, each two-body instruction 62 of the fully connected Ising Hamiltonian 200 can be implemented via single-unit quantum operation 71. Furthermore, during at least one algorithm evolution step 106 of one of the p iterations of the QAOA quantum algorithm 6 subroutine, each logical qubit 5 is directly encoded into at least one component 2. Therefore, each single-unit instruction 61 of the Ising Hamiltonian 200 can be implemented via single-unit quantum operation 71.

[0162] During at least one algorithmic evolution step 106 of the alternating sequence (in which parity checks of logical qubit 5 pairs are encoded into component 2), each of component 2 is executed as follows: each algorithmic action operation 74 implements the action of at least one two-body instruction 62 of quantum algorithm 6 acting on multiple pairs of logical qubits 5.

[0163] Through this process, apart from the repeated identical controlled NOT gate sequence of the parity check coding operation 75, only the terms induced by the Ising Hamiltonian 200 need to be implemented by applying the single quantum operation 71.

[0164] Figure 8b The following line depicts the next p iterations (k+1) of the quantum algorithm 6 subroutine of QAOA. Since the same parity coding operation 75 is performed in each coding evolution step 105, the coding evolves further in the same relative manner. The coding (given by logical (italic) index) differs from the sequence in the preceding line, but similarly, in at least one algorithm evolution step 106, the parity of each pair of logical qubits 5 is encoded into at least one component 2, and each logical qubit 5 is exclusively encoded into at least one component 2 in at least one algorithm evolution step 106. Therefore, by tracking the corresponding current coding, all instructions 61, 62 of the quantum algorithm 6 can be implemented using algorithmic action operations 74 corresponding to the individual quantum operations 71.

[0165] Then, the same encoding evolution step 105 is used to repeat the encoding of quantum computation 7, resulting in a total of p iterations. In the next iteration (k+2), the encoding will again be different from the depicted row, but will again take the form of: by following the corresponding current encoding, all instructions 61, 62 of quantum algorithm 6 can be implemented using algorithmic action operations 74 corresponding to the single quantum operation 71.

[0166] exist Figure 8b In the final algorithm evolution step 106 of the first and second rows of the circuit diagram, the following steps were executed: Base-off diagonal instruction 61 (with driver Hamilton) (Related). Additional controlled NOT gates are required for implementation. Since the encoding ensures that a particular logical qubit 5 is assigned to at most two component 2, each component 2 requires at most two controlled NOT gates. In particular, this step requires a constant controlled NOT gate depth of 4 and 2n-4 (6 in this case) controlled NOT gates.

[0167] Each encoding ensures that at most two components 2 are assigned to a specific logical qubit 5, through the fact that... Figure 8a and Figure 8bThe diagram uses "logic lines" between component 2. A logic line connects component 2 with a number in the logical index, i.e., component 2 assigned to a logical qubit 5. Dotted lines represent the logic line for logical qubit 5-0. Solid lines represent the logic line for logical qubit 5-1. Double-dotted lines represent the logic line for logical qubit 5-2. Dashed lines represent the logic line for logical qubit 5-3 (only a short horizontal line is visible due to the short distance). Double solid lines represent the logic line for logical qubit 5-4. In this diagram, the physical implementation of this logic line can be achieved by applying two controlled NOT gates between all pairs of component 2 on the logic lines. The instruction 61 is not diagonally based. Here, the logic line extends at most between two components 2.

[0168] Each two consecutive layers of controlled NOT gates (executed in parallel) in the parity coding operation 75 contain n-1 (4 here) controlled NOT gates. Due to the parity coding operation 75 performed in coding evolution step 105, one iteration of the p-th iteration of the QAOA quantum algorithm 6 subroutine has a controlled NOT gate depth of 2n-2 (8 here) and a controlled NOT gate count of n. 2 - 2n+1 (here, 16) numbers. One iteration in the p iterations of the QAOA quantum algorithm subroutine 6 corresponds to Figure 8b A row in the circuit diagram.

[0169] Based on the above considerations, for the physical implementation of one iteration in the p-th iteration of the subroutine quantum algorithm 6 of a single QAOA iteration, the total controlled NOT gate count is: (22 here) (The initialization step is not included in this count). Using known physical implementations of the swapping gate in the leading step (i.e., in...) (Before the term) there is a factor of 3 / 2. Therefore, the method of the present invention is superior to the prior art in terms of controlled NOT gate count (i.e., the number of controlled NOT gates). In addition, the circuit depth is also smaller than that of known physical implementations using swapping gates. The number of single-unit quantum operations 71 required remains the same compared to the swapping implementation.

[0170] A detailed comparison of resources with existing technologies is shown in Table A below. Note that the initialization steps are not included. Existing technology data for the swap gate is taken from Crooks’ “Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem” published on arXiv:1811.08419 [quant-ph].

[0171] A further advantage is that the number of components 2 is equal to the number of logical qubits 5 in quantum algorithm 6. Therefore, this physical implementation has no qubit overhead.

[0172] Figure 9a and Figure 9b A network of fictitious qubits (“parity network”) is shown, from which can be derived... Figure 8a , Figure 8b The physical implementation of the parity check coding operation 75 takes the form of 75 and the resulting coding sequence can be derived. The network can be a fictitious arrangement of fictitious qubits with "edges" connecting nearest-neighbor qubits. Figure 9c A circuit diagram depicting the parity check encoding operation 75 is shown.

[0173] Circles represent hypothetical qubits, their logical indices depicted in italics. Squares and triangles between qubits depict the constraints that adjacent qubits must satisfy (these regions are often called plaquettes). The network is constructed such that each index number of a qubit as part of a constraint is constrained to appear an even number of times. This means that the parity check of all qubits within the constraint is even. The network can be considered to extend periodically to the left and right (as shown by the dots).

[0174] like Figure 9a As shown, the encoding applicable to the linear chain of component 2 can be derived from encoding line 8 involving n (5 here) dummy qubits in the network. Encoding line 8 can be a connection line involving n (5 here) distinct qubits, where each number needs to be represented in the logical index of the qubits on encoding line 8. For Figure 8a , Figure 8b For example, the coding line 8 can be any zig-zag line from top to bottom. For instance, Figure 8a , Figure 8b The initial encoding with logical indices 23, 13, 14, 04, 0 is one of these zigzag encoding lines 8, from... Figure 9b This can be verified. Furthermore, Figure 8b In algorithm evolution step 106, all codes of the current encoding are zigzag lines that move to the right over time.

[0175] exist Figure 9b The diagram depicts logic lines connecting qubits with specific logical indices. Dotted lines represent logic qubit zero. Solid lines represent logic qubit one. Double-dotted lines represent logic qubit two. Dashed lines represent logic qubit three. Double-solid lines represent logic qubit four.

[0176] Figure 8a , Figure 8bThe effect of the first coding evolution step 105 is in Figure 9c The description in the middle, Figure 9c A circuit diagram of quantum computing on component 2 is depicted. The left side of the diagram is aligned with... Figure 5b and Figure 5c The same notation depicts the parity check coding operation 75. The right side of the figure decomposes the parity check coding operation 75 into a sequence of basic quantum operations, here the controlled NOT gate 77, where the dashed box represents the parity check coding operation 75. Figure 9a In this context, the encoding change caused by this step corresponds to changing the encoding line 8 that defines the encoding to another encoding line 8 that moves one step to the right in the network (moving the zigzag line to the right). Figure 8a , Figure 8b In each of the other coding evolution steps 105, the zigzag coding line 8 is moved further to the right.

[0177] The parity coding operation 75 is designed such that, when starting from one of these codes, the coding of component 2 corresponds to the coding line 8 in the network defined by its constraints. Each parity coding operation 75 corresponds to a constraint of the network. Each parity coding operation 75 contains two controlled NOT gates when corresponding to a square constraint and one controlled NOT gate when corresponding to a triangular constraint.

[0178] Specifically, the parity coding operation 75 corresponding to the triangle constraint is performed on a subset of the two component 2, wherein the subset of the two component 2 includes a boundary component 2 that is only connected to the other component 2 in the subset. The parity coding operation 75 encodes the parity of the two component 2 into the boundary component 2.

[0179] Specifically, the parity coding operation 75 corresponding to the square constraint is performed on a subset of the three component parts 2, wherein the subset of the three component parts 2 includes a central component part 2 connected to the other two component parts 2 in the subset. The parity coding operation 75 encodes the parity of the three component parts 2 into the central component part 2.

[0180] Figure 9a and Figure 9b The network is constructed such that parity for all two logical qubits 5 occurs. Therefore, a fully connected quantum algorithm 6 can be implemented by propagating the code using a parity coding operation 75 derived from the network. Note that other networks can be created for quantum algorithms 6 with less connectivity, and the parity coding operation 75 can be designed such that the code corresponds to the coding line 8 of such alternative networks.

[0181] Similarly, QAOA's quantum algorithm subroutine 6 can be physically implemented on a toroidal physical quantum system 1, such as... Figure 1bAs shown (ring connectivity). Then modify parity coding operation 75. In particular, the network used to obtain parity coding operation 75 can be embedded in a cylinder.

[0182] Quantum Approximation Optimization Algorithm on Trapezoids (QAOA) QAOA's quantum algorithm subroutine 6 can be physically implemented on a ladder-like physical quantum system 1, such as Figure 1c The depicted (trapezoidal connectivity) shows that the upper and lower rails of the trapezoid each form a linear chain of component 2 with nearest-neighbor connectivity.

[0183] A quantum algorithm 6 with n logical qubits 5 can be physically implemented on a physical quantum system 1 with trapezoidal connectivity and 2n components 2. Therefore, the number of components 2 is less than or equal to twice the number of logical qubits 5 in the quantum algorithm 6. The physical quantum system 1 is analogous to two linear chains of components 2 with nearest-neighbor connectivity, where each linear chain comprises n components 2. Furthermore, there are connections 3 between components in two different chains.

[0184] The linear chains of the two components 2 of the trapezoid can both be initialized with different encodings. Specifically, the initial encodings of the linear chains of the two components 2 can correspond to encodings from sources such as... Figure 9a Two coding lines for a network like the one shown. For example, initial encoding can be performed using two coding lines with indices 23, 13, 14, 04 and 0 and 34, 24, 2, 1 and 01 (i.e., Figure 9a (Two adjacent zigzag lines of the same form in the trapezoid). A parity check coding operation 75 can be selected, such that the code of the first linear chain in the two linear chains of the trapezoid is determined by the adjacent coding lines. Figure 9a The code changes as it propagates to the left, while the encoding of the second linear chain in the two linear chains of the trapezoid is determined by the adjacent encoding lines. Figure 9a Changes occur as the virus propagates from the center to the right (e.g.) Figure 8b (The case in the middle). For example, in the first step, the encoding of the first linear chain in the two linear chains of the trapezoid can be changed from 23, 13, 14, 04 and 0 to 12, 02, 03, 3 and 4 in encoding evolution step 105 (in Figure 9a (From left to right), and the encoding of the second linear chain in the two linear chains of the trapezoid can be changed from 34, 24, 2, 1 and 01 to 4, 3, 03, 02 and 12 in the same encoding evolution step 105 (in Figure 9a (from center to right), etc. Due to... Figure 9a The periodicity of the network (represented by points) occurs after a certain number of coding evolution steps 105 (especially... After each encoding evolution step 105, the encoding again corresponds to the adjacent encoding line, except that the logical index order of one encoding line is reversed. The parity coding operation 75 in each step has the same cost as in the linear chain case.

[0185] In this evolutionary process, algorithm step 106 is applied between encoding evolution steps 105 to enable the terms of the Ising Hamiltonian 200 to be implemented in the same way as in a one-dimensional chain, i.e., when the encoding has a suitable form (such as...). Figure 8b As shown), the dual-body instruction 62 and the single-body instruction 61 are implemented via single-body quantum operation 71 (algorithm action operation 74).

[0186] In order to execute the final encoding due to the driver Hamiltonian (i.e., due to...) The off-diagonal single-unit instruction 61, caused by the item (), removes component 2 of the first linear chain in the trapezoidal two-component linear chain from the code. Removal from the code can be performed on each component 2 in the first linear chain. Measurement, and based on the measurement results, execution on component 2 in the second linear chain. The calibration is then complete. Then, it can be done as per [the relevant information]. Figure 8b As detailed in the linear chain section, this is achieved by applying a second linear chain under the current encoding. Rotation and controlled NOT gate chains are used to physically implement off-diagonal single-unit instructions 61 due to driver Hamiltonians.

[0187] Then, the component 2 of the first linear chain (previously removed from the encoding) can be encoded again according to the desired encoding. This can be achieved by performing controlled NOT gates from each component 2 of the second linear chain to the corresponding component 2 of the first linear chain (when the first linear chain is ready to...). In this state, this copies the encoding from the second linear chain to the first linear chain to create a new initial encoding for the next p iterations of the QAOA quantum algorithm 6 subroutine. The same encoding for both linear chains can then be modified by performing encoding evolution step 105 on one of the two linear chains. This new configuration can then be used as the starting point for the next iteration.

[0188] The advantage of using a physical quantum system 1 with trapezoidal connectivity over a physical quantum system 1 with linear chain connectivity is that the parity check coding operation 75 can be parallelized. Therefore, the depth of the two-body quantum operation 72 is reduced (from 2n+2 in one-dimensional connectivity to n+4 in the trapezoidal connectivity). In other words, each iteration in the p iterations of the QAOA quantum algorithm 6 subroutine has the same depth of the two-body quantum operation 72, while involving fewer coding evolution steps 105 (see Table A).

[0189] Specifically, starting from the first linear chain that has already been encoded, execute the code derived from the Ising Hamiltonian 200. Instructions 61 and 62 require half the number of steps of the linear chain implementation, plus three additional controlled NOT gate steps for the initial encoding of the first and second linear chains in the trapezoid. In the worst case (i.e., for odd n), this results in the steps listed in Table A. The number. Derived from the driver Hamiltonian. The cost of instruction 61 is the same as that of a linear chain, plus one round of (parallelizable) measurement and one round of individual quantum operations 71 on each component 2.

[0190] A quantum approximation optimization algorithm (QAOA) on a trapezoid with diagonal connections. In an alternative embodiment, the QAOA quantum algorithm 6 subroutine can be physically implemented on a trapezoidal physical quantum system 1 with additional connections 3 located between components 2 of two adjacent crossbars of the trapezoid (referred to as "diagonal connections"), such as... Figure 1d As depicted. Apart from the component 2 on the boundary, each component 2 of the first subset (the left rail of the trapezoid) is connected to the three components 2 of the second subset (the right rail of the trapezoid) by a straight connection 3 (i.e., the crossbar of the trapezoid) and by additional first and second diagonal connections 3, and each component 2 of the second subset is connected to the three components 2 of the first subset.

[0191] In this embodiment, a quantum algorithm 6 with n logical qubits 5 can be implemented on a physical quantum system 1 with n components 2. Each side rail of the trapezoid includes n / 2 components (here, n is chosen to be an even number). An example of n=8 logical qubits 5 and components 2 is described below, where each side rail of the trapezoid has four components 2.

[0192] Similar to previous embodiments of QAOA, quantum algorithm 6 is physically implemented by performing coded quantum computation 7. A feature of this embodiment is the implementation of two-body instructions 62, typically associated with the non-nearest neighbor pairs of logical qubits 5 (i.e., two-body rotations due to the Ising Hamiltonian 200). The algorithm action operation 74 can be the nearest neighbor two-body quantum operation 72 (instead of as previously...). Figure 8a and Figure 8b The single-body quantum operation 71 in the embodiment). This may be advantageous for certain physical quantum systems 1, in which the two-body quantum operation 72 (especially in the form of The two-body quantum operation (“Rzz operation”) can be performed more efficiently or with a lower error rate compared to the equivalent single-body quantum operation sequence 71.

[0193] Figure 10a , Figure 10b and Figure 10c Quantum operations 71 and 72 are described for evolving a physical quantum system 1 according to encoded quantum computation 7. After preparing an initial quantum state, an alternating sequence of encoding evolution steps 105 and algorithm evolution steps 106 is executed to evolve the physical quantum system 1 to a final quantum state. Then, at least a portion of the final quantum state is measured to provide a readout value, and an output is determined based on the readout value. As in previous embodiments, during at least a portion of encoded quantum computation 7, the quantum state of at least a subset of components is an encoded quantum state according to the encoding. As in previous embodiments, evolving the physical quantum system 1 to the final quantum state includes executing: multiple encoding evolution steps 105 for changing the encoding of component 2, and multiple algorithm evolution steps 106 for at least a portion of the action of at least one of multiple instructions 61 and 62 for physically implementing quantum algorithm 6 (according to QAOA) under the current encoding. At least some of the plurality of coding evolution steps 105 and at least some of the plurality of algorithm evolution steps 106 are executed according to an alternating sequence that alternates between coding evolution steps 105 and algorithm evolution steps 106.

[0194] Figure 10a The coding evolution steps 105 of the alternating sequence of coding quantum computing 7 are described. The coding evolution steps 105 include three sub-steps that can be executed sequentially. The first sub-step includes a parity check coding operation 75 along at least some first diagonal connections 3, the second sub-step includes a parity check coding operation 75 along at least some second diagonal connections 3, and the third sub-step includes a parity check coding operation 75 along at least some direct connections ("crossbars") of the physical quantum system 1.

[0195] Specifically, in the first sub-step, a set of parity coding operations 75 are performed in parallel, wherein the parity coding operations 75 are performed along all n / 2-1 first diagonal connections 3. The parity of the two components 2 on each first diagonal connection 3 is encoded into the component 2 on the left rail of the corresponding first diagonal connection 3.

[0196] Specifically, in the second sub-step, a set of parity coding operations 75 are performed in parallel, wherein the parity coding operations 75 are performed along all n / 2-1 second diagonal connections 3. The parity of the two corresponding components 2 on each second diagonal connection 3 is encoded into the component 2 on the left rail of the corresponding second diagonal connection 3.

[0197] Specifically, in the third sub-step, a set of parity coding operations 75 are performed in parallel, wherein the parity coding operations 75 are performed along two direct connections 3 on the boundary. The parity of the two corresponding components 2 on each direct connection 3 is encoded into the component 2 on the left rail of the corresponding direct connection 3.

[0198] In one particular embodiment, the connectivity of the physical quantum system 1 can be changed during operation. In particular, the connectivity in the first sub-step can be different from the connectivity in the second sub-step, the connectivity in the first sub-step can be different from the connectivity in the third sub-step, and / or the connectivity in the second sub-step can be different from the connectivity in the third sub-step.

[0199] Encoding evolution step 105 is for subsequent... Figure 10b or Figure 10c (as well as Figure 10d The algorithm evolution step 106 shown in the figure changes the encoding.

[0200] The first variant of algorithm evolution step 106 is as follows: Figure 10b As shown.

[0201] exist Figure 10b In the first sub-step of algorithm evolution step 106, the two-body instruction 62 (specifically two-body rotation) is implemented, which is usually associated with the non-nearest neighbor pair of logical qubit 5. The algorithm for the action operation 74 is performed as a two-body quantum operation 72 on the two connected components 2 (specifically, as indicated, the two-body quantum operation). These operations are performed along the straight (crossbar) connection 3 and along the side rail, in the following pattern: Figure 10b As shown.

[0202] exist Figure 10b In the second sub-step of algorithm evolution step 106, the single-unit instruction 61 (especially single-unit rotation) associated with a single logical qubit 5 is implemented. The algorithmic action operation 74 (related to the driver Hamiltonian) is performed as a single quantum operation 71 on at least one component 2 (specifically, a single quantum operation). (Rotation around the x-axis) is executed.

[0203] The encoding in each algorithm evolution step 106 ensures that a specific logical qubit 5 is assigned exactly to one component 2 (and there are no other component 2s). In a suitable algorithm evolution step 106, a quantum operation is performed on that component 2. Thus, quantum operations implement the action of instruction 61 associated with the driver Hamiltonian Hx without applying an additional controlled NOT gate, if the logical qubit 5 might be assigned to other components 2 in other encodings (such as...). Figure 8b As shown), additional controlled NOT gates need to be performed on these other components 2. An alternating sequence between encoding evolution step 105 and algorithm evolution step 106 ensures that for all logical qubits 5, there exists at least one algorithm evolution step 105 in which at least one logical qubit 5 is assigned to only one component 2. Therefore, all quantum operations... It can be applied in one of the algorithm evolution steps 106 during the alternating sequence, but it is distributed in different algorithm evolution steps 106.

[0204] The second variant of algorithm evolution step 106 is as follows: Figure 10c As shown. The first sub-step and Figure 10b Same as, but the second sub-step is the same as Figure 10c The differences. In Figure 10c In the second sub-step of algorithm evolution step 106, the single-unit rotation Simultaneously applied to all components 2. This particularly simple replacement of the second sub-step implements the action of the modified quantum algorithm 6 subroutine of QAOA. In particular, the form of the driver Hamiltonian is modified according to the encoding.

[0205] In the further encoding evolution step 105 and algorithm evolution step 106 of the alternating sequence, the form of the quantum operation can be slightly modified. In particular, the form of the quantum operation can alternate in each encoding evolution step 105 and every other algorithm evolution step 106.

[0206] Encoding evolution step 105 can alternate between two versions, where the first version can be... Figure 10a The second version described could be Figure 10a The depicted state is reversed, but the controlled NOT gate direction is reversed. In the first version, the state of component 2 on the left rail was modified, while in the second version, the state of component 2 on the right rail was modified.

[0207] Two variants ( Figure 10b , Figure 10c The first sub-step of algorithm evolution step 106 can alternate between two versions, where the first version can be... Figure 10b , Figure 10c The second version, as depicted, can have, for example... Figure 10d The described mirror Rzz operation mode.

[0208] The alternating sequence of encoding evolution step 105 and algorithm evolution step 106 only needs to be executed n / 2-1 (3 times in this case) times to implement all instructions 61 and 62 of quantum algorithm 6. The following two-body quantum operations are required: each encoding evolution step 105 involves n (8 in this case) controlled NOT gates. In total, for all encoding evolution steps 105, this totals n2 / 2-n controlled NOT gates. Each algorithm evolution step 106 involves n-1 (7 in this case) Rzz operations. In total, for all algorithm evolution steps 106, this totals n 2 / 2 - 3 / 2 n + 1 Rzz operations.

[0209] Figures 10a-10d The forms of quantum operations 71, 72, 74, and 75 performed in alternating sequences are described. Figure 11 and Figures 12a-12c The encoding for specific categories illustrates the forms of quantum operations 71, 72, 74, and 75. The encoding of component 2 (i.e., the allocation from logical qubit 5 to component 2) may be related to... Figure 8a and Figure 8b The implementation methods differ.

[0210] Figure 11 The representations of two networks (i.e., fictitious arrangements of fictitious qubits) are shown, from which the following can be derived. Figure 10a , Figure 10b , Figure 10c and Figure 10d The physical implementation of the parity check coding operation 75 and the resulting coding sequence. Figure 12a and Figure 12b It shows the use of from Figure 11 The specific encoding derived from the network, Figure 10a and Figure 10b The process.

[0211] Figure 11 The first network, as shown in the diagram, includes 91 fictitious "parity qubits" (small dashed circles). This first network is referred to below as the parity network (similar to...). Figure 9a Each of the 91 parity check qubits has a logical index involving two logical qubits. (And...) Figure 9a Similarly, the squares and triangles between parity qubits depict exemplary constraint 93, which the adjacent parity qubits 91 need to satisfy. The network is constructed such that each number of the index of the qubits 91, which is part of constraint 93, is constrained to appear an even number of times (i.e., the total parity is even). Each constraint 93 can be achieved through regions ( Figure 11 Visualized as squares and triangles, this region is defined by the boundaries between 91 parity qubits constrained by the network; this region is referred to as the patch below. The network can be considered to extend periodically to the left and right.

[0212] Figure 11The second network, as shown in the diagram, comprises fictitious "base qubits" 92 (large solid circles). This second network is referred to below as the base network. The base qubits 92 are placed around parity qubits 91 such that each edge between the two nearest neighbor base qubits 92 can be assigned to a single parity qubit 91, and each parity qubit 91 can be assigned to an edge between two base qubits 92 (i.e., there is a one-to-one correspondence between parity qubits 91 and edges of the base network). A base network can be defined for any parity network. The columns of the base qubits 92 are... This indicates that c is the column index.

[0213] The base qubit 92 is placed in every other constraint 93 block of the parity qubit 91 according to a checkerboard pattern. More specifically, the constraint 93 blocks of the parity qubit 91 are divided into a first subset 96 and a second subset 95. The base qubit 92 is placed in each constraint 93 block of the parity qubit 91 in the first subset 96, but not in the second subset 95 (i.e., in either a "white" or "black" square of the checkerboard pattern).

[0214] The constraint 93 on parity qubit 91 is transformed into constraint 94 on base qubit 92, as detailed later. Exemplary constraints 94 on the base qubit are depicted by squares and triangles with double solid lines, solid lines, dashed lines, and dotted lines, respectively.

[0215] Note that, compared to Figure 11 More general networks are also possible. To construct a more general network, the constraints 93 of the parity network can be chosen such that they form patches of non-overlapping constraint 93 blocks of parity qubits 91. “Non-overlapping” means that the regions of the patches do not overlap (but at least one parity qubit 91 can be part of two different constraint 93 blocks). The constraint 93 blocks are divided into two subsets 95 and 96 such that any pair of constraints 93 in the same subset shares at most one parity qubit 91. Typically, the base network can be constructed by placing the base qubits 92 in each constraint 93 block of the first subset 96. Furthermore, the base qubits 92 are connected to their nearest neighbors such that the patches of the base network include constraint 93 blocks from the second subset 95. The patches of the base network can be considered as regions between edges connecting the nearest neighbors of the base qubits 92. In this more general way, base networks can also be constructed for Ising Hamiltonians that are not fully connected or contain higher-order interactions.

[0216] If the constraint 93 blocks of the parity check network form dense patches on a rectangular lattice, then the number of base qubits is half the number of parity check qubits (e.g., Figure 11 (As shown).

[0217] Half of the constraints 93 on the parity qubit 91 are automatically satisfied through the construction of the base qubit 92. These are the constraints 93 on the parity qubit 91 from the second subset 95 mentioned above, that is, those constraints 93 on the parity qubit 91 that relate to the edges assigned to a particular small block in the base network.

[0218] The remaining half of the constraints 93 on parity qubits 91 are not automatically satisfied. These are constraints 93 on parity qubits from the first subset 96, affecting all parity qubits 91 assigned to edges between base qubits 92 involving a specific base qubit 92. The constraints 93 on parity qubits 91 translate into constraints 94 on base qubits 92. Specifically, square constraints 93 on parity qubits 91 translate into square constraints 94 on base qubits 92, involving the four base qubits 92 connected to the specific base qubit 92, excluding the specific base qubit 92 itself. Furthermore, triangular constraints 93 on parity qubits 91 translate into triangular constraints 94 on base qubits 92, involving the three base qubits 92 connected to the specific base qubit 92, as well as the specific base qubit 92 itself. Therefore, all constraints 94 on base qubits 92 involve four base qubits 92.

[0219] Similar to constraint 93 on parity qubit 91, each number of the logical index of base qubit 92, which is part of constraint 94 of base qubit 92, is constrained to appear an even number of times in the base network (i.e., the product of the parity of the base qubits is even).

[0220] To define the encoding of quantum computing 7, arbitrarily choose the logical index of a fictitious base qubit 92. It can be any tuple of the index of logical qubit 5 of quantum algorithm 6 (in...). Figure 11 (Written as concatenation in Chinese). The logical indices of all other base qubits 92 can be constructed by moving along the edges of the base network and adding the index of the parity qubit 91 assigned to each edge to the index of the base qubits 92. When an index number appears an even number of times, it is removed from the tuple; otherwise, it is added to the tuple. For example, as... Figure 11 As shown, moving down from the base qubit 92 with logical index 145, we pass the edge assigned to the parity qubit 91 with logical index 12. Therefore, the logical index of the next base qubit 92 in the downward direction is 245 (1 appears twice and cancels out, 2 is added, and 45 is retained). In this way, logical indices can be assigned to each base qubit 92.

[0221] The logical index of base qubit 92 defines their relationship to logical qubit 5.

[0222] The encoding of component 2 of the trapezoidal physical quantum system 1 can be given by the logical index of two columns of base qubits 92. Each column of base qubits 92 is assigned to a side rail of the trapezoid (i.e., physical quantum system 1). As an example, when component 2 has logical index 145, the parity of logical qubits 5-1, 5-4, and 5 is encoded into component 2. This encoding needs to be taken into account when performing algorithmic action operation 75, and the physical quantum operation needs to be adjusted accordingly, as discussed earlier in this application. Furthermore, this encoding needs to be taken into account when determining the output based on the read value.

[0223] Figure 12a This shows that for a specific encoding, the... Figure 10a The described physical quantum system 1 performs coded evolution step 105. The coding of component 2 originates from the column. The fictitious base qubit 92 (assigned to left-hand orbital component 2) and The fictitious basis qubit 92 (assigned to right-hand rail component 2). Parity check encoding operation 75 corresponds to Figure 10a Those described in [the text]. Selecting them ensures that, after executing them, the encoding of the left-hand rail is from the column [the text is incomplete]. Transform into a column (Compare Figure 11 Therefore, after coding evolution step 105, the left-hand rail has a sequence from column... The encoding, while the right rail (still) has the encoding from the column. The encoding. Specifically, parity coding operation 75 can be used from... Figure 11 The constraints 94 on the base qubit 92 shown are derived, which impose restrictions on the two diagonal connections (square and triangle constraints 94) and the direct connections (triangle constraints 94).

[0224] Another parity coding operation 75 with an inverted controlled NOT gate, in coding evolution step 105, removes the coding of the right-hand rail from the column. Transform into a column ( Figure 12c Therefore, after the further coding evolution step 105, the left-hand rail (still) has the characteristics derived from the column. The encoding, while the right rail has the encoding from the column. The encoding (not depicted). The next encoding evolution step 105 has the parity check encoding operation 75 of the first encoding evolution step, i.e., as... Figure 12a The controlled NOT gate shown.

[0225] In this way, from Figure 11The encoding of each pair of adjacent columns of the base network is the current encoding in an algorithm evolution step 106 (which will be executed after each encoding evolution step 105). The actions of all two-body instructions 62 caused by the Ising Hamiltonian 200 can be implemented in at least one algorithm evolution step 106 by executing two-body quantum operations 72 (specifically the Rzz ​​operation).

[0226] Figure 12b It shows in Figure 12a The algorithm evolution step 106 follows the encoding evolution step 105. For example, for... Figure 10b and Figure 10c As detailed in the description, the algorithmic action operation 74, in the form of an Rzz operation, is performed on the nearest neighbor component 2. The Rzz ​​operation implements the action of the instruction to perform the Rzz ​​operation on logical qubit 5 according to the quantum algorithm 6 subroutine iterated by QAOA. In this encoding, a pair of logical qubits 5 are assigned to the connection 3 between the two components 2 (instead of as from...). Figure 8a and Figure 8b The encoding is assigned to component 2 itself. For example... Figure 12b The topmost Rzz operation physically implements the action of instruction 62, which performs an Rzz operation on a pair of logical qubits 5 and 3, because the connection 3 between components 2, which have logical indices 01345 and 045, has a logical index 13 (indices 0, 4, and 5 cancel each other out). This can also be seen from... Figure 11 In the context of this understanding: a pair of logical qubits 5 corresponds to an edge between two base qubits 94, and thus corresponds to a parity qubit 91. In physical implementation, two columns of base qubits 92 are assigned one-to-one to the (physical) component 2, and the edge between the base qubits 92 (or the parity qubit 91) is assigned to the connection 3 between the two components 2.

[0227] The algorithmic action operation 74 used to implement the action of the driver Hamiltonian can be as follows: Figure 10b The execution is described as follows: as a single Rx rotation on a component 2, logical qubit 5 is assigned to component 2, and during that time step, logical qubit 5 is not assigned to any other component 2. Figure 12b As shown, for columns involved and The encoding of the Rx rotation instruction 61 for logical qubit 5 can be achieved by rotating the left rail (corresponding to column 5). The corresponding Rx rotation is performed on the top component 2 of the logic qubit 5, as this is the only component 2 assigned to logic qubit 5. Similarly, the Rx rotation instruction 61 for logic qubit 5 can be performed on the left rail (corresponding to column 6). The bottom component of the algorithm performs the corresponding Rx rotation, as this is the only component 2 assigned logical qubit 5. Due to the way the base network is constructed from the parity network, the Rx rotations of all logical qubit 5 can be implemented in the algorithm evolution step 105 of the alternating sequence. Alternatively, the Rx rotations can be performed simultaneously on each component 2, for example, in the last algorithm evolution step 106. As described above, this modifies the driver Hamiltonian, thereby modifying a portion of the quantum algorithm 6.

[0228] Through repetition Figure 12a However, after performing another encoding evolution step 105 using an inverted controlled NOT gate, another algorithmic evolution step 106 is performed under a different current encoding. Figure 12c Again, as Figure 12c As specified in the first sub-step, an Rzz operation is performed on nearest neighbor component 2 to implement the further Rzz operation indicated by quantum algorithm 6. This mode is relative to Figure 12b It is mirrored. Similarly, it can be viewed on the left rail (corresponding to the column). The top and bottom components 2 of the ) perform Rx quantum operations in a single component to implement instructions for performing Rx associated with logic qubits 5 and 2, respectively.

[0229] 2. Quantum Fourier Transform (QFT) QFT is a subroutine quantum algorithm for many important algorithms (e.g., Shor's decomposition algorithm). The standard quantum algorithm for QFT is as follows: Figure 13 The circuit diagram is shown. Quantum algorithm 6 includes a single-body instruction 61 in the form of an Adama gate (a box denoted by H) and a two-body instruction 62 in the form of a controlled phase gate (a box with an internal angle). The two-body instruction 62 involves all 5 pairs of logical qubits respectively. Therefore, quantum algorithm 6 will require a physical quantum system 1 with full pair connectivity to directly physically implement quantum algorithm 6.

[0230] The initial state of Quantum Algorithm 6 is not a specific state, but can be any input state that depends on QFT as a subroutine of the quantum algorithm, such as the Shor algorithm. The final state of Quantum Algorithm 6 produces the results of QFT in reverse order.

[0231] Controlled phase gate Instruction 72 is depicted by black dots and boxes connected by lines. The positions of the dots and boxes indicate the 5 pairs of logical qubits involved in instruction 62. The angles within the boxes indicate the phase shift. The size. Indicates when both logical qubits 5 are in the state. During the state transition, the state of logic qubit 5 shifts. The effect of the controlled phase gate on the two logic qubits 5 can be summarized as follows: , , and .

[0232] Figure 14 A circuit diagram of coded quantum computing 7 is shown, which is physically implemented. Figure 13 The quantum algorithm 6 is depicted. The encoded quantum computation takes the form of an alternating sequence between encoding evolution step 105 and algorithm evolution step 106. Boxes marked with H represent single-unit quantum operations 71 performing the Adama gate. (Solid lines and angles are used.) The box indicates that the angle inside the box is rotated around the z-axis. Single-unit quantum operation 71. (with dashed lines and angles) The box indicates that the angle inside the box is rotated around the x-axis. The single-unit quantum operation 71. Each line represents component 2 in the physical quantum system 1 with linear nearest neighbor connectivity. The italicized numbers in the circles represent the logical index of the corresponding component 2, that is, the index of the logical qubit 5 assigned to component 2.

[0233] Controlled phase gates can, under appropriate encoding, due to the relationship These are physically implemented as three individual quantum operations 71. For the central term in the above decomposition, the encoding requires that logical qubits i and j (i.e., the parity check of logical qubits i and j is encoded into component 2) be assigned to a component 2. For the external term in the above decomposition, the encoding requires that only one logical qubit i or j be assigned to a component 2. The three individual algorithmic actions 74 can be executed under different encodings, i.e., in different algorithmic evolution steps 106 of the alternating sequence.

[0234] Adama gates can be implemented as three single-unit quantum operations in 71 physical forms. The Adama gate acting on component 2 zero and four (i.e., external component 2) is implemented by directly executing the Adama gate (of course, this gate can also be decomposed).

[0235] Component 2 is initially prepared in any quantum state. The preparation of the quantum state can be accomplished using a prior quantum algorithm. Alternatively, an algorithm using QFT as its subroutine can define the input quantum state.

[0236] Component 2 is initially in an uncoded state, meaning that the italicized numbers of the logical index can directly correspond to the unique identifier of Component 2. In the following text, the bottom Component 2 is represented by the unique identifier zero, where the unique identifier increments from bottom to top.

[0237] Algorithm evolution step 106 involves executing the implementation under the current encoding. Figure 13 The quantum algorithm operation 74 is at least a partial action of certain instructions 61, 62 of the quantum algorithm 6. The "current encoding" of the first and last algorithm evolution steps 106 is an uncoded state, while in all other algorithm evolution steps 106, the parity of two logical qubits 5 is encoded into at least one component 2.

[0238] In this embodiment, achieving "at least some actions" means that the instruction can be decomposed and the decomposed components can be assigned to different algorithm evolution steps 106. In one algorithm evolution step 106, only a portion of the original instruction of the quantum algorithm 6 can be implemented.

[0239] The first encoding evolution step 105 involves a parity check encoding operation 75. This parity check encoding operation 75 takes the form of a controlled NOT gate. This parity check encoding operation 75 encodes the parity of component 2 zero and one into component 2 zero. Therefore, the logical index of component 2 zero changes from 0 to 01.

[0240] The second encoding evolution step 105 involves a parity check encoding operation 75. This parity check encoding operation 75 is implemented as a sequence of two controlled NOT gates. This parity check encoding operation 75 encodes the parity checks of component 2 zero, one, and two into component 2 one. The parity checks of the three components 2 correspond to the parity checks of logical qubit 5 zero and two, because component zero has already encoded the parity checks of logical qubit 5 zero and one.

[0241] The third coding evolution step 105 involves a set of two parity coding operations 75. The first parity coding operation 75 includes a controlled NOT gate that encodes the parity of component 2 zero and one into component zero (corresponding to the parity coding operation 75 of the first coding evolution step 105). The second parity coding operation 75 includes a sequence of two controlled NOT gates that encode the parity of component 2 one, two, and three into component two.

[0242] Similarly, the subsequent encoding evolution step 105 involves a set of parity check encoding operations 75 (where the set may contain only one element). These are formed such that the final state is unencoded, but the mapping of logical qubit 5 to component 2 has the reverse order (the italicized numbers have the reverse order).

[0243] The parity coding operation 75 of the first coding evolution step 105 is repeated in every other coding evolution step 105 of the alternating sequence. Other parity coding operations 75 are repeated in at least a portion of the alternating sequence in every other coding evolution step 105 of the alternating sequence.

[0244] In every two subsequent coding evolution steps 105 of the alternating sequence, a different set of parity check coding operations 75 are performed.

[0245] Figure 14 The coded quantum computing described in the text uses 7 QFT is physically implemented using controlled NOT gates and a total circuit depth of 5n-3. This outperforms existing techniques using swap gates, which require [a certain number of] preambles. A controlled NOT gate (see Holmes et al., “Impact of qubit connectivity on quantum algorithm performance”, Quantum Science and Technology 5 025009 (2020)) or the introduction of a second-order circuit depth (see Parks et al., “Reducing CNOT count in quantum Fourier transform for the linear nearest-neighbor architecture”, Scientific Reports (2023) 13:8638). Furthermore, regarding the number of individual quantum operations 71 and the total depth of individual quantum operations 71, Figure 14 The encoded quantum computing described in the paper 7 is superior to the standard QFT implementation on a fully paired, fully connected physical quantum system 1.

[0246] A comparison of resources for different methods is shown in Table B below. Existing technology I refers to "Impact of qubit connectivity on quantum algorithm performance" published by Holmes et al. in Quantum Science and Technology 5 025009 (2020), and existing technology II refers to "Reducing CNOT count in quantum Fourier transform for the linear nearest-neighbor architecture" published by Parks et al. in Scientific Reports (2023) 13:8638.

[0247] according to Figure 14 Another advantage of the encoded quantum computing 7 is that the reverse order inherent in quantum algorithm 6 is canceled out due to the reverse encoding following the encoded quantum computing 7.

[0248] On fully connected devices, reversing the order will require One controlled NOT gate and one time step are required, while on a physical quantum system 1 with linear nearest neighbor connectivity, 3n(n-1) / 2 controlled NOT gates and 3n time steps are needed (where the factor of 3 comes from decomposing the commutation gate into controlled NOT gates). When using Figure 14 When quantum computing reaches level 7, this additional overhead can be further saved.

[0249] General definition A set is non-empty and can contain one or more elements.

[0250] A subset is nonempty. A subset can contain all elements of a set (i.e., it does not have to be a proper subset). For example, a subset of the constituent parts can contain all the constituent parts of a quantum physical system.

[0251] A sequence can contain one or more elements.

[0252] Reference number list 1. Physical Quantum Systems 2 Components 3 Connections 4 devices 41 Control Unit 42 logic units 5 logical qubits 6. Quantum Algorithms 61 Instructions for performing single-unit quantum operations (single-unit instructions) 62 Instructions for performing many-body quantum operations (many-body instructions) 7. Quantum Computing 71 Single-unit quantum operations 72 Many-body quantum operations 73 Switching Gate 74 Algorithm Action Operations 75 Parity check encoding operation 76 Basic Quantum Operations 77 Controlled NOT gate 8 coding lines 91 parity check qubits 92-bit quantum bits 93. Constraints on Parity Check Quantum Bits 94. Constraints on the basis qubit 95. Constraints on parity-check qubits for the first subset 96. Constraints on parity-check qubits for the second subset 10 Quantum Computing Methods 100 Steps to prepare the initial quantum state 101 Steps in the Evolution of Physics Quantum Systems 102 Steps for measuring the final quantum state 103 Steps to determine the output 104 Output of quantum computing 105 Coding Evolution Steps 106 Algorithm Evolution Steps 200 Isin Hamiltonian 201 Steps to determine parameters 202 Steps for executing the subroutine quantum algorithm 203 Steps to read energy 204 Steps for checking termination conditions 205 Steps to read out a quantum state 206 Approximate ground state of the Ising Hamiltonian

Claims

1. A quantum computing method, comprising: Provides a physical quantum system (1) including component (2); Performing coded quantum computation (7) on the physical quantum system (1) includes: Prepare at least a portion of the physical quantum system (1) in an initial quantum state; Evolve the physical quantum system (1) to its final quantum state; Measuring at least a portion of the physical quantum system (1) to provide readout values; and The output of the encoded quantum computation (7) is determined based on the readout value. During at least a portion of the encoded quantum computation (7), the quantum states of at least a subset of components (2) are based on the encoded encoded quantum states. The evolution of the physical quantum system (1) to a final quantum state includes performing: a plurality of encoding evolution steps (105) for changing the encoding of the component (2), and a plurality of algorithm evolution steps (106) for at least a partial action of at least one of a plurality of instructions (61, 62) for physically implementing the quantum algorithm (6) under the current encoding, wherein at least some of the plurality of encoding evolution steps (105) and at least some of the plurality of algorithm evolution steps (106) are performed according to an alternating sequence, the alternating sequence alternating between the encoding evolution steps (105) and the algorithm evolution steps (106). At least one coding evolution step (105) in the alternating sequence includes performing a set of parity coding operations (75), wherein each parity coding operation (75) in the set of parity coding operations (75) is performed on a corresponding subset comprising at least two components (2), wherein each parity coding operation (75) in the set of parity coding operations (75) encodes the parity of all components (2) in the corresponding subset comprising at least two components (2) into at least one component (2) of the subset. The at least one algorithmic evolution step (106) in the alternating sequence includes performing at least one algorithmic action operation (74) on at least one component (2), wherein the at least one algorithmic action operation (74) physically implements at least a portion of the action of at least one of the plurality of instructions (61, 62) of the quantum algorithm (6) under the current encoding of the component (2).

2. The quantum computing method according to claim 1, wherein, The parity coding operation (75) in the set of parity coding operations (75) is executed in parallel in at least one coding evolution step (105) of the alternating sequence.

3. The quantum computing method according to claim 1 or 2, wherein, At least one parity coding operation (75) of the set of parity coding operations (75) performed in at least one coding evolution step (105) (preferably each parity coding operation (75) is performed by executing a basic quantum operation sequence, Wherein, the depth of the basic quantum operation sequence is less than five (preferably less than three); and / or The basic quantum operation sequence includes a subsequence of many-body quantum operations (72), wherein the depth of the subsequence is less than five (preferably less than three); and / or Wherein, at least one basic quantum operation in the basic quantum operation sequence (preferably each basic quantum operation) is performed on at most four (preferably at most two) components (2); and / or Wherein, at least one (preferably each) basic quantum operation is a controlled NOT gate (77), or an Rzz gate, or a gate corresponding to the controlled NOT gate (77), or an Rzz gate transformed by a single qubit basis transformation.

4. The quantum computing method according to any one of the preceding claims, wherein, At least one of the parity coding operations (75) is repeated in at least a portion of the alternating sequence, in each coding evolution step (105) of the alternating sequence, or every other coding evolution step (105).

5. The quantum computing method according to any one of the preceding claims, wherein, The instructions (61, 62) of the quantum algorithm (6) involve multiple logical qubits (5), wherein the encoding is represented by a mapping (preferably a birayed mapping) between the eigenstates of the logical qubits (5) under the selected basis and the eigenstates of the component (2).

6. The quantum computing method according to claim 5, wherein, The mapping enables: Each logical qubit (5) is assigned to at least one component (2), preferably wherein each logical qubit (5) is assigned to at most two components (2); and / or Each logical qubit (5) is assigned to a corresponding subset of component (2) of the connected component (2); and / or At least two logical qubits (5) are assigned to a component (2) and the parity of the at least two logical qubits (5) is encoded into the component (2).

7. The quantum computing method according to any one of the preceding claims, wherein, Each parity check coding operation (75) and / or each algorithm action operation (74) in the set of parity check coding operations (75) is performed on a subset of the connected components (2) or on a single component (2).

8. The quantum computing method according to any one of the preceding claims, wherein, The component (2) is connected to at most two other components (2) of the physical quantum system (1).

9. The quantum computing method according to any one of the preceding claims, wherein, A component (2) in a first subset of a component is connected to at most two other components (2) in the first subset, and a component (2) in a second subset of a component is connected to at most two other components (2) in the second subset, wherein the first subset and the second subset do not intersect, and wherein at least one component (2) in the first subset is connected to at least one component (2) in the second subset.

10. The quantum computing method according to claim 9, wherein, Each component (2) in the first subset is connected to at least one component (2) in the second subset (preferably one, two, or three components (2)), and each component (2) in the second subset is connected to at least one component (2) in the first subset (preferably one, two, or three components (2)).

11. The quantum computing method according to any one of the preceding claims, wherein, The number of the component (2) is less than or equal to the number of logical qubits (5) of the quantum algorithm (6), or less than or equal to twice the number of logical qubits (5) of the quantum algorithm (6).

12. The quantum computing method according to any one of the preceding claims, wherein, The quantum algorithm (6) includes multiple multibody instructions (62) associated with multiple subsets of logical qubits (5), wherein, during at least one algorithm evolution step (106) of the alternating sequence, the parity check of the logical qubits (5) in each subset of logical qubits (5) is encoded into at least one component (2) of the physical quantum system (1) according to the current encoding.

13. The quantum computing method according to any one of the preceding claims, wherein, The quantum algorithm (6) includes at least one multibody instruction (62) associated with at least one subset of logical qubits (5), wherein the at least one algorithmic action operation (74) that implements at least a portion of the action of the at least one multibody instruction (62) is performed on the component (2) during an algorithm evolution step (106) with a current encoding in which parity of the at least one subset of logical qubits (5) is encoded into the component (2), preferably wherein the at least one algorithmic action operation (74) is a single quantum operation (71).

14. The quantum computing method according to any one of the preceding claims, wherein, The quantum algorithm (6) includes at least one multibody instruction (62) associated with at least one subset of logical qubits (5), wherein the at least one algorithmic action operation (74) implementing at least a portion of the action of the at least one multibody instruction (62) includes one or more single-unit quantum operations (71) performed on one or more individual components (2), preferably wherein the at least one multibody instruction (62) instructs the execution of an Rzz operation or a controlled phase gate, and preferably wherein the at least one algorithmic action operation (74) includes performing a single-unit rotation on one or three individual components (2).

15. The quantum computing method according to any one of the preceding claims, wherein, The quantum algorithm (6) includes at least one multibody instruction (62) associated with at least one subset of logical qubits (5), wherein the at least one algorithmic action operation (74) implementing at least a portion of the action of the at least one multibody instruction (62) includes at least one multibody quantum operation (72) performed on a subset of the connected components (2), preferably wherein the at least one multibody instruction (62) instructs the execution of an Rzz operation or a controlled phase gate, and preferably wherein the at least one algorithmic action operation (74) includes the execution of an Rzz operation on a pair of connected components (2).

16. The quantum computing method according to any one of the preceding claims, wherein, The quantum algorithm (6) is a subroutine of the quantum Fourier transform algorithm or the variable quantum algorithm, preferably a subroutine of the quantum approximation optimization algorithm.

17. A device (4) for quantum computing, comprising: A physical quantum system (1), the physical quantum system (1) comprising components (2); Control unit (41), the control unit (41) is used to evolve and measure at least some of the components (2) in the components (2); A logic unit (42) is connected to the control unit (41). The logic unit (42) is configured to instruct the control unit (41) to perform coded quantum computation (7) on the physical quantum system (1), wherein the coded quantum computation (7) includes: Using the control unit (41), at least a portion of the physical quantum system (1) is prepared in an initial quantum state; Using the control unit (41), at least a portion of the physical quantum system (1) is evolved to the final quantum state; Using the control unit (41), at least a portion of the physical quantum system (1) is measured and readout values ​​are provided; During at least a portion of the encoded quantum computation (7), the quantum states of at least a subset of components (2) are based on the encoded encoded quantum states. The evolution of the physical quantum system (1) to a final quantum state includes performing: a plurality of encoding evolution steps (105) for changing the encoding of the component (2), and a plurality of algorithm evolution steps (106) for at least a partial action of at least one of a plurality of instructions (61, 62) for physically implementing the quantum algorithm (6) under the current encoding, wherein at least some of the plurality of encoding evolution steps (105) and at least some of the plurality of algorithm evolution steps (106) are performed according to an alternating sequence, the alternating sequence alternating between the encoding evolution steps (105) and the algorithm evolution steps (106). At least one coding evolution step (105) in the alternating sequence includes performing a set of parity coding operations (75), wherein each parity coding operation (75) in the set of parity coding operations (75) is performed on a corresponding subset comprising at least two components (2), wherein each parity coding operation (75) in the set of parity coding operations (75) encodes the parity of all components (2) in the corresponding subset comprising at least two components (2) into at least one component (2) of the subset. Wherein, at least one algorithmic evolution step (106) in the alternating sequence includes performing at least one algorithmic action operation (74) on at least one component (2), wherein the at least one algorithmic action operation (74) physically implements at least a portion of the action of at least one of the plurality of instructions (61, 62) of the quantum algorithm (6) under the current encoding of the component (2). Furthermore, the logic unit (42) is also configured to determine the output of the encoded quantum computation (7) based on the readout value.

18. The apparatus (4) according to claim 17, wherein, The device (4) is configured to perform the quantum computing method according to any one of claims 1 to 16.

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