Three-way hybrid quantum computing system and method

Abstract

The present disclosure describes a three-way hybrid quantum computing system that includes a classical computer, a quantum annealer, and a gate-based quantum computer. The system combines the unique strengths of each component to more efficiently solve complex computational tasks. The classical computer is responsible for general-purpose tasks, data storage, and control of the quantum components. The quantum annealer is used to solve optimization problems, while the gate-based quantum computer is used to execute more general algorithms. The system converts problems that group the commutants of a Hamiltonian into a quadratic unconstrained binary optimization (QUBO) problem, instructs a hybrid combination of the classical computer and the quantum annealer to solve and validate the results, and then utilizes a hybrid combination of the classical computer and the gate-based quantum computer to deploy the results to determine the results of all terms in each commutant group in the Hamiltonian in parallel. The system provides an output representing a solution to the original problem.

Description

Technical Field

[0001] This disclosure relates to a hybrid quantum computing system, and more particularly to a three-way hybrid quantum computing system comprising a classical computer, a quantum annealer, and a gate-based quantum computer, as well as a method for using said three-way hybrid quantum computing system. Furthermore, this disclosure relates to a classical processing unit and method for establishing a three-way hybrid quantum computing system. Background Technology

[0002] Currently, there are two main types of quantum computers under research and development: gate-based quantum computers and quantum annealers. Gate-based quantum computers are considered general-purpose machines because they can implement arbitrary quantum algorithms. These computers use quantum gates to manipulate qubits, the basic units of quantum information. Some quantum gates are similar to classical logic gates, but they operate on quantum states. Gate-based quantum computers perform complex computations by applying a series of quantum gates to qubits. These gates change the state of the qubits, thereby enabling the manipulation and computation of quantum information. Computation is performed through the interaction of qubits, and the quantum mechanical description of their states uses concepts such as entanglement and superposition.

[0003] On the other hand, quantum annealers are dedicated quantum computers designed primarily for optimization problems. Quantum annealing works by modeling the problem mathematically and then searching for the lowest energy state corresponding to the optimal solution. The system starts from a superposition state and gradually finds the lowest energy state through quantum fluctuations. If successful, the final state represents the solution to the optimization problem. The advantage of quantum annealers is that they can solve certain optimization problems more efficiently than classical computers. Problems such as the traveling salesman problem, protein folding, and supply chain optimization can all be solved using quantum annealing. However, these computers lack the general computational power of gate-based quantum computers, thus limiting their applicability to specific problem domains.

[0004] Current generation quantum computing algorithms typically employ a hybrid approach, strategically combining the advantages of quantum and classical computing. In this hybrid model, quantum resources (such as gate-based quantum computers, or alternatively quantum annealers) are used to perform specific tasks that can benefit from quantum advantages, such as performing complex computations or handling superposition and entanglement. Classical computers are then used to perform more conventional tasks, manage error correction, or process the output of quantum computations.

[0005] This dual-path hybrid design is widely adopted because it helps address one of the major challenges facing current quantum technologies—noise. Quantum systems are extremely sensitive to external disturbances that can lead to errors and loss of coherence. By employing a hybrid framework, the load on the quantum computer is reduced, and the classical system can handle the error-prone parts, such as the optimized loops used for fine-tuning quantum operations.

[0006] The purpose of this disclosure is to utilize the special capabilities of different types of quantum computers and the various technological advancements in hybrid quantum computer systems in an improved manner. Summary of the Invention

[0007] A hybrid quantum computing system is proposed, which utilizes classical processing units, quantum annealing units, and quantum gate-based digital units, aiming to leverage the unique advantages of each computing paradigm to solve complex computational tasks more efficiently.

[0008] Each component in this three-way hybrid quantum computing system contributes to the overall computational task. The classical processing units excel at performing a variety of general-purpose tasks, including data input / output (I / O) operations, processing classical algorithms, data storage, and error correction / mitigation. They also manage and control the operation of the quantum components and run the software that interfaces with them.

[0009] Classical processing units operate using binary data (bits) in one of two states (representing 0 or 1), based on classical computing principles. Classical processing units include any of the following: personal computers, laptops, or desktops that rely on a CPU to perform general-purpose tasks, such as running software applications; high-performance computers (HPCs), also known as supercomputers, which consist of thousands of CPUs and GPUs working together to perform highly complex calculations at high speeds, often used for scientific research, weather modeling, and simulation; computer clusters, consisting of a loosely or tightly connected group of computers that work together and can thus be considered a single system; CPUs (central processing units) that perform the calculations that enable the computer to run; CPU cores in a multi-core processor, or a combination of CPU and GPU (graphics processing unit). CPUs excel at general-purpose task management and decision-making, while GPUs specialize in image rendering and parallel execution of complex mathematical calculations. Together, they accelerate various types of computation, particularly tasks involving graphics, video processing, and certain scientific calculations. These systems are fundamentally different from quantum computers, which use qubits, which are in a superposition of states. Quantum computers are based on quantum mechanics, so they may be more powerful for certain tasks, such as factoring large numbers, optimizing complex systems, and simulating quantum phenomena.

[0010] Quantum annealing is a quantum computing paradigm primarily used for solving optimization problems. D-Wave is one of the most well-known companies manufacturing quantum annealing computers, such as the D-Wave Advantage. Their various quantum annealers have been commercialized and are used by many organizations and research institutions for complex optimization tasks. It is worth noting that the field of quantum computing, including quantum annealing, is rapidly evolving, and new advancements and market players are likely to emerge. This solution is not limited to or dependent on quantum annealing units from any particular company.

[0011] Quantum gate-based digital units (GNUs) are based on universal quantum processors and are capable of running any quantum algorithm. They are highly flexible and can use quantum gates to manipulate qubits to perform the widest range of quantum operations. They excel at executing universal quantum algorithms and provide a powerful approach to handling tasks requiring entanglement or superposition. Several companies offer GNUs, such as IBM, Rigetti Computing, IonQ, and Google Quantum. It should be noted that the field of quantum computing, including GNUs, is rapidly evolving, and new developments and market players may emerge. This solution is not limited to or dependent on GNUs from any particular company.

[0012] The proposed hybrid quantum computing system effectively combines classical computing with two quantum computing techniques: quantum annealing and gate-based quantum computing. This combination leverages the unique strengths of each component to solve complex problems described by Hamiltonians. The system includes a classical processing unit with input / output interfaces, a quantum annealing unit communicatively connected to the classical processing unit, and a quantum gate-based digital unit communicatively connected to the classical processing unit. The classical processing unit includes an input interface for inputting string representations of the Hamiltonians. The classical processing unit is configured to transform the problem of grouping commutation terms of the Hamiltonians into a representation of a quadratic unconstrained binary optimization (QUBO) problem and instruct the quantum annealing unit to process this QUBO problem. The quantum annealing unit is configured to process the QUBO problem and send the result to the classical processing unit. The classical processing unit is also configured to verify the result and, based on the result, determine one or more groups of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital unit, and instruct the quantum gate-based digital unit to process one or more groups of terms of the Hamiltonian. The quantum gate-based digital unit is configured to process each term in at least one set simultaneously and send the result to the classical processing unit. The classical processing unit also includes an output interface for outputting the result of processing the string representation of a given Hamiltonian.

[0013] The classical processing unit acts as the orchestrator for the entire system. It allows users or other systems to input Hamiltonians, which in physics are mathematical expressions describing the total energy of a system; in this context, however, they represent the problem to be solved. The classical processing unit transforms the Hamiltonian grouping problem into a quadratic unconstrained binary optimization (QUBO) form, the standard representation of optimization problems that quantum annealers can handle. It instructs the quantum annealing unit to solve this QUBO, receives the solution, and then verifies it. Based on the result, it identifies groups of terms in the Hamiltonian that can be processed in parallel by quantum-gate-based digital units. After the quantum units have completed their computations, the CPU collects the results, integrates them, and provides an output representing the solution to the original problem.

[0014] Quantum annealing units are specifically designed for solving optimization problems, particularly those that can be formulated as QUBO problems. Quantum annealers utilize quantum fluctuations (tunneling) to find the minimum energy state, which corresponds to the optimal solution to the QUBO problem. For certain types of difficult optimization problems, they can be faster than classical optimizers. Quantum annealers like the D-Wave system, designed specifically for QUBO problems, may offer more efficient solution paths than classical computers or gate-based quantum computers for certain complex optimization tasks.

[0015] Quantum gate-based digital units use gated quantum circuits to manipulate qubits and perform quantum computations. This type of quantum computation is applicable to a wider range of algorithms beyond optimization, such as factoring large numbers, searching unsorted databases, and simulating quantum systems.

[0016] Classical processing units further identify groups of Hamiltonian terms that can be processed simultaneously, meaning that quantum gate-based digital units can find the expected values ​​of many terms at the same time.

[0017] The described hybrid quantum computing system aims to optimize problem-solving capabilities by leveraging the strengths of classical computing, quantum annealing, and gate-based quantum computing in a coordinated manner. This approach aims to solve complex Hamiltonian-based problems more efficiently than each type of computation used individually.

[0018] In hybrid quantum computing systems, it is advantageous that the classical processing unit is configured to transform the representation of the Hamiltonian grouping problem into a representation of the quadratic unconstrained binary optimization (QUBO) problem by: the classical processing unit being configured to create a representation of the graph starting from a null graph, where vertices represent terms of the Hamiltonian; the classical processing unit being configured to determine the commutativity of each term of the Hamiltonian; and the classical processing unit being configured to add edges on the graph between two vertices representing non-commutative terms of the Hamiltonian.

[0019] Transforming the Hamiltonian grouping problem into a QUBO and subsequent graph representation (as described) is part of an optimization strategy for quantum computing. This approach is particularly advantageous for solving optimization problems and for leveraging the nature of quantum physics to achieve computational efficiency. By creating a graph where each vertex represents a term of the Hamiltonian, classical processing units effectively map the problem to a structure more suitable for analysis and optimization. This transformation leads to the formation of a graph coloring problem.

[0020] In quantum mechanics, two operators (or terms in a Hamiltonian) are said to commutate if the order of their actions does not change the result. In other words, when

[0021] (1)

[0022] When, that is, when their commutators (represented by the symbol [ ]) are zero, the two terms and Easy. Note that when At time, any two terms commutate trivially. The commutativity of terms in the Hamiltonian can be described in two different ways: qubit-wise commutativity (QWC) and generalized commutativity (GC).

[0023] In QWC, two Pauli terms are said to commute if they correspond to the same index in each other. For example, terms... and Easy, but with Not commutative. We can use QWC to create a set of terms such that all terms in the set commute bit-by-bit with every other term, for example... The idea is that all terms in a set can be measured simultaneously in the QDU 106, thus facilitating faster computation. QWC has been used in experimental demonstrations of searching for the expected value of small systems on quantum processors.

[0024] In GC (Garbage Collector), two Pauli strings are said to commute if the number of per-qubit commutations corresponding to the same index is not even. The advantage of GC is that it can contain more items in a group compared to QWC (Quadrant-Wave Collector). However, the advantage of QWC is the simplicity of simultaneously measuring items within a QWC group.

[0025] Knowing which terms commutate is crucial for parallel computation in quantum algorithms. The CPU checks the commutativity between terms.

[0026] In the diagram, an edge is added between the vertices representing non-commuting terms in the Hamiltonian. This edge indicates that, without additional consideration, these terms cannot be processed simultaneously directly within the same quantum gate sequence because their order affects the final quantum state. By calculating which operators commute, the CPU can determine which operators can be grouped and processed in parallel by quantum gate-based digital units. This parallel processing is a major advantage of quantum computing, enabling more efficient use of quantum resources.

[0027] The problem of grouping commutation terms of the Hamiltonian is transformed into a QUBO and its graph representation, making it possible to solve this grouping problem on a quantum annealer. The graph, with edges between vertices, represents the non-commutation terms and directly describes the constraints of the problem in the form required by these devices. The graph, and the number of colors required to color it, can be used to estimate the required physical quantum resources, such as the number of qubits needed to implement the problem on a quantum processor and the complexity of the connections between qubits.

[0028] Preferably, the configuration of the quantum annealing unit for handling quadratic unconstrained binary optimization (QUBO) problems includes: the quantum annealing unit is configured to group the vertices of the graph such that no two adjacent vertices are in the same group.

[0029] In the described hybrid quantum computing system, the quantum annealing unit processes the quadratic unconstrained binary optimization (QUBO) problem by grouping the vertices of the graph such that no two adjacent vertices are in the same group. This configuration is similar to the graph coloring problem—a combinatorial optimization problem. This strategy effectively corresponds to dividing the problem into subsets, where each group contains operations that can be executed in parallel without interfering with each other.

[0030] Graph coloring strategies advantageously simplify problem-solving by decomposing complex Hamiltonians into smaller, more manageable subproblems. Each group can be treated as a separate subproblem, rather than each Hamiltonian term being processed individually. Quantum annealers naturally evolve toward the system's ground state, represented by QUBO. Preprocessing and grouping problems using annealers enables faster computation when using a mix of gate-based and CPU-based systems.

[0031] Advantageously, the classical processing unit is configured to estimate the required number of groups such that no two adjacent vertices are in the same group, and instructs the quantum annealing unit to group the vertices into the estimated number of groups. This function is analogous to solving a graph coloring problem, where colors represent groups and the goal is to color the graph with as few colors as possible such that no two connected vertices share the same color. The CPU uses classical algorithms to estimate the required number of groups. These algorithms can range from heuristics to more complex approximate or even exact algorithms, depending on the problem size and time constraints. Once the number of groups is estimated, the CPU instructs the quantum annealing unit on how to group the vertices in a manner consistent with the estimated colors / classifications. By pre-estimating the groupings, the system can ensure that the quantum annealing unit can be configured with an efficient allocation of quantum resources (qubits and interactions) tailored to the problem structure. The CPU can use different strategies to estimate the groupings based on the complexity and nature of the specific problem, providing flexibility. For simpler problems, a simple greedy algorithm may suffice, while for more complex problems, more sophisticated techniques can be employed.

[0032] Preferably, in a hybrid quantum computing system, the classical processing unit is configured to instruct the quantum annealing unit to group vertices into a predetermined number of groups, wherein the predetermined number of groups is equal to the estimated number of groups minus 1. In a further configuration, the classical processing unit may be configured to further reduce the predetermined number of groups and instruct the quantum annealing unit to group vertices into the predetermined number of groups. Furthermore, the classical processing unit may be configured to further reduce the predetermined number of groups and instruct the quantum annealing unit to perform a predetermined number of annealing operations.

[0033] In the described hybrid quantum computing system, the classical processing unit employs an iterative approach, instructing the quantum annealing unit to group the vertices into several groups, where the initial number of groups equals the estimated number required for proper graph coloring minus 1. The classical processing unit then iteratively reduces the number of groups with each instruction, essentially attempting to find the minimum coloring required for a given graph.

[0034] By continuing to use a number of groups fewer than the estimated minimum, the system is essentially testing the boundaries of resource efficiency. It attempts to optimize the problem with fewer resources, thereby reducing the number of qubits and quantum operations required for computation. The strategy of the classical processing unit iteratively reducing the number of groups prompts the system to continuously improve its solution. If an efficient coloring is found using fewer groups, it indicates that the initial estimate was conservative and the system has found a more resource-efficient solution. If the quantum annealing unit can successfully group the vertices with fewer groups, computation can be saved. Fewer groups mean that more operations can be performed in parallel, thus reducing the overall computation time. Reducing the number of groups forces the quantum annealing unit to explore alternative configurations in the solution space. This may lead to the discovery of better solutions that were not apparent in the initial, fewer constraint iterations. The iteration stops when no efficient solution is found or when 1 is reached.

[0035] Advantageously, in hybrid quantum computing systems, classical processing units are configured to instruct quantum annealing units to process quadratic unconstrained binary optimization (QUBO) problems a predetermined number of times.

[0036] Repeated QUBO runs allow for statistical sampling of the solution space. Since quantum annealing is probabilistic, multiple runs may produce different solutions, and sampling these runs provides a more comprehensive understanding of the solution space's shape. Furthermore, like other quantum systems, quantum annealers are susceptible to noise and errors. Multiple runs of QUBO help find valid solutions when invalid solutions may initially arise due to errors. Additionally, quantum annealers work by finding the lowest energy state corresponding to the optimal solution in QUBO. Multiple iterations increase the likelihood of finding the global minimum because, due to the system's finite non-zero temperature, each run explores a different part of the solution space during annealing. However, during each run, a quantum annealing unit may get trapped in a local minimum—a solution that appears optimal within a finite range but is not globally optimal. Multiple runs mitigate this problem by providing more opportunities for the system to find a path to the global minimum.

[0037] Preferably, in a quantum computing system, the classical processing unit is further configured to instruct a quantum gate-based digital unit to process one or more sets of terms of the Hamiltonian a predetermined number of times, and to accumulate the results received from the quantum gate-based digital unit. By employing iterative quantum processing, the quantum gate-based digital unit is invoked multiple times to process terms of the Hamiltonian. Iteration can advantageously improve the accuracy of the results through repeated measurements and data accumulation. Quantum gate operations are prone to error due to decoherence and other quantum noise. Accumulating results across multiple iterations helps to average out random errors, thus providing a more accurate true value estimate. By processing each set multiple times, the CPU can use techniques such as error correction or mitigation algorithms to reduce the impact of noise inherent in current quantum gate-based systems. Quantum computing produces probabilistic results; by accumulating these results over multiple runs, the accuracy of the expected value can be significantly improved, making it possible to distinguish closely competing quantum states.

[0038] Furthermore, a method for processing Hamiltonians is provided, executed by a hybrid quantum computing system including a classical processing unit, a quantum annealing unit, and quantum gate-based digital units. The classical processing unit includes an input / output interface for inputting a representation of the Hamiltonian. The quantum annealing unit is communicatively connected to the classical processing unit, and the quantum gate-based digital units are also communicatively connected to the classical processing unit. The provided method includes the following steps: The classical processing unit receives a representation of the Hamiltonian via the input interface, converts the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization problem (QUBO), and instructs the quantum annealing unit to process the QUBO. The quantum annealing unit processes the QUBO and sends the result to the classical processing unit. The classical processing unit verifies the result and, based on the result, determines one or more sets of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital units, and instructs the quantum gate-based digital units to process the one or more sets of terms of the Hamiltonian. The quantum-gate-based digital unit outputs the bit string required to simultaneously process the expected values ​​of at least one item in a group and sends the result to the classical processing unit. The classical processing unit uses the bit string accumulated from the quantum-gate-based unit to calculate the expected value of each item in the group. This process is repeated iteratively until all groups have been processed.

[0039] The described method for processing Hamiltonians using a hybrid quantum computing system is a sophisticated process that invokes both classical and quantum computing resources. The system architecture combines classical processing units with quantum computing units (specifically quantum annealing units and quantum gate-based digital units) configured to handle different aspects of the overall problem.

[0040] Using classical front-ends as input enables seamless integration with existing computing systems and facilitates the preparation of complex quantum problems. The step of converting the Hamiltonian to a QUBO makes the problem suitable for processing by a quantum annealer, which leverages its native hardware design to efficiently solve optimization problems. By entrusting the problem to a quantum annealer, the system utilizes quantum tunneling and superposition, allowing it to reach the optimal solution faster than classical algorithms. This is because quantum annealing explores multiple solutions even under the same input conditions, potentially leading to a globally optimal solution.

[0041] This method advantageously employs a coordinated approach that combines classical problem formulation and verification with the capabilities of quantum computing, thereby handling complex problems represented by Hamiltonians more efficiently than either classical or quantum methods alone.

[0042] Advantageously, the classical processing unit transforms the representation of the Hamiltonian into a representation of a quadratic unconstrained binary optimization (QUBO) problem by the following steps: the classical processing unit creates a graph representation starting from the zero graph, where vertices represent terms of the Hamiltonian; determines the commutativity of each term of the Hamiltonian; and adds an edge on the zero graph between two vertices representing non-commutative terms of the Hamiltonian.

[0043] Advantageously, the steps of a quantum annealing unit in handling quadratic unconstrained binary optimization (QUBO) problems include the following: the quantum annealing unit groups the vertices of the graph such that no two adjacent vertices are in the same group. Knowing which terms commute allows for grouping terms that can be processed simultaneously, thereby optimizing computational efficiency.

[0044] Advantageously, the provided method further includes the following steps: the classical processing unit estimates the required number of groups such that no two adjacent vertices are in the same group, and instructs the quantum annealing unit to group the vertices into the estimated number of groups. Advantageously, the classical processing unit instructs the quantum annealing unit to group the vertices into a predetermined number of groups, wherein the predetermined number of groups is equal to the estimated number of groups minus 1. Advantageously, the classical processing unit further reduces the predetermined number of groups and instructs the quantum annealing unit to group the vertices into the predetermined number of groups. Advantageously, the step of reducing the predetermined number of groups and instructing the quantum annealing unit is performed a predetermined number of times.

[0045] Advantageously, the method also includes a step in which a classical processing unit accumulates the results received from a quantum gate-based digital unit, wherein the steps of the classical processing unit instructing the quantum gate-based digital unit to process one or more sets of Hamiltonian terms and the steps of accumulating the results received from the quantum gate-based digital unit are repeated a predetermined number of times.

[0046] A classical processing unit for establishing a hybrid quantum computing system is also provided, wherein the classical processing unit is communicatively connected to a quantum annealing unit and to a quantum gate-based digital unit. The classical processing unit includes an input interface for inputting a representation of the Hamiltonian. The classical processing unit is configured to convert a representation of a Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization problem (QUBO), instruct the quantum annealing unit to process the QUBO, receive results from the quantum annealing unit, verify the results, and based on the results determine one or more sets of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital unit, instruct the quantum gate-based digital unit to process at least one set of terms of the Hamiltonian simultaneously, and receive results from the quantum gate-based digital unit. The classical processing unit also includes an output interface for outputting a representation of the result of processing the Hamiltonian.

[0047] Preferably, the configuration of the classical processing unit to transform the representation of the Hamiltonian grouping problem into a representation of the quadratic unconstrained binary optimization (QUBO) problem includes: the classical processing unit being configured to create a graph representation starting from the zero graph, wherein vertices represent terms of the Hamiltonian; the classical processing unit being configured to determine the commutativity of each term of the Hamiltonian; and the classical processing unit being configured to add edges on the zero graph between two vertices representing non-commutative terms of the Hamiltonian.

[0048] The classical processing unit is also advantageously configured to estimate the number of groups required such that no two adjacent vertices are in the same group, and to instruct the quantum annealing unit to group the vertices into the estimated number of groups.

[0049] Preferably, the classical processing unit is further configured to instruct the quantum annealing unit to group vertices into a predetermined number of groups, wherein the predetermined number of groups is equal to the estimated number of groups minus 1.

[0050] The classical processing unit is also advantageously configured to further reduce the predetermined number of groups, and instructs the quantum annealing unit to group the vertices into the predetermined number of groups.

[0051] The classical processing unit is also configured to further reduce the predetermined number of groups and instruct the quantum annealing unit to reach a predetermined number of times.

[0052] Preferably, the classical processing unit is also configured to instruct the quantum annealing unit to process the quadratic unconstrained binary optimization (QUBO) problem a predetermined number of times.

[0053] The classical processing unit is also advantageously configured to instruct the quantum gate-based digital unit to process one or more sets of Hamiltonian terms a predetermined number of times, and to accumulate the results received from the quantum gate-based digital unit.

[0054] A method for processing Hamiltonians is also provided, executed by a classical processing unit including an input / output interface for inputting a representation of the Hamiltonian and communicatively connected to a quantum annealing unit and a quantum gate-based digital unit. The method includes the following steps: receiving a representation of the Hamiltonian via the input interface; converting the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization problem (QUBO); instructing the quantum annealing unit to process the quadratic unconstrained binary optimization problem (QUBO); receiving a result from the quantum annealing unit; verifying the result; determining, based on the result, one or more sets of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital unit; instructing the quantum gate-based digital unit to process each term in at least one set of terms of the Hamiltonian simultaneously; receiving the result from the quantum gate-based digital unit; and outputting a representation of the result of processing the Hamiltonian.

[0055] Advantageously, the classical processing unit transforms the representation of the Hamiltonian grouping problem into a representation of the quadratic unconstrained binary optimization (QUBO) problem by the following steps: the classical processing unit creates a graph representation starting from the zero graph, where vertices represent terms of the Hamiltonian; determines the commutativity of each term of the Hamiltonian; and adds an edge on the zero graph between two vertices representing non-commutative terms of the Hamiltonian.

[0056] Preferably, the method further includes the steps of: estimating the number of required groups such that no two adjacent vertices are in the same group, and instructing the quantum annealing unit to group the vertices into the estimated number of groups.

[0057] The method advantageously further includes the step of instructing the quantum annealing unit to group the vertices into a predetermined number of groups, wherein the predetermined number of groups is equal to the estimated number of groups minus 1.

[0058] Preferably, the method further includes the steps of: further reducing the predetermined number of groups, and instructing the quantum annealing unit to group the vertices into the predetermined number of groups.

[0059] Advantageously, the predetermined number of groups is reduced and the step of instructing the quantum annealing unit to be performed a predetermined number of times is executed.

[0060] Preferably, the method further includes the step of accumulating the results received from the quantum gate-based digital unit, wherein the steps of the classical processing unit instructing the quantum gate-based digital unit to process one or more sets of Hamiltonian terms and the step of accumulating the results received from the quantum gate-based digital unit are repeated a predetermined number of times. Attached Figure Description

[0061] Figure 1 A high-level schematic diagram outlining the components and connections of a hybrid quantum computing system is shown.

[0062] Figure 2 A graph is shown, in which indexed vertices represent terms and edges represent noncommutativity between terms for the example Hamiltonians given in equation (3).

[0063] Figure 3 A graph is shown that visualizes the QUBO expressions for the different problem Hamiltonians given in Table 3 when 10... 3 The total number of valid solutions obtained in each sampling is a function of the number of qubits required to implement the problem on a QAU. Detailed Implementation

[0064] Figure 1 A high-level schematic diagram outlining the components and connections of a hybrid quantum computing system 100 is shown. The system includes a classical processing unit 102 (CPU), a quantum annealing unit 104 (QAU), and a quantum gate-based digital unit 106 (QDU).

[0065] The classical processing unit 102 manages the system's inputs and outputs and orchestrates the interaction between quantum computing and classical computing. The classical processing unit 102 has an input / output interface (not shown). This interface acts as the point of interaction with the external world, whether it be other computer systems, sensors, or human operators.

[0066] Quantum annealing unit 104 is connected to classical processing unit 102. The quantum annealing unit is a module specifically designed for solving certain types of optimization problems. The connection indicates that the classical processing unit can send instructions 108 to the annealing unit and receive results 110 (preferably in bit string form), as indicated by the corresponding arrows. Quantum gate-based digital unit 106 is also connected to classical processing unit 102. Quantum gate-based digital unit 106 represents another quantum processing mode, capable of running a different set of algorithms than the annealing unit. Again, the connection indicates bidirectional communication (see corresponding arrows), with classical processing unit 102 sending parameters 112 (such as variational parameters) and instructions 114 to this unit and receiving outputs 116 (preferably in bit string form) from the corresponding output interface 118. Parameters from classical processing unit 102 are received by quantum gate-based digital unit 106 via input interface 120. Correspondingly, quantum annealing unit 104 receives instructions 108 via input interface 122 and sends its output via output interface 124.

[0067] The overall layout is designed to demonstrate how these disparate elements can be integrated into a single system. The classical processing unit 102 acts as a coordinator and controller, transforming the Hamiltonian into a format suitable for each quantum unit, and then combining the strengths of the two quantum processors to address the complexity of the current problem. Each unit is shown as an integral part of the system, working collaboratively under the management of the classical processing unit 102 to achieve results that are difficult to handle individually by either classical or single quantum systems.

[0068] In the following sections, we further describe this by focusing on the problem of finding the ground-state energy of a given N-qubit Hamiltonian with m terms. Figure 1 ,

[0069] (2)

[0070] in, In the above equation (2), ,in, , , It is a Pauli matrix, and Let be the identity matrix. It is known that finding the ground state energy of a problem described in the form of equation (2) is classically intractable in general. This is because the classical memory required to store quantum state vectors composed of complex numbers grows exponentially.

[0071] Figure 1 This illustrates how a quantum computer can be used to find the ground state energy. The problem Hamiltonian (see Equation (2)) is input as a string representation into the classical central processing unit 102. This information is stored in a corresponding storage device 126 for ungrouped terms. These ungrouped terms undergo several stages of processing within the CPU 102 to transform them into a quadratic unconstrained binary optimization problem (QUBO), which is stored in a storage device 128 for the QUBO and then sent to the QAU 104 along with other instructions 108. These instructions 108 may include annealing time (as shown by arrow 130), qubit mapping, chain strength, number of samples, etc., and are controlled by predetermined settings (such as default values) or settings provided via an input interface (not shown) along with the representation of the Hamiltonian. The QAU 104 attempts to solve the QUBO problem and outputs a bit string 110, which is processed in the CPU 102. The CPU 102 checks the validity of the solution obtained from the QAU 104 in a verifier 132 provided by the CPU 102. Valid solutions are stored in the corresponding storage device 134 for grouping items. A valid solution is then selected from the storage device 134 for grouping items and used for the next stage of calculation, and forwarded to the energy calculator 136 provided as part of the CPU 102.

[0072] The next stage involves the integration of CPU 102 with quantum gate-based digital unit 106. This setup is preferably used within the context of a variational quantum eigenvalue solver. Computation begins by providing initial parameters to a classical optimization algorithm (described as optimizer 138) provided by CPU 102. CPU 102 then passes these parameters 140, embedded in the quantum circuitry, to QDU 106. CPU 102 also passes additional instructions 114 to QDU 106. For our purposes, the relevant instructions 114 are the number of samples and the measurement basis of a set of terms in the problem Hamiltonian, but may also include hardware-specific instructions such as microwave pulses.

[0073] QDU 106 executes circuit 142 for a given set of parameters 140 and instructions 114, generating bit strings as output 116. These bit strings are accumulated in CPU 102 using accumulator 144, which also serves as a storage unit. Accumulator 144 holds bit strings corresponding to different groups obtained from QAU 104. Once enough bit strings have been accumulated, they are used to calculate the energy of all items in all groups, thus obtaining the energy of the entire Hamiltonian. This energy is then a scalar value minimized by the optimizer in subsequent iterations. Processing stops when the optimizer can no longer minimize the energy or when a predetermined number of iterations is reached.

[0074] In the following sections, we will explain in detail how the above process is implemented. We will discuss the commutativity of the terms given in Equation (1) and how to use the graph coloring problem to form commutative groups. We will illustrate the process step by step with a simple example.

[0075] While we aim to maximize the size of each group, the core problem is minimizing the number of groups. Therefore, we seek to solve the minimum clique cover problem, where each clique is a set of commutation terms. If the minimum clique cover problem is represented by a graph... Given, its supplementary diagram The corresponding graph coloring problem is given. Both of these belong to the category of problems generally considered NP-hard. The graph coloring problem can be transformed into a quadratic unconstrained bivariate optimization (QUBO) problem and solved on QAU 104. This section briefly describes the steps required to achieve this goal.

[0076] The problem is input as a list of strings, where each string of length N corresponds to an item in a Hamiltonian and is converted into an integer format representing the index of a Pauli term. This format facilitates manipulation to find the commutativity of each item with every other item. The commutativity information is encoded into the graph as follows: [The graph is then constructed with...] A graph with nodes, where... It is the total number of terms in the Hamiltonian. If a term is given... With another item Not easy, that is Then at index and Add an edge between the vertices.

[0077] In graph coloring, two adjacent vertices are not allowed to have the same color. In our problem, two non-commuting items cannot be in the same group. Therefore, by creating edges between the indices representing non-commuting items, we successfully transform the problem into a graph coloring problem. Solving the graph coloring problem will provide us with a solution to the original problem (i.e., finding groups of commuting items).

[0078] As an example, consider the following arbitrary Hamiltonian:

[0079] (3)

[0080] Commutativity between items, such as Figure 2 As shown in the figure. Figure 2 A graph is shown, in which indexed vertices represent terms, and edges represent noncommutativity between terms for the example Hamiltonians given in equation (3), while vertex coloring (solid circle, dashed circle, thin dashed circle) represents a way of coloring the graph.

[0081] The terms are indexed from left to right in the order they appear in Equation (3). An edge between any two terms represents the per-qubit noncommutativity of those terms. For general noncommutativity, the graph will differ. The minimum number of colors required to color this graph is 3, which is called the graph's chromatic number. Figure 2 In the diagram, different colors are represented by solid circles (vertices 1, 2, and 4), dashed lines (vertices 0), and thin dashed lines (vertices 3). Note that... Figure 2 The coloring shown is not unique; for example, vertex 1 can also have a dashed line. According to Figure 2 With this coloring scheme, we can simultaneously measure the items. , and .

[0082] In the following sections, we briefly summarize the steps required to transform the graph coloring problem into a QUBO problem. Suppose we want to color a graph using exactly K colors. Let... For a binary variable, if the vertex Assigned color ,but Otherwise, it is 0. Graph coloring has two constraints: (a) each vertex must be assigned a color, and (b) adjacent nodes are always assigned different colors.

[0083] Apply constraint (a) such that:

[0084] (4)

[0085] Here, N is the number of vertices in the graph. Therefore, the binary variable takes the value 1 for only one of the K colors. We note... Because the variable is binary. Constraint (b) is applied such that:

[0086] in (5)

[0087] And this applies to all adjacent vertices i and j. The task then is to find the minimum value of the following problem:

[0088] (6)

[0089] in, It is equivalent to our model The matrix, and incorporates all information about our problem. Equations (4) and (5) are transformed into... The steps involve using two different transformations and using a single subscript to penalize violations of the problem constraints. For a given graph... , The creation was completed automatically on a CPU 102. In this work, we used the qubogen package to generate... matrix.

[0090] In this section, we present the results for two cases. First, we demonstrate one use case of our process where we find the ground-state energy of a small two-qubit Hamiltonian using a hybrid QAU-CPU-QDU process. Second, we employ Hamiltonians with different numbers of qubits and terms, and use both QWC and GC, utilizing QAU104 to group the terms into commutation sets.

[0091] This process is demonstrated by searching for the ground-state energy of the H2 molecule, whose Hamiltonian is given by the following equation:

[0092] (7)

[0093] The commutativity of each item is computed relative to all other items using QWC. In this process, an edge is added between two non-commuting vertices (representing items) on the zero graph using the Python package networkx. If we remove vertex 0 and its edge, and then... Assigned to vertex 3. Assigned to vertex 1, Assigned to vertex 2, Assigning vertex 4, the final shape is... Figure 2 The same applies. The networkx package provides a built-in greedy algorithm that can color the graph with two colors, which are also chromatic numbers.

[0094] The penalty variable was set to 4, and the number of colors was set to 2. The required number of qubits is equal to the product of the number of colors and the number of vertices. Eight qubits were used in this example. The sample size was set to 1000. The QAU 104 used was DWaveAdvantage System version 5.3. The raw data obtained are listed in Table 1. Table 1 shows the energy and occurrence frequency associated with five unique bit strings obtained from QAU 104 when sampling 1000 times. The energy in this table is dimensionless.

[0095]

[0096] Table 1

[0097] The bit string obtained from QAU 104 is in the "verifier" (see Figure 1 The data in Table 1, with an energy of -16, are processed to check if they satisfy all the constraints of the problem. Only the top two rows of data in Table 1 satisfy the constraints. These two bit strings correspond to the data that will be used with... The vertex corresponding to an item is colored to distinguish it from the other three vertices. From the first bit string, we obtain the group. and We note that sampling QAU 104 automatically yields multiple possible valid solutions (if they exist). Invalid solutions also appear in the samples, though very infrequently in this case.

[0098] The next step is to prepare the parameterized hypothesis (ansatz) on QDU 106. For our problem, we adopt the following hypothesis:

[0099] (8)

[0100] for For any value within the range, the energy is determined by Given, where, assuming It is normalized. The ground state energy is given by the following equation:

[0101] (9)

[0102] in, Corresponding to the location of the global minimum Value. For the Hamiltonian given by equation (7) and the hypothesis given by equation (8), the global minimum is located at For demonstration purposes, we have omitted the search... Instead of using the optimization process, it directly uses it to calculate the ground state energy on IBM-Q QDU Jakarta, Manila, Perth, Nairobi, and ideal simulators.

[0103] Using the naive method, all four items are measured separately, thus requiring four trials. The QWC grouping method requires only two trials, one in... Under the base, another time in The base is prepared using a suitable rotation gate. When using QWC, and The energy used by the item is We use the obtained bit string for calculation. In each experiment, we sample 2 bits from the QDU 106. 13 The accuracy of the final energy can be improved by sampling more times.

[0104] The energies obtained from QDU 106 are listed in Table 2. Table 2 shows the ground state energies obtained for different QDUs using naive grouping and QWC grouping. The theoretical value is -0.192. The energies in this table are in Hartley atomic units.

[0105]

[0106] Table 2

[0107] Results from the ideal simulator can be used as a benchmark for comparison with results from IBM Q devices. We used four different devices and found the energy using (1) naive grouping (where all terms are measured separately) and (2) QWC grouping, respectively. We found that the energies in both cases were close to each other, as expected. The advantage of the QWC grouping method in this case is that it requires only half the computation time of the naive grouping method, as it only requires two runs. We noted that the device performance varied, and no device was able to find a ground-state energy that matched the accuracy of the simulator. This reflects the fact that the current generation of devices is in the era of noisy medium-scale quantum (NISQ). The energy might be slightly improved if the circuit parameters were optimized individually for each device; however, this is not relevant to the demonstration in our setup.

[0108] This section demonstrates how QAU 104, QDU 106, and CPU 102 can be used together in a hybrid setup to execute the proposed method. This hybrid method is executed on a currently available practical quantum computer.

[0109] We now shift our focus to graph coloring problems for solving larger problems on QAU 104. We consider Hamiltonians that are either already used as prototypes on current-generation QDUs or have the potential to be used soon. These include small molecules, Hubbard models, and Heisenberg models. We use the Open-Fermion package to generate Hamiltonians for Hubbard models. The QAU 104 used is DWave Advantage System version 5.3 and DWave Advantage2 prototype 1.1.

[0110] Hamiltonians from quantum chemistry and Hubbard models are difficult problems to group into commutative terms. They offer the advantage that the number of terms in molecular Hamiltonians can be increased or decreased by choosing smaller or larger basis sets, thus altering the problem size and difficulty as needed. Alternatively, the one-dimensional Heisenberg model is trivially divided into three groups using QWC and serves as a benchmark problem for QAU 104 and classical greedy solvers.

[0111] Sometimes, a Hamiltonian may contain terms that commutate with all other terms. In graph coloring, these terms are not part of the connected graph because their commutators with all other terms are zero. These terms can be grouped into any group. In the example below, we simplify the problem by removing these terms from the Hamiltonian. Furthermore, when using the Jordan-Wigner (JW) transformation, it is common to encounter terms that only have The terms of a matrix product. Since only terms containing such products are trivially commutative, we can remove them from the terms and group them separately.

[0112] Table 3 shows the term grouping results for the greedy algorithm and the QAU 104 solver. Except for three cases, QWC and GC used the same number of terms. The terms in parentheses are for the GC term. G and QAU 104 represent the greedy algorithm and the quantum annealing unit, respectively. QAU104 cannot solve the per-qubit case of Hubbard model lattices.

[0113]

[0114] Table 3

[0115] Table 3 shows the results of grouping the commutation terms for different Hamiltonians. The number of terms is listed for each case. Note that in equation (7)... The term commutes with all terms when using GC. Therefore, it is removed when using GC. The number of terms for the LiH molecule is too large for the available QAU. Therefore, we only selected a subset. In the case of the Hubbard model with a 2×2 lattice, it has 28 terms, and we removed 8 Z-only terms in the QWC case. In some cases, QWC or GC does not use the same number of terms due to term removal, and in such cases, the number of terms in parentheses is the number of terms in the GC case.

[0116] We first run a greedy algorithm to find the minimum number of colors required to color the graph. Then we let QAU104 color the same graph using this number of colors. Molecules and Hubbard Hamiltonians need to be converted to spin Hamiltonians using parity transformations, Jordan-Wigner (JW) transformations, or Bravyi-Kitaev (BK) transformations. This is one of the reasons why H2 Hamiltonians have different numbers of terms. We observe that, except for the QWC of the Hubbard model, QAU 104 correctly colors the graph in all cases.

[0117] Figure 3 For each question given in Table 3, QAU was sampled 10. 3 The number of valid solution samples obtained at this time. The x-axis enumerates the number of qubits required to implement the problem on QAU 104, which is the product of the number of terms and the number of colors for a given problem. We observe a general trend that the frequency of obtaining valid samples decreases as the number of qubits increases, eventually approaching zero. No valid solutions were found in both cases. There are two outliers in the data, located at qubit numbers of 120 and 180, corresponding to the GC and QWC cases for a 1×20 Heisenberg model lattice. These are benchmark problems with known solutions, but provide a relatively large problem size to test QAU 104. However, they also follow the general trend that the number of valid samples decreases as the number of qubits increases.

[0118] Greedy algorithms are a useful tool for finding the optimal coloring for the prototype problem we demonstrated, as well as some other small-scale problems we tested. However, because it is heuristic, it is likely to fail to find the coloring with the fewest colors as the problem size increases. Furthermore, greedy algorithms employ different strategies to find solutions. For example, we used a maximum-first strategy, which has a time complexity of O(n log n). ,in, and They are The number of vertices and edges in the array. For one problem we tested, namely the GC case of a 3×3 Heisenberg lattice (see Table 3), this strategy failed to find the optimal coloring. Interestingly, QAU 104 was able to find the correct solution using three instead of four colors.

[0119] Due to the way QUBO is constructed, QAU 104 always requires the desired number of colors as input. Finding the minimum number of colors required is typically an NP-hard problem. Therefore, a hybrid approach is preferred, which begins with a solution obtained from a greedy algorithm and feeds it into an annealer, which then attempts to improve the solution by using fewer colors. This can be achieved using reverse annealing. This approach will have a QAU-CPU loop, similar to the QDU-CPU loop in variational methods.

Claims

1. A hybrid quantum computing system (100), comprising: Classic processing unit (102). The quantum annealing unit (104) is communicatively connected to the classical processing unit. The quantum gate-based digital unit (106) is communicatively connected to the classical processing unit. The classical processing unit (102) includes an input interface for inputting the representation of the Hamiltonian. The classical processing unit (102) is configured to convert the representation of the Hamiltonian into a representation of the quadratic unconstrained binary optimization problem (QUBO). The classical processing unit (102) is configured to instruct the quantum annealing unit (104) to process the quadratic unconstrained binary optimization problem (QUBO). The quantum annealing unit (104) is configured to process the quadratic unconstrained binary optimization QUBO problem and send the result to the classical processing unit (102). The classical processing unit (102) is configured to verify the result and, based on the result, determine one or more sets of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital unit (106). The classical processing unit (102) is configured to instruct the quantum gate-based digital unit (106) to process one or more sets of terms of the Hamiltonian. The quantum gate-based digital unit (106) is configured to process at least one item in a set simultaneously and send the result to the classical processing unit (102). The classical processing unit (102) includes an output interface for outputting a representation of the result of processing the Hamiltonian.

2. The hybrid quantum computing system according to claim 1, wherein, The configuration of the classical processing unit to convert the representation of the Hamiltonian into a representation of a quadratic unconstrained binary optimization (QUBO) problem includes: the classical processing unit (102) being configured to create a graph representation starting from a zero graph, wherein vertices represent terms of the Hamiltonian; the classical processing unit (102) being configured to determine the commutativity of each term of the Hamiltonian; and the classical processing unit (102) being configured to add an edge on the zero graph between two vertices representing non-commutative terms of the Hamiltonian.

3. The hybrid quantum computing system according to claim 2, wherein, The configuration of the quantum annealing unit for processing the quadratic unconstrained binary optimization (QUBO) problem includes: the quantum annealing unit (104) is configured to group the vertices of the graph into groups such that no two adjacent vertices are in the same group.

4. The hybrid quantum computing system according to claim 3, wherein, The classical processing unit (102) is configured to estimate the number of required groups such that no two adjacent vertices are in the same group, and instruct the quantum annealing unit (104) to group the vertices into the estimated number of groups.

5. The hybrid quantum computing system according to claim 4, wherein, The classical processing unit (102) is configured to instruct the quantum annealing unit (104) to group the vertices into a predetermined number of groups, wherein the predetermined number of groups is equal to the estimated number of groups minus 1.

6. The hybrid quantum computing system according to claim 5, wherein, The classical processing unit (102) is configured to further reduce the predetermined number of groups and instructs the quantum annealing unit (104) to group the vertices into the predetermined number of groups.

7. The hybrid quantum computing system according to claim 6, wherein, The classical processing unit (102) is configured to further reduce the predetermined number of groups and instruct the quantum annealing unit (104) to reach a predetermined number of times.

8. The hybrid quantum computing system according to any one of the preceding claims, wherein, The classical processing unit (102) is configured to instruct the quantum annealing unit (104) to process the quadratic unconstrained binary optimization QUBO problem a predetermined number of times.

9. The quantum computing system according to any one of the preceding claims, wherein, The classical processing unit (102) is also configured to instruct the quantum gate-based digital unit (106) to process the one or more sets of items of the Hamiltonian a predetermined number of times, and to accumulate the results received from the quantum gate-based digital unit (106).

10. A method for processing Hamiltonians, said method being performed by a hybrid quantum computing system (100), said hybrid quantum computing system comprising: A classical processing unit (102) includes an input interface and an output interface for inputting representations of Hamiltonians; a quantum annealing unit (104) communicatively connected to the classical processing unit (102); and a quantum gate-based digital unit (106) communicatively connected to the classical processing unit (102); the method includes the following steps: The classical processing unit (102) receives the representation of the Hamiltonian via the input interface. The representation of the Hamiltonian is transformed into a representation of the quadratic unconstrained binary optimization problem (QUBO). The quantum annealing unit (104) is instructed to process the quadratic unconstrained binary optimization problem QUBO. The quantum annealing unit (104) processes the quadratic unconstrained binary optimization QUBO problem and sends the result to the classical processing unit (102). The classical processing unit (102) verifies the result and, based on the result, determines one or more sets of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital unit (106). The quantum gate-based digital unit (106) is instructed to process the one or more sets of terms of the Hamiltonian. The quantum gate-based digital unit (106) processes at least one item in a set simultaneously and sends the result to the classical processing unit (102). The classical processing unit (102) outputs a representation of the result of processing the Hamiltonian via the output interface.

11. The method according to claim 10, wherein, The step of the classical processing unit (102) converting the representation of the Hamiltonian into a representation of a quadratic unconstrained binary optimization (QUBO) problem includes the following steps: The classical processing unit (102) creates a graph representation starting from the zero graph, where vertices represent terms of the Hamiltonian; determines the commutativity of each term of the Hamiltonian; and adds an edge on the zero graph between two vertices representing non-commutative terms of the Hamiltonian.

12. The method according to claim 11, wherein, The steps of the quantum annealing unit (104) in processing the quadratic unconstrained binary optimization QUBO problem include the following steps: The quantum annealing unit (104) groups the vertices of the graph into groups such that no two adjacent vertices are in the same group.

13. The method according to claim 12, wherein, It also includes the following steps: The classical processing unit (102) estimates the number of groups required such that no two adjacent vertices are in the same group, and instructs the quantum annealing unit (104) to group the vertices into the estimated number of groups.

14. The method of claim 13, further comprising the step of: The classical processing unit (102) instructs the quantum annealing unit (104) to group the vertices into a predetermined number of groups, wherein the predetermined number of groups is equal to the estimated number of groups minus 1.

15. The method of claim 14, further comprising the step of: The classical processing unit (102) further reduces the predetermined number of groups and instructs the quantum annealing unit (104) to group the vertices into the predetermined number of groups.

16. The method according to claim 15, wherein, The steps of reducing the predetermined number of groups and instructing the quantum annealing unit (104) to be performed a predetermined number of times.

17. The method according to any one of claims 10 to 16, wherein, It also includes the step of the classical processing unit (102) accumulating the results received from the quantum gate-based digital unit (106), wherein the classical processing unit (102) instructs the quantum gate-based digital unit (106) to process the one or more sets of items of the Hamiltonian and the step of accumulating the results received from the quantum gate-based digital unit (106) are repeated a predetermined number of times.

18. A classical processing unit (102) for establishing a hybrid quantum computing system (100), the classical processing unit (102) being communicatively connected to a quantum annealing unit and to a quantum gate-based digital unit, wherein, The classical processing unit (102) includes an input interface for inputting a representation of a Hamiltonian, and The classical processing unit (102) is configured as follows: The representation of the Hamiltonian is transformed into a representation of the quadratic unconstrained binary optimization problem (QUBO). The quantum annealing unit (104) is instructed to process the quadratic unconstrained binary optimization problem QUBO. Receive the result from the quantum annealing unit (104). Verify the results, and based on the results determine one or more sets of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital unit (106). The quantum gate-based digital unit (106) is instructed to simultaneously process at least one term from a set of terms of the Hamiltonian. Receive the result from the quantum gate-based digital unit (106). The classical processing unit (102) further includes an output interface for outputting a representation of the result of processing the Hamiltonian.

19. The classical processing unit according to claim 18, wherein, The configuration of the classical processing unit to convert the representation of the Hamiltonian into a representation of a quadratic unconstrained binary optimization (QUBO) problem includes: the classical processing unit (102) being configured to create a graph representation starting from a zero graph, wherein vertices represent terms of the Hamiltonian; the classical processing unit (102) being configured to determine the commutativity of each term of the Hamiltonian; and the classical processing unit (102) being configured to add an edge on the zero graph between two vertices representing non-commutative terms of the Hamiltonian.

20. The classical processing unit of claim 19 is further configured to estimate the number of required groups such that no two adjacent vertices are in the same group, and to instruct the quantum annealing unit (104) to group the vertices into the estimated number of groups.

21. The classical processing unit according to claim 20 is further configured to instruct the quantum annealing unit (104) to group the vertices into a predetermined number of groups, wherein, The predetermined number of groups is equal to the estimated number of groups minus 1.

22. The classical processing unit of claim 21 is further configured to further reduce the predetermined number of groups and instruct the quantum annealing unit (104) to group the vertices into the predetermined number of groups.

23. The classical processing unit according to claim 22 is further configured to further reduce the predetermined number of groups and instruct the quantum annealing unit (104) to reach a predetermined number of times.

24. The classical processing unit according to any one of claims 18 to 23 is further configured to instruct the quantum annealing unit (104) to process the quadratic unconstrained binary optimization QUBO problem a predetermined number of times.

25. The classical processing unit according to any one of claims 18 to 24 is further configured to instruct the quantum gate-based digital unit (106) to process the set or more items of the Hamiltonian a predetermined number of times, and to accumulate the results received from the quantum gate-based digital unit (106).

26. A method for processing Hamiltonians, the method being performed by a classical processing unit (102), the classical processing unit (102) including an input interface and an output interface for inputting representations of Hamiltonians, and communicatively connected to a quantum annealing unit (104) and a quantum gate-based digital unit (106), the method comprising the following steps: The representation of the Hamiltonian is received via the input interface. The representation of the Hamiltonian is transformed into a representation of the quadratic unconstrained binary optimization problem (QUBO). The quantum annealing unit (104) is instructed to process the quadratic unconstrained binary optimization problem QUBO. Receive the result from the quantum annealing unit (104). Verify the results. Based on the results, determine one or more sets of terms of the Hamiltonian that can be processed simultaneously by the quantum gate-based digital unit (106). The quantum gate-based digital unit (106) is instructed to simultaneously process at least one term from a set of terms of the Hamiltonian. Receive the result from the quantum gate-based digital unit (106). The result of processing the Hamiltonian is output via the input / output interface.

27. The method according to claim 26, wherein, The step of the classical processing unit (102) converting the representation of the Hamiltonian into a representation of a quadratic unconstrained binary optimization (QUBO) problem includes the following steps: The classical processing unit (102) creates a graph representation starting from the zero graph, where vertices represent terms of the Hamiltonian; determines the commutativity of each term of the Hamiltonian; and adds an edge on the zero graph between two vertices representing non-commutative terms of the Hamiltonian.

28. The method of claim 27, further comprising the step of: Estimate the number of groups required such that no two adjacent vertices are in the same group, and instruct the quantum annealing unit (104) to group the vertices into the estimated number of groups.

29. The method of claim 28, further comprising the step of: The quantum annealing unit (104) is instructed to group the vertices into a predetermined number of groups, wherein the predetermined number of groups is equal to the estimated number of groups minus 1.

30. The method according to claim 29, wherein, It also includes the following steps: The predetermined number of groups is further reduced, and the quantum annealing unit (104) is instructed to group the vertices into the predetermined number of groups.

31. The method according to claim 30, wherein, The steps of reducing the predetermined number of groups and instructing the quantum annealing unit (104) to be performed a predetermined number of times.

32. The method according to any one of claims 26 to 31, further comprising the step of accumulating the result received from the quantum gate-based digital unit (106), wherein, The classical processing unit (102) instructs the quantum gate-based digital unit (106) to process the one or more sets of items of the Hamiltonian and to accumulate the results received from the quantum gate-based digital unit (106) a predetermined number of times.

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