Three-way hybrid quantum computing system and method

Abstract

The present invention 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 distinct strengths of each component to solve complex computational tasks more efficiently. The classical computer is responsible for general-purpose tasks, data storage, and control of the quantum components. The quantum annealer is used for solving optimization problems, while the gate-based quantum computer is used for performing a wider range of algorithms. The system converts the problem of creating groups of commuting terms of a Hamiltonian into a quadratic unconstrained binary optimization (QUBO) problem, instructs a hybrid combination of a classical computer and a quantum annealer to solve and validate the result, and then deploys the outcome to determine results for all items in each commuting group of the Hamiltonian in parallel using a hybrid combination of a classical computer and a gate-based quantum computer. The system provides an output that represents the solution to the original problem.

Description

[0001] THREE-WAY HYBRID QUANTUM COMPUTING SYSTEM AND METHOD

[0002] The present invention relates to a hybrid quantum computing system, particularly to a three- way hybrid quantum computing system including a classical computer, a quantum annealer, and a gate-based quantum computer, and the method for said three-way hybrid quantum computing system. Further, it relates to a classical processing unit for establishing a three- way hybrid quantum computing system and a method.

[0003] Background of the Invention

[0004] Two major types of quantum computers are currently under research and development. These are gate-based quantum computers and quantum annealers. Gate-based quantum computers are considered universal machines because they can implement any quantum algorithm. These computers use quantum gates to manipulate qubits, which are the basic units of quantum information. Some quantum gates are like classical logic gates, but they operate on quantum states. Gate-based quantum computers can perform complex computations by applying a sequence of quantum gates to qubits. These gates change the state of qubits, allowing for the manipulation and calculation of quantum information. The computation is performed through the interaction of qubits, the quantum mechanical description of whose states uses concepts like entanglement and superposition.

[0005] Quantum annealers, on the other hand, are specialized quantum computers primarily designed for optimization problems. Quantum annealing works by setting up a problem as a mathematical model and then finding the lowest energy state, which corresponds to the optimal solution. The system starts in a superposition state and can gradually find the lowest energy state through quantum fluctuations. If done successfully, the final state represents the solution to the optimization problem. The advantage of quantum annealers is their ability to solve certain optimization problems more efficiently than classical computers. Problems like traveling salesmen, protein folding, and supply chain optimization can be tackled using quantum annealing. However, these computers lack the universal computational capabilities of gate-based quantum computers, limiting their applicability to specific problem domains.

[0006] The current generation of quantum computing algorithms often adopts a two-way hybrid approach, which strategically merges the strengths of quantum and classical computing. In this hybrid model, quantum resources, such as a gate-based quantum computer or, alternatively, a quantum annealer, are used for specific tasks that can benefit from quantum advantage, such as performing complex calculations or handling superposition and entanglement. Classical computers are simultaneously used to perform more routine tasks, manage error correction, or process the outputs of quantum computations.

[0007] This two-way hybrid design is particularly employed as it helps to address one of the major challenges of current quantum technology - noise. Quantum systems are extremely sensitive to external disturbances, leading to errors and loss of coherence. By employing a hybrid framework, the load on the quantum computer is reduced and classical systems can handle the error-prone aspects, such as optimization loops to fine-tune the quantum operations.

[0008] The object of the present invention is to utilize the special features and different technological advancements of the different types of quantum computers in a hybrid quantum computer system in an improved manner.

[0009] Brief Summary of the Invention

[0010] Proposed is a hybrid quantum computing system that utilizes a classical processing unit, a quantum annealer unit, and a quantum gate-based digital unit, designed to leverage the distinct strengths of each computing paradigm to tackle complex computational tasks more efficiently.

[0011] Each component in this three-way hybrid quantum computing system contributes to an overall computational task. The classical processing unit is excellent at performing a wide range of general-purpose tasks, including data input / output (I / O) operations, handling classical algorithms, data storage, and error correction / mitigation. They can also manage and control the operation of the quantum components, running the software that interfaces with them.

[0012] A classical processing unit operates on classical computing principles, using binary data (bits) that exist in one of two states, representing 0 or 1. Classical processing units include any one of the following. A personal computer, laptop or desktop, that relies on a CPU 102 to perform general-purpose tasks such as running software applications. A high-performance computer (HPC), also known as a supercomputer, these systems consist of thousands of CPUs and GPUs working in concert to perform highly complex calculations at high speeds, often used in scientific research, weather modelling, and simulations. A computer cluster is formed by a set of loosely or tightly connected computers that work together so that they can be viewed as a single system. A CPU (Central Processing Unit) performs the calculations which enable a computer to function. A CPU-core in a multicore processor, or a combination of CPU and GPU (Graphics Processing Unit). While the CPU excels at general-purpose task management and decision-making, the GPU specializes in rendering images and performing complex mathematical calculations in parallel. Together, they can accelerate various types of computations, particularly those involving graphics, video processing, and certain scientific calculations. These systems are fundamentally different from quantum computers, which use quantum bits (qubits) that can be in superpositions of states. Quantum computers are based on quantum mechanics, making them potentially more powerful for certain tasks, such as factoring large numbers, optimizing complex systems, and simulating quantum phenomena.

[0013] Quantum annealing is a type of quantum computation paradigm used primarily for solving optimization problems. D-Wave is among the most recognized companies that manufacture quantum annealing computers, such as D-Wave Advantage. Their various quantum annealers have been available commercially 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 developments and market entrants may emerge, and the present solution is not limited to or dependent on a quantum annealing unit from a particular company.

[0014] Quantum gate-based digital units are based on universal quantum processors capable of running any quantum algorithm. They are flexible and can execute the widest range of quantum operations using quantum gates to manipulate qubits. They function well for executing general quantum algorithms and provide a powerful way to handle tasks requiring entanglement or superposition. Several companies provide quantum gate-based digital unit, such as IBM, Rigetti Computing, lonQ, Google Quantum. It should be noted that the field of quantum computing, including quantum gate-based digital units, is rapidly evolving, and new developments and market entrants may emerge, and that the present solution is not limited to or dependent on a quantum gate-based digital unit from a particular company.

[0015] The proposed hybrid quantum computing system effectively combines classical computing with two types of quantum computing technologies, namely quantum annealing and gatebased quantum computing. This combination leverages the distinct advantages of each component to solve complex problems that are described by a Hamiltonian. It comprises a classical processing unit with an input / output interface, a quantum annealing unit communicatively connected to the classical processing unit, a quantum gate-based digital unit communicatively connected to the classical processing unit, wherein the classical processing unit includes an input interface for inputting a string representation of a Hamiltonian. The classical processing unit is configured to convert the problem of grouping the commuting terms of a Hamiltonian into a representation of a quadratic unconstrained binary optimization (QllBO) problem and to instruct the quantum annealing unit to process the quadratic unconstrained binary optimization (QllBO) problem. The quantum annealing unit is configured to process the quadratic unconstrained binary optimization (QU BO) problem and to send the result to the classical processing unit. The classical processing unit is further configured to validate the result and to determine based on the result one or more groups of terms of the Hamiltonian that can be simultaneously processed by the quantum gate-based digital unit, and to instruct the quantum gate-based digital unit to process the one or more groups of terms of the Hamiltonian. The quantum gate-based digital unit is configured to simultaneously process the terms of at least one of the groups and to send the result to the classical processing unit. The classical processing unit further comprises an output interface for outputting a representation of the result of processing the string representation of the given Hamiltonian.

[0016] The classical processing unit acts as the orchestrator of the entire system. It allows the user or another system to input a Hamiltonian, which is a mathematical expression used to describe the total energy of a system in physics, but in the present context, it represents the problem to be solved. The classical processing unit converts the Hamiltonian grouping problem into a quadratic unconstrained binary optimization (QUBO) form, which is a standard representation for optimization problems that quantum annealers can process. It instructs the quantum annealing unit to solve the QUBO, receives the solution, and then validates it. Based on the results, it identifies groups whose terms from the Hamiltonian can be processed in parallel by the quantum gate-based digital unit. After the quantum units perform their computations, the CPU gathers the results, consolidates them, and provides an output that represents the solution to the original problem.

[0017] The quantum annealing unit is specialized in solving optimization problems, particularly those that can be formulated as QUBO. Quantum annealers use quantum fluctuation (tunneling) to find the minima of the energy landscape which corresponds to the optimal solution of the QUBO problem. They can be faster for certain types of difficult optimization problems compared to classical optimizers. Quantum annealers like the D-Wave systems are designed specifically for QUBO problems, potentially providing a more efficient solution path for certain complex optimization tasks than classical or gate-based quantum computers. The quantum gate-based digital unit uses quantum circuits with gates to manipulate qubits and perform quantum computations. This type of quantum computing is suitable for a broader range of algorithms beyond optimization, such as factoring large numbers, searching unsorted databases, and simulating quantum systems.

[0018] The classical processing unit further identifies groups of Hamiltonian terms that can be processed simultaneously, which means the quantum gate-based digital unit can find the expectation values of many terms simultaneously.

[0019] The described hybrid quantum computing system is designed to optimize problem-solving capabilities by leveraging the strengths of classical computing, quantum annealing, and gatebased quantum computing in a coordinated fashion. This approach aims to solve complex Hamiltonian-based problems more efficiently than each type of computing could on its own.

[0020] In the hybrid quantum computing system, advantageously the classical processing unit's configuration to convert the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization (QllBO) problem includes the classical processing unit being configured to create a representation of a graph starting from a null graph, in which vertices representing the terms of the Hamiltonian, the classical processing unit being configured to determine the commutativity of each term of the Hamiltonian, the classical processing unit being configured to add an edge on the graph between two vertices representing terms of the Hamiltonian which do not commute.

[0021] The conversion of a Hamiltonian grouping problem into a QllBO and the subsequent graph representation as described is part of a strategy to optimize quantum computation. This approach is particularly advantageous for solving optimization problems and for leveraging the nature of quantum physics to gain computational efficiency. By creating a graph where each vertex represents a term of the Hamiltonian, the classical processing unit effectively maps the problem onto a structure that is more suitable for analysis and optimization. This conversion will lead to the formulation of a graph coloring problem.

[0022] In quantum mechanics, two operators (or terms in the Hamiltonian) are said to commute if their order of application does not change the outcome. In other words, two terms htand hj commute when [hi, hj] = hihj - hjhi = 0 (1) i.e., when their commutator, given by the [ ] symbol, is zero. Note that any two terms commute trivially for i = j. The commutativity of terms in a Hamiltonian can be formulated in two different ways, namely, qubit-wise commutativity (QWC) and general commutativity (GC).

[0023] In QWC, two terms are said to commute if the Pauli terms corresponding to the same index between two Pauli strings commute with one another. For example, the term h = X X2commutes with h2= X2but not with h3= Y^. We can create a set of terms using QWC such that all the terms in this group qubit-wise commute with every other term, e.g. h2}. The idea is that all the terms of a group can be measured simultaneously in a QDU 106, thereby facilitating quicker computation. QWC has been used in experimental demonstrations of finding expectation values for small systems on quantum processors.

[0024] In GC, two terms are said to commute if the Pauli terms corresponding to the same index between two Pauli strings fail to qubit-wise commute an even number of times. The benefit of using GC is that it can potentially include more terms in a group compared to using QWC. However, the advantage of using QWC is that the simultaneous measurement of terms in a QWC group is trivial.

[0025] Knowing which terms commute is crucial for parallelizing computations in quantum algorithms. The CPU checks for commutativity amongst terms.

[0026] In the graph, an edge is added between vertices representing terms of the Hamiltonian that do not commute. This edge signifies that these terms cannot be directly processed simultaneously within the same quantum gate sequence without additional considerations because their order matters in the resultant quantum state. By computing which operators commute, the CPU can determine which operators can be grouped and processed in parallel by the quantum gate-based digital unit. This parallel processing is a significant advantage for quantum computing, enabling more efficient use of quantum resources.

[0027] The conversion of the problem to group commuting terms of a Hamiltonian to QllBO and its graph representation make it possible to solve the grouping problem on quantum annealers. The graph with edges between vertices represents non-commuting terms and describes the problem's constraints directly in the form required by these devices. The graph and the number of colors required to color it give an estimate of the physical quantum resources needed, such as the number of qubits and the complexity of inter-qubit connections required to implement the problem on a quantum processor.

[0028] Preferably, the quantum annealing unit's configuration to process the quadratic unconstrained binary optimization (QllBO) problem includes the quantum annealing unit being configured to group the vertices of the graph into groups, such that no two adjacent vertices are in the same group.

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

[0030] The graph coloring strategy advantageously simplifies problem-solving by breaking a complex Hamiltonian into smaller, more manageable subproblems. Each group can be tackled as a separate mini problem, rather than dealing with each Hamiltonian term individually. Quantum annealers naturally evolve towards the ground state of a system represented by the QllBO. The pre-processed grouping of the problem using the Annealer allows a quicker computation when using the gate-based and CPU systems in hybrid.

[0031] Advantageously, the classical processing unit is configured to estimate the number of groups needed, 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. This functionality is akin to solving a "graph coloring problem," where colors represent groups, and the aim is to use the fewest colors possible to color the graph such that no two connected vertices share the same color. The CPU uses classical algorithms to estimate the number of groups needed. These algorithms might range from heuristic methods to more complex approximation or even exact algorithms, depending on the problem's size and time constraints. Once the number of groups is estimated, the CPU instructs the quantum annealing unit on how to partition the vertices into groups in a way that aligns with the estimated color / classification. By pre-estimating the groupings, the system ensures that the quantum annealing unit can be set up with an efficient allocation of quantum resources (qubits and interactions) tailored to the problem structure. The CPU can use different strategies to estimate the grouping based on the complexity and nature of the specific problem, offering flexibility. For simpler problems, a straightforward greedy algorithm may suffice, while for more complex problems, more sophisticated techniques may be employed.

[0032] Preferably, in the hybrid quantum computing system, the classical processing unit is configured to instruct the quantum annealing unit to group the vertices into a predetermined number of groups, wherein the predetermined number of groups equals 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 to instruct the quantum annealing unit to group the vertices into the predetermined number of groups. And further the classical processing unit may be configured to further reduce the predetermined number of groups and to instruct the quantum annealing unit for a predetermined number of times.

[0033] In the described hybrid quantum computing system, the classical processing unit employs an iterative method to instruct the quantum annealing unit to group vertices into a number of 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 necessary for the given graph.

[0034] By continuing with one less group than the estimated minimum, the system is effectively testing the bounds of resource efficiency. It attempts to optimize the problem with even fewer resources, potentially lowering the number of qubits and quantum operations required for computation. The classical processing unit's strategy to iteratively reduce the number of groups encourages the system to constantly improve the solution. If a valid coloring is found with fewer groups, it implies that the initial estimation was conservative, and the system has found a more resource-efficient solution. If the quantum annealing unit can successfully group vertices with fewer groups, it can lead to computational savings. Less groupings mean that potentially more operations can be executed in parallel, decreasing overall computation time. Reducing the number of groups forces the quantum annealing unit to explore alternative configurations of the solution space. This may lead to the discovery of better solutions that were not apparent in an initial, less constrained iteration. The iteration is stopped when either no useful solutions could be found or when reaching 1. Advantageously, in the hybrid quantum computing system, the classical processing unit is configured to instruct the quantum annealing unit to process the quadratic unconstrained binary optimization (QllBO) problem for a predetermined number of times.

[0035] Repeatedly processing the QU BO allows for statistical sampling of the solutions space. Since quantum annealing is influenced by probabilistic factors, multiple runs may yield different solutions, and sampling across these runs can give a better overall picture of the solution landscape. Further, quantum annealers, like other quantum systems, can be susceptible to noise and errors. Running the QU BO multiple times can help find a valid solution when invalid solutions may occur at first due to errors. Additionally, quantum annealers work by seeking the lowest energy state, corresponding to the optimal solution for the QUBO. Multiple iterations can increase the likelihood of finding the global minimum, as due to the finite non-zero temperature of the system, each run can explore different parts of the solution space during the annealing process. Also, during each run, the quantum annealing unit can get trapped in a local minimum, which is a solution that seems optimal within a limited scope but is not the best overall answer. Multiple runs mitigate this by providing more opportunities for the system to find paths to the global minimum.

[0036] Preferably, in the quantum computing system, the classical processing unit is further configured, for a predetermined number of times, to instruct the quantum gate-based digital unit to process the one or more groups of terms of the Hamiltonian, 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 engaged multiple times to process the terms of the Hamiltonian. Iteration can advantageously lead to an increased accuracy of results through repeated measurements and data accumulation. Quantum gate operations are subject to errors due to decoherence and other quantum noise. Accumulating results across multiple iterations helps to average out stochastic errors, providing a more accurate estimation of the true value. By processing the groups multiple times, the CPU can use techniques like error correction or mitigation algorithms to reduce the influence of noise that is inherent in current quantum gate-based systems. Quantum computations can yield probabilistic results; by accumulating these over multiple runs, the precision of expected values can be significantly enhanced, making it possible to distinguish between closely competing quantum states.

[0037] Further, a method for processing a Hamiltonian is provided, performed by a hybrid quantum computing system, comprising a classical processing unit including an input / output interface for inputting a representation of a Hamiltonian, 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 provided method includes the following steps. The classical processing unit, receives a representation of a Hamiltonian via the input interface, converts the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization Problem (QllBO), and instructs the quantum annealing unit to process the quadratic unconstrained binary optimization Problem (QllBO). The quantum annealing unit processes the quadratic unconstrained binary optimization (QllBO) problem and sends the result to the classical processing unit. The classical processing unit validates the result and determines, based on the result, one or more groups of terms of the Hamiltonian that can be simultaneously processed by the quantum gate-based digital unit and instruct the quantum gate-based digital unit to process the one or more groups of terms of the Hamiltonian. The quantum gate-based digital unit outputs the bitstrings needed to simultaneously process the expectations values of the terms of at least one of the groups and sends the result to the classical processing unit. The classical processing unit calculates the expectation values for each term in the group using the bitstrings accumulated from the quantum gate-based unit. This process is iteratively repeated until all the groups are processed.

[0038] The described method for processing a Hamiltonian with a hybrid quantum computing system is an intricate procedure that engages both classical and quantum computational resources. The system architecture combines a classical processing unit with quantum computing units, specifically, a quantum annealing unit and a quantum gate-based digital unit, configured to tackle different aspects of the overall problem.

[0039] Utilizing a classical front-end for input allows for seamless integration with existing computational systems and easy preparation of complex quantum problems. The step of converting a Hamiltonian to QUBO adapts the problem for processing by the quantum annealer, which can address optimization problems efficiently using its native hardware design. By delegating the problem to the quantum annealer, the system leverages quantum tunneling and superposition to potentially arrive at an optimal solution faster than classical algorithms, since quantum annealing can explore multiple solutions even when repeated under the same input conditions, potentially leading to a global optimum.

[0040] The method advantageously utilizes a harmonized approach, combining classical problem formulation and validation with quantum computation's power to process complex problems represented by a Hamiltonian more effectively than either classical or quantum approaches could achieve independently.

[0041] Advantageously, the step of the classical processing unit converting the representation of the Hamiltonian into a representation of a quadratic unconstrained binary optimization (QllBO) problem includes the steps of the classical processing unit creating a representation of a graph starting from a null graph, in which vertices representing the terms of the Hamiltonian, determining the commutativity of each term of the Hamiltonian, adding an edge on the null graph between two vertices representing terms of the Hamiltonian which do not commute.

[0042] Advantageously, the step of the quantum annealing unit processing the quadratic unconstrained binary optimization (QllBO) problem includes the step of the quantum annealing unit grouping the vertices of the graph into groups, such that no two adjacent vertices are in the same group. Knowing which terms commute allows for grouping of terms that can be processed simultaneously, optimizing computational efficiency.

[0043] Advantageously, the provided method further comprising the steps that the classical processing unit estimates the number of groups needed, such that no two adjacent vertices are in the same group, instructing 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 equals 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 steps of reducing the predetermined number of groups and instructing the quantum annealing unit are performed for a predetermined number of times.

[0044] Advantageously, further, the method comprises the step of the classical processing unit accumulating the results received from the quantum gate-based digital unit, wherein the steps of the classical processing unit instruct the quantum gate-based digital unit to process one or more groups of terms of the Hamiltonian and the step of accumulating the results received from the quantum gate-based digital unit, is repeated a predetermined number of times. Further provided is a classical processing unit for establishing a hybrid quantum computing system, wherein the classical processing unit is communicatively connected to a quantum annealing unit and to a quantum gate-based digital unit, wherein the classical processing unit includes an input interface for inputting a representation of a Hamiltonian. The classical processing unit is configured to convert the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization problem (QllBO), to instruct the quantum annealing unit to process the quadratic unconstrained binary optimization problem (QllBO), to receive the result from the quantum annealing unit, to validate the result and to determine based on the result one or more groups of terms of the Hamiltonian that can be simultaneously processed by the quantum gate-based digital unit, to instruct the quantum gate-based digital unit to simultaneously process the terms of at least one of the groups of terms of the Hamiltonian, to receive the result from the quantum gatebased digital unit, wherein the classical processing unit further comprises an output interface for outputting a representation of the result of processing the Hamiltonian.

[0045] Preferably, the classical processing unit's configuration to convert the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization (QllBO) problem includes the classical processing unit being configured to create a representation of a graph starting from a null graph, in which vertices representing the terms of the Hamiltonian, the classical processing unit being configured to determine the commutativity of each term of the Hamiltonian, the classical processing unit being configured to add an edge on the null graph between two vertices representing terms of the Hamiltonian which do not commute.

[0046] The classical processing is advantageously further configured to estimate the number of groups needed, 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.

[0047] Preferably, the classical processing unit according is further configured to instruct the quantum annealing unit to group the vertices into a predetermined number of groups, wherein the predetermined number of groups equals to the estimated number of groups minus 1.

[0048] The classical processing unit is advantageously further configured to further reduce the predetermined number of groups and to instruct the quantum annealing unit to group the vertices into the predetermined number of groups. The classical processing unit according is further configured to further reduce the predetermined number of groups and to instruct the quantum annealing unit for a predetermined number of times.

[0049] Preferably, the classical processing unit is further configured to instruct the quantum annealing unit to process the quadratic unconstrained binary optimization (QllBO) problem for a predetermined number of times.

[0050] The classical processing is advantageously further configured, for a predetermined number of times, to instruct the quantum gate-based digital unit to process the one or more groups of terms of the Hamiltonian, and to accumulate the results received from the quantum gatebased digital unit.

[0051] Further provided is a method for processing a Hamiltonian, performed by classical processing unit including an input / output interface for inputting a representation of a Hamiltonian, and being communicatively connected to a quantum annealing unit, and being communicatively connected to a quantum gate-based digital unit. The method includes the steps of receiving a representation of a Hamiltonian via the input interface, converting the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization problem (QllBO), instructing the quantum annealing unit to process the quadratic unconstrained binary optimization problem (QllBO), receiving from the quantum annealing unit the result, validating the result, determining based on the result one or more groups of terms of the Hamiltonian that can be simultaneously processed by the quantum gate-based digital unit, instructing the quantum gate-based digital unit to simultaneously process the terms of at least one of the groups of terms of the Hamiltonian, receiving the result from the quantum gate-based digital unit, and outputting a representation of the result of processing the Hamiltonian.

[0052] Advantageously the step of the classical processing unit converting the representation of the Hamiltonian grouping problem into a representation of a quadratic unconstrained binary optimization (QllBO) problem includes the steps of the classical processing unit, creating a representation of a graph starting from a null graph, in which vertices representing the terms of the Hamiltonian, determining the commutativity of each term of the Hamiltonian, adding an edge on the null graph between two vertices representing terms of the Hamiltonian which do not commute. Preferably, the method further comprising the steps of estimating the number of groups needed, such that no two adjacent vertices are in the same group, instructing the quantum annealing unit to group the vertices into the estimated number of groups.

[0053] The method advantageously further comprising the steps of instructing the quantum annealing unit to group the vertices into a predetermined number of groups, wherein the predetermined number of groups equals to the estimated number of groups minus 1.

[0054] Preferably the method further comprising 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.

[0055] Advantageously, the steps of reducing the predetermined number of groups and instructing the quantum annealing unit is performed for a predetermined number of times.

[0056] Preferably, the method further comprising 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 the one or more groups of terms of the Hamiltonian and the step of accumulating the results received from the quantum gatebased digital unit, is repeated a predetermined number of times.

[0057] Brief Description of the Drawings

[0058] Fig. 1 shows a high-level diagram outlining the components and connections of the hybrid quantum computing system.

[0059] Fig. 2 shows a graph in which the indexed vertices represent the terms, and the edges represent the non-commutativity between the terms for an example Hamiltonian given in Eq. (3).

[0060] Fig. 3 shows a diagram visualizing the total number of valid solutions obtained when sampling 103times the QU BO formulation of different problem Hamiltonians given in Table 3 as a function of the number of qubits needed to implement the problem on a QAU.

[0061] Detailed Description of the Invention Fig. 1 shows a high-level diagram outlining the components and connections of the hybrid quantum computing system 100. It comprises a classical processing unit 102 (CPU), quantum annealing unit 104 (QAU), and a quantum gate-based digital unit 106 (QDU).

[0062] The classical processing unit 102 manages the input and output of the system and orchestrates the interactions between quantum and classical computation. The classical processing unit 102 has an input / output interface (not shown). The interface serves as the point of interaction with the outside world, be it other computer systems, sensors, or human operators.

[0063] A quantum annealing unit 104 is connected to the classical processing unit 102. The quantum annealing unit is a specialized module optimized to solve certain types of optimization problems. The connections indicate that the classical processing unit can send instructions 108 to the annealing unit and receive results 110, preferably in form of bitstrings, from it, as indicated by the respective arrows. The quantum gate-based digital unit 106 is similarly connected to the classical processing unit 102. The quantum gate-based digital unit 106 represents another quantum processing modality, one capable of running a different set of algorithms from the annealing unit. Again, the connections denote two-way communication (see respective arrows), with the classical processing unit 102 issuing parameters 112, such as variational parameters, and instructions 114 and receiving output 116 from a respective output interface 118, preferably in form of bitstrings, from this unit as well. The parameters from the classical processing unit 102 are received by the quantum gate-based digital unit 106 via input interface 120. Correspondingly, the quantum annealing unit 104 receives the instructions 108 by an input interface 122 and issues its output via an output interface 124.

[0064] The overall layout is designed to show how these different elements form an integrated system. The classical processing unit 102 acts as the mediator and controller, converting the Hamiltonian into formats suitable for each quantum unit, and then combines the strengths of both quantum processors to tackle the complexity of the problem at hand. Each unit is shown to be an integral part of the system, working in concert under the management of the classical processing unit 102 to achieve results that would be challenging for classical or singular quantum systems to handle alone.

[0065] In the following we further describe Fig. 1 by focusing on the problem of finding the ground state energy of a given / V-qubit Hamiltonian having m terms, Z = ozare the Pauli matrices, and I is the identity matrix. Finding the ground state energy of problems written in the form of Eq. (2) is known to be classically intractable in general. The reason for that is the exponential scaling of the classical memory required to store the quantum statevector made up of complex numbers.

[0066] Fig. 1 shows how to find the ground state energy using quantum computers. The problem Hamiltonian (see Eq. (2)) is input as a string representation to the classical central processing unit 102. This information is stored in a respective storage 126 for ungrouped terms. These ungrouped terms go through several levels of processing inside the CPU 102 to convert them into a quadratic unconstrained binary optimization problem (QUBO), which is stored in storage for QUBO 128, before it is sent to the QAU 104 along with other instructions 108. These instructions 108 can include the annealing time, as illustrated by arrow 130, qubit mapping, chain strength, number of samples, etc., and are controlled by predetermined setting, such as default values, or settings provided together with the representation of the Hamiltonian via the input interface (not shown). The QAU 104 tries to solve the QUBO problem and outputs bitstrings 110 that are processed in the CPU 102. The CPU 102 checks the validity of the solutions obtained from the QAU 104 in a validator 132 provided by the CPU 102. The valid solutions are stored in a respective storage for grouped terms 134. One of the valid solutions is then chosen from the storage for grouped terms 134 and used for the next stage of computation and forwarded to an energy calculator 136 provided as part of the CPU 102.

[0067] The next stage is a hybrid between a CPU 102 and a quantum gate-based digital unit 106. This setup can preferably be used in the context of a variational quantum eigensolver. The computation is started by giving initial parameters to a classical optimization algorithm, depicted as optimizer 138, provided by the CPU 102. The CPU 102 then passes these parameters 140 embedded into a quantum circuit to the QDU 106. The CPU 102 also passes additional instructions 114 to the QDU 106. The relevant instructions 114 for our purposes are the number of samples and the measurement basis for a group of terms in the problem Hamiltonian, but can also include hardware-specific instructions like microwave pulses. The QDU 106 executes the circuit 142 for the given set of parameters 140 and instructions 114 and produces bitstrings as an output 116. These bitstrings are accumulated in the CPU 102 using an accumulator 144, which also functions as a storage unit. The accumulator 144 keeps the bitstrings corresponding to the different groups obtained from the QAU 104. Once sufficient bitstrings are accumulated, they are used to calculate the energy for all the terms in all the groups to obtain the energy of the entire Hamiltonian. This energy is then the scalar quantity minimized by the optimizer in subsequent iterations. The processing stops when the optimizer can no longer further minimize the energy, or a certain preordained number of iterations have been reached.

[0068] In the following sections, we go through the details of how the above process is realized. We discuss the commutativity of the terms given in Eq. (1) and how commuting groups are formed using the graph coloring problem. We illustrate the process step-by-step using simple examples.

[0069] Although we want to maximize the size of each group, the central problem is to minimize the number of groups. Thus, we are looking to solve a minimum clique cover problem where each clique is the group of commuting terms. If the minimum clique cover problem is given by a graph G, then the complement graph G gives the corresponding graph coloring problem. Both these belong to the class of problems considered to be NP-hard in general. The graph coloring problem can be converted to a quadratic unconstrained binary optimization (QU BO) problem and solved on a QAU 104. This section briefly explains the steps needed to achieve this objective.

[0070] The problem is input as a list of strings, each string of length N corresponding to one term in the Hamiltonian and converted to an integer format representing the indices of the Pauli terms. This format is conveniently manipulated to find out the commutativity of each term with every other. The commutativity information is encoded into a graph as follows. Create a graph with m nodes, where m is the total number of terms in the Hamiltonian. If a given term hi does not commute with another term hj, i.e. [hi, hj] #= 0, add an edge between the vertices indexed i and j.

[0071] In graph coloring, no two neighbors are allowed to have the same color. In our problem, no two non-commuting terms can be in the same group. Therefore, by creating edges between indices representing non-commuting terms, we have successfully translated our problem into a graph coloring problem. Solving the graph coloring problem will now yield us the solution to our original problem of finding commuting groups of terms.

[0072] As an example, consider the following arbitrary Hamiltonian:

[0073] Hex. = X1X2+ X1+ Y2+ Z1Z2Z3+ X1Y2Z3(3)

[0074] The commutativity between the terms is shown in the graph in Fig. 2. Fig. 2 shows a graph in which the indexed vertices represent the terms, and the edges represent the noncommutativity between the terms for an example Hamiltonian given in Eq. (3), whereas the coloring (solid, dashed, finely dashed circles) of the vertices represents one way to color the graph.

[0075] The terms are indexed in the sequence they appear in Eq. (3) from left to right. The edges between any two terms represent the qubit-wise non-commutativity of those terms. The graph would look different for general non-commutativity. The minimum colors required to color this graph are 3, which is known as the chromatic number of the graph. In Fig. 2 the different colors are illustrated by solid circle lines (vertices 1 , 2 and 4), dashed lines (vertex 0) and finely dashed lines (vertex 3). Note that the coloring shown in Fig. 2 is not unique, for example, vertex 1 could also have the dashed line. According to the coloring scheme in Fig. 2, we can measure the terms XltY2, and X1Y2Z3simultaneously.

[0076] In the following section, we briefly summarize the steps required to convert the graph coloring problem to a QllBO problem. Assume that we wish to color a graph with exactly K- colors. Let x be a binary variable such that x^ = 1 if vertex i is assigned color j, and 0 otherwise. The graph coloring has two constraints, namely, (a) each vertex must receive a color, and (b) adjacent nodes are always assigned different colors.

[0077] The constraint (a) is imposed such that: where N is the number of vertices in the graph. Thus, the binary variable is 1 only for one out of K colours. We observe that x^ = x?- , since the variable is binary. The constraint (b) is imposed such that: and for all adjacent vertices i and j. The task is then to find the minimum of the problem,

[0078] QUBO: min xfQx, (6) where Q is the QUBO matrix equivalent of our model and incorporates all the information about our problem. The steps to convert Eq. (4) and Eq. (5) into Q include using two different transformations and using single subscripts to impose penalties for violating the problem constraints. The creation of Q is automated on a CPU 102 for a given graph G. We generate the Q matrices in this work using the qubogen package.

[0079] In this section, we show results for two cases. First, we demonstrate a use-case of our process where we find the ground state energy of a small two-qubit Hamiltonian using a QAU-CPU-QDU hybrid process. Second, we take Hamiltonians with different number of qubits and terms and use both QWC and GC to group the terms into commuting sets using a QAU 104.

[0080] The process is demonstrated by finding the ground state energy of the H2 molecule whose Hamiltonian is given by

[0081] Hh2= 0.011 * ZiZ2+ 0.398 * Zi + 0.398 * Z2+ 0.181 * XiX2. (7)

[0082] By using QWC, the commutativity of each term is computed in relation to every other term. During this process, by using the Python package networkx, an edge is added on a null graph between two vertices (representing terms) which do not commute. The final graph looks the same as Fig. 2, if we remove the vertex 0 and its edges and assign the term z1z2to vertex 3, Zi to vertex 1 , z2to vertex 2, and ZiZ2to vertex 4. The networkx package offers an in-built greedy algorithm which could color the graph using two colors, which is also the chromatic number. The penalty variable was set to 4 and the number of colors to 2. The number of qubits required equals the product of the number of colors and vertices. Eight qubits were used for this case. The number of samples was set to 1000. The QAU 104 used was the DWave Advantage System version 5.3. The raw data obtained are tabulated in Table 1. Table 1 shows the energy and frequency of occurrence related to the five unique bitstrings obtained from the QAU 104 when sampling 1000 times. Energy in this table is a dimensionless quantity.

[0083] Indexed bitstring

[0084] 1 2 3 4 5 6 7 8 | Energy | Frequency |

[0085] Table 1

[0086] The bitstrings obtained from the QAU 104 are processed in a “Validator” (see Fig. 1) to check if they satisfy all the constraints of the problem. Only the data in the top two rows of Table 1 with energy -16 satisfies the constraints. These two bitstrings correspond to coloring the vertex corresponding to the z1z2term differently from the other three. From the first bitstring, we make the groups {z1z2} and {Zi,z2,ZiZ2}. We note that sampling the QAU 104 automatically gives more than one possible valid solution (if it exists). Invalid solutions also appear in the samples, in this case with a very low frequency of occurrence.

[0087] The next step is to prepare a parametrized ansatz on the QDU 106. For our problem, we take the ansatz given by

[0088] The energy for an arbitrary value of 6 e [0,2TT] is given by E(0) = (^(9)\Hh2\ p(9)), where \ / J) is assumed to be normalized. The ground state energy is then given by

[0089] Eo= (m\Hh2\m) (9) where 0 corresponds to that value of 6 where the global minimum is located. For the Hamiltonian given in Eq. (7) and the ansatz given in Eq. (8), the global minimum is located at 0 = 7T / 2. For the sake of our demonstration, we forgo the optimization process to find 0 = 7T / 2 but use it directly to calculate the ground state energy on the IBM-Q QDlls Jakarta, Manila, Perth, Nairobi, and on an ideal emulator.

[0090] Using the naive method, all four terms are measured separately, thus requiring four experiments. The QWC grouping method requires only two experiments, one in the Z,Z2basis and the other in the X X2basis. A basis is prepared using appropriate rotation gates. When using QWC, the energy for the and Z2terms is calculated using the bit-strings obtained forZ1Z2. We sample the QDU 106 in each experiment 213times. The precision of the final energy can be improved by sampling more times.

[0091] The energies obtained from the QDU 106 are tabulated in Table 2. Table 2 shows the ground state energies obtained for different QDUs using naive and QWC grouping. The theoretical value is -0.192. Energy in this table has the Hartree atomic units.

[0092] | Naive grouping | QWC grouping Device | Runs Energy Runs Energy

[0093] -0.192

[0094] -0.141

[0095] -0.116

[0096] -0.104 -0.130

[0097] Table 2

[0098] The results from the ideal emulator can be used as a benchmark to compare the results from the IBM Q devices. We used four different devices and found the energies using (1) the naive grouping, where all terms are measured separately, and (2) the QWC grouping. We found that the energies in both cases were close to one another, as expected. The benefit of the QWC grouping method, in this case, is that it needs only half the computational time than the naive grouping method since only two runs are required. We note that the device performances varied, and none of the devices could find the ground state energy which matches the accuracy of the emulator. This reflects the fact that the current generation devices are in the noisy intermediate scale quantum (NISQ) era. Minor improvements in the energy may have been possible if the circuit parameter optimization was performed individually for each device; however, this was not relevant for the demonstration of our setup.

[0099] In this section, it was shown that a QAU 104, QDU 106, and a CPU 102 can be used together in a hybrid setup to execute the proposed method. The hybrid method was performed on currently available actual quantum computers.

[0100] We now shift our focus to solving the graph coloring problem for larger problems on the QAU 104. We consider those Hamiltonians that have either already been used as prototypes on current generation QDUs or have the potential to be used soon. These include small molecules, the Hubbard model, and the Heisenberg model. We use the Open-Fermion package to generate Hamiltonians for the Hubbard model. The QAU 104 used were the DWave Advantage System version 5.3 and DWave Advantage2 prototype1.1.

[0101] The Hamiltonians from quantum chemistry and the Hubbard model are hard problems to group into commuting terms. They offer the benefit that the number of terms in a molecular Hamiltonian can be increased or decreased by selecting a smaller or a larger basis, thus, changing the problem size and difficulty as necessary. Alternatively, the Heisenberg model in one dimension is trivially grouped into three groups using QWC and serves as a benchmarking problem for the QAU 104 as well as the classical greedy solvers.

[0102] Sometimes a few terms appear in a Hamiltonian that commute with all other terms. In graph coloring, these terms are not part of the connected graph because their commutator is zero with all the terms. These terms can be grouped into any of the groups. We simplify our problem by removing these terms from the Hamiltonian in the examples below. Additionally, when using the Jordan-Wigner (JW) transformation, there are often terms with products of only Z matrices. Since terms with only such products trivially commute with each other, one can remove them from the terms and make one group out of them.

[0103] Table 3 shows term grouping results from Greedy and QAU 104 solvers. Except for three cases, the same number of terms were used for QWC and GC. Parenthesis is for GC terms. G and QAU 104 stand for Greedy algorithm and quantum annealing unit, respectively. QAU 104 was not able to solve the qubit-wise case for the Hubbard model lattices. | Qubit-wise | General |

[0104] Hamiltonian | Terms | G | QAU | G | QAU |

[0105] Table 3

[0106] Table 3 shows the results of grouping commuting terms for different Hamiltonians. The number of terms is listed for each case. Note that the Z,Z2term in Eq. (7) commutes with all terms using GC; therefore, it was removed when using GC. The number of terms for Li H molecule was too large for the QAlls available; therefore, we selected only a subset. In the case of the Hubbard model on a 2 x 2 lattice, which had 28 terms, we removed 8 Z-only terms for the QWC case. In some cases, due to the removal of the terms, not the same number of terms was used for QWC or GC, and in this case the number of terms in the parenthesis is the number of terms for the GC case.

[0107] We first run the greedy algorithm to find the minimum number of colors needed to color the graph. We then task the QAU 104 to color the same graph using this number of colors. The molecular and Hubbard Hamiltonians need to be converted to the spin Hamiltonians using either the parity, Jordan-Wigner (JW), or the Bravyi-Kitaev (BK) transformations. This is one of the reasons why the H2 Hamiltonian has a different number of terms. We observe that the QAU 104 can correctly color the graph in all cases except for QWC of Hubbard models.

[0108] Fig. 3 plots the number of valid solution samples obtained when sampling a QAU 103times for each of the problems given in Table 3. The x-axis enumerates the number of qubits needed to implement the problem on the QAU 104, which is the product of the number of terms and colors for a given problem. We observe the general trend that the frequency of obtaining a valid sample reduces as we increase the number of qubits, eventually going to zero. In two cases, no valid solution was found. There are two outliers in the data at qubits 120 and 180 which correspond to GC and QWC of the Heisenberg model lattices of size 1 x 20, respectively. These are the benchmarking problems whose solutions are known but offer relatively large problems sizes to test a QAU 104. However, they too follow the general trend that the valid samples decrease with increasing number of qubits.

[0109] The greedy algorithm is a useful tool to find optimal coloring for the prototype problem we demonstrated and some other small-scale problems we tested. However, since it is a heuristic, it will likely fail to find the coloring with the least number of colors when the problem size is increased. Furthermore, the greedy algorithm employs different strategies to find the solution. For example, we used the largest first strategy with a runtime of order O(m + e) where m and e are the number of vertices and edges in G, respectively. This strategy failed to find the optimal coloring for one of the problems we tested, namely, the GC case of 3 x 3 Heisenberg lattice (see Table 3). Interestingly, the QAU 104 was able to find the correct solution using three instead of four colors.

[0110] Due to the way in which a QU BO is formulated, a QAU 104 always needs the number of colors needed as an input. Finding the lowest number of colors needed is itself NP-hard in general. Therefore, preferably a hybrid method is used which starts with the solution obtained from a greedy algorithm and inputs it to an annealer which then tries to improve the solution by using fewer colors. This can be achieved by using reverse annealing. Such a method would have QAU-CPU loop like the QDU-CPU loop of variational methods.

Claims

Claims1. A hybrid quantum computing system (100), comprising: a classical processing unit (102), a quantum annealing unit (104) communicatively connected to said classical processing unit, a quantum gate-based digital unit (106) communicatively connected to said classical processing unit, wherein said classical processing unit (102) includes an input interface for inputting a representation of a Hamiltonian, wherein said classical processing unit (102) is configured to convert said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization problem (QllBO), wherein said classical processing unit (102) is configured to instruct said quantum annealing unit (104) to process said quadratic unconstrained binary optimization problem (QllBO), wherein said quantum annealing unit (104) is configured to process said quadratic unconstrained binary optimization (QllBO) problem and to send the result to said classical processing unit (102), wherein said classical processing unit (102) is configured to validate said result and to determine based on said result one or more groups of terms of said Hamiltonian that can be simultaneously processed by said quantum gate-based digital unit (106), wherein said classical processing unit (102) is configured to instruct said quantum gate-based digital unit (106) to process said one or more groups of terms of said Hamiltonian, wherein said quantum gate-based digital unit (106) is configured to simultaneously process the terms of at least one of the groups and to send the result to said classical processing unit (102), wherein said classical processing unit (102) comprises an output interface for outputting a representation of the result of processing said Hamiltonian.

2. The hybrid quantum computing system according to claim 1 , wherein said classical processing unit's configuration to convert said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization (QllBO) problem includes said classical processing unit (102) being configured to create arepresentation of a graph starting from a null graph, in which vertices representing the terms of said Hamiltonian, said classical processing unit (102) being configured to determine the commutativity of each term of said Hamiltonian, said classical processing unit (102) being configured to add an edge on said null graph between two vertices representing terms of said Hamiltonian which do not commute.

3. The hybrid quantum computing system according to claim 2, wherein said quantum annealing unit's configuration to process said quadratic unconstrained binary optimization (QllBO) problem includes said quantum annealing unit (104) being configured to group the vertices of said 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 said classical processing unit (102) is configured to estimate the number of groups needed, such that no two adjacent vertices are in the same group, and to instruct said quantum annealing unit (104) to group the vertices into said estimated number of groups.

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

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

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

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

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

10. A method for processing a Hamiltonian, performed by a hybrid quantum computing system (100), comprising a classical processing unit (102) including an input interface for inputting a representation of a Hamiltonian and an output interface, a quantum annealing unit (104) communicatively connected to said classical processing unit (102), and a quantum gate-based digital unit (106) communicatively connected to said classical processing unit (102), said method including the following steps: said classical processing unit (102), receiving a representation of a Hamiltonian via said input interface, converting said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization problem (QllBO), instructing said quantum annealing unit (104) to process said quadratic unconstrained binary optimization problem (QllBO), said quantum annealing unit (104), processing said quadratic unconstrained binary optimization (QllBO) problem and sending the result to said classical processing unit (102), said classical processing unit (102), validating said result and determining based on said result one or more groups of terms of said Hamiltonian that can be simultaneously processed by said quantum gate-based digital unit (106), instructing said quantum gate-based digital unit (106) to process said one or more groups of terms of said Hamiltonian, said quantum gate-based digital unit (106), simultaneously processing the terms of at least one of the groups and sending the result to said classical processing unit (102), said classical processing unit (102), outputting a representation of the result of processing said Hamiltonian via said output interface.

11. The method according to claim 10, wherein the step of said classical processing unit (102) converting said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization (QllBO) problem includes the steps:said classical processing unit (102), creating a representation of a graph starting from a null graph, in which vertices representing the terms of said Hamiltonian, determining the commutativity of each term of said Hamiltonian, adding an edge on said null graph between two vertices representing terms of said Hamiltonian which do not commute.

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

13. The method according to claim 12, further comprising the steps: said classical processing unit (102), estimating the number of groups needed, such that no two adjacent vertices are in the same group, instructing said quantum annealing unit (104) to group the vertices into said estimated number of groups.

14. The method according to claim 13, further comprising the steps: said classical processing unit (102), instructing said quantum annealing unit (104) to group the vertices into a predetermined number of groups, wherein said predetermined number of groups equals to said estimated number of groups minus 1.

15. The method according to claim 14, further comprising the steps: said classical processing unit (102), further reducing said predetermined number of groups and instructing said quantum annealing unit (104) to group the vertices into said predetermined number of groups.

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

17. The method according to any of the claims 10 to 16, further comprising the step of said classical processing unit (102) accumulating said results received from said quantum gate-based digital unit (106), wherein the steps of said classical processing unit (102) instructing said quantum gate-based digital unit (106) to process said one or more groups of terms of said Hamiltonian and the step of accumulating said resultsreceived from said quantum gate-based digital unit (106), is repeated a predetermined number of times.

18. A classical processing unit (102) for establishing a hybrid quantum computing system (100), said classical processing unit (102) being communicatively connected to a quantum annealing unit, and being communicatively connected to a quantum gatebased digital unit, wherein said classical processing unit (102) includes an input interface for inputting a representation of a Hamiltonian, and wherein said classical processing unit (102) is configured: to convert said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization problem (QU BO), to instruct said quantum annealing unit (104) to process said quadratic unconstrained binary optimization problem (QUBO), to receive the result from said quantum annealing unit (104), to validate said result and to determine based on said result one or more groups of terms of said Hamiltonian that can be simultaneously processed by said quantum gate-based digital unit (106), to instruct said quantum gate-based digital unit (106) to simultaneously process the terms of at least one of the groups of terms of said Hamiltonian, to receive the result from said quantum gate-based digital unit (106), wherein said classical processing unit (102) further comprises an output interface for outputting a representation of the result of processing said Hamiltonian.

19. The classical processing unit according to claim 18, wherein said classical processing unit's configuration to convert said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization (QUBO) problem includes said classical processing unit (102) being configured to create a representation of a graph starting from a null graph, in which vertices representing the terms of said Hamiltonian, said classical processing unit (102) being configured to determine the commutativity of each term of said Hamiltonian, said classical processing unit (102) being configured to add an edge on said null graph between two vertices representing terms of said Hamiltonian which do not commute.

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

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

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

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

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

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

26. A method for processing a Hamiltonian, performed by classical processing unit (102) including an input interface for inputting a representation of a Hamiltonian and an output interface, and being communicatively connected to a quantum annealing unit (104), and being communicatively connected to a quantum gate-based digital unit (106), said method including the following steps: receiving a representation of a Hamiltonian via said input interface, converting said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization problem (QU BO),instructing said quantum annealing unit (104) to process said quadratic unconstrained binary optimization problem (QllBO), receiving from said quantum annealing unit (104) the result, validating said result, determining based on said result one or more groups of terms of said Hamiltonian that can be simultaneously processed by said quantum gate-based digital unit (106), instructing said quantum gate-based digital unit (106) to simultaneously process the terms of at least one of the groups of terms of said Hamiltonian, receiving the result from said quantum gate-based digital unit (106), outputting a representation of the result of processing said Hamiltonian via said input / output interface.

27. The method according to claim 26, wherein the step of said classical processing unit (102) converting said representation of said Hamiltonian into a representation of a quadratic unconstrained binary optimization (QllBO) problem includes the steps: said classical processing unit (102), creating a representation of a graph starting from a null graph, in which vertices representing the terms of said Hamiltonian, determining the commutativity of each term of said Hamiltonian, adding an edge on said null graph between two vertices representing terms of said Hamiltonian which do not commute.

28. The method according to claim 27, further comprising the steps: estimating the number of groups needed, such that no two adjacent vertices are in the same group, instructing said quantum annealing unit (104) to group the vertices into said estimated number of groups.

29. The method according to claim 28, further comprising the steps: instructing said quantum annealing unit (104) to group the vertices into a predetermined number of groups, wherein said predetermined number of groups equals to said estimated number of groups minus 1.

30. The method according to claim 29, further comprising the steps: further reducing said predetermined number of groups and instructing said quantum annealing unit (104) to group the vertices into said predetermined number of groups.

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

32. The method according to any of the claims 26 to 31 , further comprising the step of accumulating said results received from said quantum gate-based digital unit (106), wherein the steps of said classical processing unit (102) instructing said quantum gate-based digital unit (106) to process said one or more groups of terms of said Hamiltonian and the step of accumulating said results received from said quantum gate-based digital unit (106), is repeated a predetermined number of times.