Apparatus for providing control signals for controlling a quantum computer - Patent Application 20070122997

Abstract

The present invention refers to an apparatus (720) for determining signals for generating a solution to a problem using a quantum computer. A providing unit (721) provides a problem description indicating a first part and a second part of the problem. A determining unit (722) determines a trial state representation based on a variational approach. The trial state representation includes a first part and a second part representing the first part and the second part, respectively. A transforming unit (723) converts the trial state representation into an operation trial state description including a) a second operation determined based on the second part, and b) a first operation determined based on the first part. A providing unit (724) provides signals for controlling the quantum computer to prepare a representation of the trial state representation. The signals referring to the first operation and the signals referring to the second operation are executed by different parts of the quantum computer.

Description

[Technical Field]

[0001] FIELD OF THE INVENTION The present invention relates to an apparatus, method, and computer program product for providing control signals for controlling a quantum computer to solve a problem. Additionally, the present invention refers to a system for identifying a solution to a problem, including the apparatus. [Background technology]

[0002] Background of the Invention Quantum computers are generally a new class of computing systems that exploit the unique behavior of quantum mechanical systems to enable computations of problems that, under appropriate conditions, would be impossible on conventional computers in a reasonable time or with reasonable resource and energy consumption. Furthermore, quantum computers have already been shown to be particularly well-suited for solving problems that may be relevant to the quantum mechanical world, i.e., problems that can be transformed into quantum mechanical descriptions. Such problems relate, for example, to electronic structure problems, molecular problems, condensed matter problems, etc. However, it is known that problems outside the description of physical quantum mechanical systems can also be transformed into quantum mechanical descriptions, such as encoding and decoding problems, complex analysis problems, and optimization problems, which can be transformed into quantum mechanical descriptions that can be processed by quantum computers. Examples of such problem transformations can generally be found, for example, in the paper "Quantum algorithms: an overview" by Montanaro, A., npj Quantum Inf 2, 15023 (2016). However, quantum computers already in existence today often suffer from inherent susceptibility to errors due to relaxation and decoherence, as well as imperfect control or readout errors of the quantum mechanical systems that form the heart of quantum computers. These difficulties with the accuracy of quantum mechanical calculations are directly related to the number of qubits, i.e., quantum mechanical elements containing at least two states, used, the time of the quantum mechanical calculation, and even the amount of qubit operations performed in the quantum mechanical system. Thus, to date, problems that can be solved with quantum mechanical computers are often limited by the burden of the necessary quantum mechanical calculations. Therefore, it would be advantageous if a solution were provided that reduced the requirements for quantum resources of a quantum computer and enabled the calculation of more advanced problems on a quantum computer. Summary of the Invention [Problem to be solved by the invention]

[0003] Summary of the Invention The object of the present invention is to provide an apparatus, system, method, and computer program product that allows for reducing the requirements for quantum resources of a quantum computer, and thus allows for solving problems of increased complexity. Furthermore, the present invention can be used to solve a wider variety of problems on a quantum computer. In particular, problems derived from perturbation theory applied to certain problems, such as problems derived using the restricted random phase approximation (cRPA), that involve frequency-dependent dynamic interactions of the quantities in question.

[0004] In a first aspect of the present invention, there is provided an apparatus for determining control signals for generating a solution to a problem convertible to a quantum mechanical description using a quantum computer, the apparatus comprising: i) a problem providing unit for providing a problem description indicating a problem to be solved, the problem description indicating a first part and a second part of the problem, the first part including quantities describing the problem that interact with each other, and the second part including quantities describing the problem that do not interact with each other; ii) a trial state determination unit for determining a trial state representation of the problem description based on a variational technique, the trial state representation including one or more variational parameters, the trial state representation including first and second parts representing the first and second parts of the problem, respectively; and iii) a trial state determination unit for generating a trial state representation for a particular value of the one or more variational parameters, the trial state representation comprising a first part and a second part representing the first and second parts of the problem, a transformation unit for transforming a trial state description into an operation trial state description comprising a series of quantum operations to be applied to quantum representation elements of the quantum computer to prepare a representation of the trial state representation, the series of operations comprising: a) a second operation determined based on the second part of the trial state representation; and b) a first operation determined based on the first part of the trial state representation; and iv) a control signal providing unit for providing control signals for controlling the application of the determined series of quantum operations on the quantum computer such that a representation of the trial state representation is prepared, and further for controlling a readout of the quantum computer to measure at least one observable quantity of a quantum mechanical state of the prepared representation of the trial state representation after application of the determined series of quantum operations, wherein the control signals are provided such that a control signal referring to the first operation and a control signal referring to the second operation are performed by different parts of the quantum computer.

[0005] The trial state representation includes first and second parts representing first and second parts of the problem, the conversion unit is adapted to convert the trial state representation for a particular value of one or more variational parameters into a representative quantum trial state description including a) a second operation determined based on the second part of the problem and b) a first operation determined based on the first part of the problem, and the control signal providing unit is adapted to provide control signals for controlling the application of the determined sequence of quantum operations to the quantum computer such that the control signals referring to the first operation and the control signals referring to the second operation are executed in different parts of the quantum computer, so that the control and also the required quantum resources can be specifically adapted to each part of the problem. In particular, the first part, for example referring to fermion-boson interactions or spin-boson interactions, can be implemented by utilizing specially adapted control signals and quantum computing resources. This makes it possible to reduce the general requirements for quantum mechanical resources, in particular quantum mechanical hardware. Furthermore, due to the division of the problem into first and second parts that are treated differently, more efficient control of the quantum mechanical resources of the quantum computer is possible, for example, because the first part of the problem can be implemented on components of the quantum mechanical hardware of the quantum computer that are easier to control than quantum devices. Thus, in general, the quantum resources required to solve a problem can be reduced, allowing for the solution of more sophisticated problems.

[0006] Furthermore, because variational methods are chosen in this context, the complex time evolution resulting from the coupling of boson modes to fermion or spin modes in the first part of the problem can be avoided by variational optimization techniques, for example, by providing the possibility of introducing optimization parameters that can be adjusted on a classical computer. This reduces the complexity of quantum mechanical calculations, enabling a reduction in the quantum computer resources required to solve the problem, directly leading to easier and less complex control of quantum mechanical components on a quantum computer. Since the error rate of a quantum computer is directly related to the computation time and therefore the amount of quantum computing resources used, this not only makes control more effective, but also further improves the reliability of the results of quantum mechanical calculations.

[0007] In general, the apparatus can be implemented in software or hardware, or a combination thereof, where the hardware can correspond to any known dedicated or general-purpose classical computer hardware. For example, the apparatus can be implemented as a known computing device, such as a PC. However, the apparatus can also be implemented in a cloud environment, a computer network, etc., where at least parts of the apparatus can also be implemented as a network solution and distributed across multiple computing devices. The apparatus is adapted to provide control signals that can be provided to, i.e., interpreted by, any known quantum computer hardware architecture. However, in a preferred embodiment, the quantum computer utilized for the quantum mechanical calculation of the problem for which the apparatus provides control signals is specifically adapted and dedicated to solving the problem including the first and second parts.

[0008] The problem to be solved by the quantum computer corresponds to a problem including a first part and a second part, where the first part includes quantities that describe the problem as they interact with each other, and the second part includes quantities that describe the problem without interacting with each other. In one embodiment, the first part may include only quantities that describe the problem as they interact with each other, and / or the second part may include only quantities that describe the problem without interacting with each other. Preferably, the problem can be provided in the form of a quantum mechanical description or in a form that can be converted into a quantum mechanical description, where the first part is represented by boson fields that interact with fermions or spins, and thus describe the quantities in the problem as they interact with each other, and the second part is represented by fermions or spins that do not interact with each other, and thus describe the quantities in the problem without interacting with each other. Preferably, the interaction of the quantities that describe the problem in the first part refers to a dynamical interaction, i.e., a frequency- or time-dependent interaction of each interacting quantity, and the interaction may be a delayed or transient interaction. Furthermore, the problem may include a third part, which also includes quantities describing problems that interact with each other, in particular that interact with each other statically, i.e., that there is no time or frequency dependence on the interaction between each interacting quantity. The third part of the problem is preferably also processed by a second sub-operational unit of the quantum computer. Thus, in some embodiments, the third part of the problem can be considered to be part of the second part of the problem, which is also processed by the second sub-operational unit of the quantum computer. If the problem is provided in a quantum mechanical description, the third part of the problem may, for example, correspond to statically interacting fermions, e.g., fermion density-density interactions.

[0009] The problem providing unit is adapted to provide a problem description that indicates a problem that can be converted into a quantum mechanical description that indicates or includes a first part and a second part to be solved, in particular a problem description that indicates or includes fermion-boson or spin-boson interactions. In particular, the problem providing unit may correspond to a storage unit in which the problem description is already stored. However, the problem providing unit may also include an input unit, for example, by which a user can indicate the problem description to the problem providing unit. The problem description may correspond to any format that allows determining the quantities that describe the problem and the form of interaction between these quantities. Preferably, the problem description corresponds to a mathematical description of the problem. However, the problem description may also correspond to any other clear notation format of the problem. In a preferred embodiment, the problem description is already provided in the form of a quantum mechanical description, which expresses the problem in terms of quantities that obey quantum mechanical rules, i.e., refers to the representation of the problem in the quantum mechanical world. However, the problem description can also be provided in any other format, in which case the providing unit is preferably adapted to convert the provided problem description into a quantum mechanical problem description before providing it to the trial state determination unit. However, this conversion can also be omitted, in which case the trial state determination unit and the conversion unit are preferably adapted to process the respective form of problem description accordingly, for example by utilizing principles derived from the processing of problem descriptions in quantum mechanical descriptions.

[0010] The trial state determination unit is adapted to determine a trial state representation of the problem statement based on a variational approach. In particular, the trial state representation is optimizable with respect to one or more variational parameters, and an optimized state of the trial state representation indicates a solution to the problem. In general, a variational approach refers to solving a problem using a calculation of variations, which refers to finding a function that, when optimized with respect to optimization parameters, also called variational parameters, provides a solution to the problem. In general, the trial state representation of the problem statement refers to a function that, in its optimized state, provides an indication of the solution to the problem, and the trial state representation is optimized with respect to one or more variational parameters. The trial state determination unit may be adapted to determine a trial state representation of each problem statement using any known method for a variational approach. Some exemplary methods and principles for variational approaches and for finding a trial state representation for a given problem statement can be found, for example, in the paper “Variational Quantum Algorithms”, Cerezo, M., et al., Nat Rev Phys 3, 625-644 (2021). Preferably, the variational approach refers to a variational Hamiltonian hypothesis or a variational quantum eigensolver. In general, the trial state determination unit may be adapted to determine a trial state representation by determining a unitary evolution operator to be applied to a predetermined initial state of the quantum mechanical system described by the problem. The unitary evolution operator may be any operator that transforms the predetermined initial state into the determined trial state representation. This determination of the trial state representation may be directly considered as a representation of a computation to be performed on a quantum computer, in which a sequence of quantum operations is applied to initial states of quantum representation elements of the quantum computer.

[0011] The variational parameters are generally abstract parameters defined solely to enable optimization of the trial state representation. Thus, the variational parameters need not refer to specific physical or problem-related quantities. Since the problem to be solved includes a first part and a second part, the trial state determination unit is adapted to determine a trial state representation that includes a first part and a second part representing the first part and the second part of the problem, respectively. In particular, the first part of the trial state representation is also preferably convertible into a quantum mechanical description that references fermion-boson interactions or spin-boson interactions, and the second part of the trial state representation is also preferably convertible into a quantum mechanical description that references non-interacting fermions or non-interacting spins, respectively. Thus, the general structure of the problem as described above is maintained during the transformation to the trial state representation.

[0012] The transformation unit is adapted to transform the trial state representation for a particular value of one or more variational parameters into a representative operational trial state description. In particular, the transformation unit is adapted to determine a representative operational trial state description from the problem description, the representative operational trial state description including a series of operations to be performed by the quantum computer to prepare a representation of the trial state representation on the quantum computer. Generally, operations are performed by the quantum computer by manipulating the states of quantum representation elements of the quantum computer. A quantum representation element refers to an element of the quantum computer used to simulate the problem; for example, a quantum representation element may refer to a quantum element forming a qubit, but may also refer to a boson field representing a boson mode during the problem's calculation. The transformation unit is adapted to transform the trial state representation into a representative operational trial state description such that the series of quantum operations includes a) a second operation determined based on the second part of the trial state representation and b) a first operation determined based on the first part of the trial state representation. Thus, even during this determination of the series of operations, the problem is divided into two different parts that can be specifically adapted to be applied to different parts of the quantum computer. Preferably, the first operation is determined to be executable by a first sub-operational unit of a quantum computer, as described below, and the second operation is specifically adapted to be executed by a second sub-operational unit of a specially modified quantum computer. Thus, to prepare a trial state on a quantum computer, the quantum mechanical description portion of the trial state representation referencing boson-fermion or boson-spin interactions can be implemented in the first sub-operational unit of the quantum computer, and the portion of the trial state representation referencing non-interacting fermions or spins or, optionally, statically interacting fermions or spins can be prepared in the second sub-operational unit of the quantum computer. Preferably, the transformation of the trial state representation with respect to a particular variational parameter into a representative operational trial state representation is based on the Jordan-Wigner or Blavi-Kitaev transformation. In particular, these transformations are applied to the fermion portion of the trial state representation, while other known transformations can be utilized for the boson or spin portion.In particular, the conversion can be omitted for the spin part, and for the bosonic part, standard binary coding, Gray coding and / or unary coding, as described in, for example, the paper "Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians", Sawaya, NPD, Menke, T., Kyaw, TH et al., npj Quantum Inf 6, 49 (2020), which is incorporated herein by reference, can be used when a generally known quantum computer is used, especially when the bosonic part is represented by a quantum element of the quantum computer. However, if the quantum computer used includes a first sub-operation unit specially adapted to represent the bosonic part, especially the bosonic element, the conversion can also be omitted. When the trial state representation is determined by determining a unitary evolution operator and an initial state of the quantum mechanical system described by the problem, determining the sequence of operations for the representative computational trial state description may include determining an operation for preparing a representation of the initial state on a quantum computer and a sequence of operations for applying the representation of the unitary evolution operator to quantum representation elements in the representative initial state so that the representation of the trial state representation, i.e., the trial state, is prepared on the quantum computer. However, in some cases, the initial state can be determined in advance so that it is automatically prepared on the quantum computer at the start of the computation. In such cases, the sequence of operations may also include a sequence of operations for applying the representation of the unitary evolution operator to quantum representation elements in the representative initial state so that the representation of the trial state representation, i.e., the trial state, is prepared on the quantum computer.

[0013] If the problem description is not provided in the form of a quantum mechanical description, the conversion unit is preferably further adapted to appropriately convert the problem description, e.g., by mapping the problem description to a Hamiltonian of a quantum mechanical system that defines the problem as a set of similar relationships and influences between quantities. Thus, for example, an optimization problem corresponding to the optimization of production parameters, such as temperature, pressure, and flow rate, for producing a product, can be converted into a quantum mechanical description that represents the problem in the quantum mechanical world of a quantum computer. In such a case, for example, an Ising model can be used for the conversion. However, if the problem already represents a quantum mechanical problem, e.g., an electronic structure problem, this particular step of converting the problem into a quantum mechanical description can be omitted. In general, the conversion unit may be adapted to convert the problem description based on predetermined rules or predetermined models for a particular problem category, or it can be adapted to convert the problem description interactively based on user input. In the case of interactive processing, a user interface may be provided that allows the user to select different problem categories, e.g., optimization problems, electronic structure problems, etc., to determine the category of the provided problem, and further select a respective set of rules or model to be applied to transform the provided problem. However, other interactions may also be performed by the user interface to transform the problem. Furthermore, to transform the provided problem, the transformation unit may also be adapted to access a storage device in which transformations for a particular problem have already been saved.

[0014] The control signal providing unit is configured to provide control signals for controlling the execution of the determined series of quantum operations on the quantum computer such that a representation of the trial state representation is prepared. In particular, the control signals are provided such that a control signal referring to a first operation and a control signal referring to a second operation are executed by different parts of the quantum computer. Preferably, the different parts of the quantum computer refer to different hardware parts of the quantum computer. The different parts of the quantum computer may be different hardware parts controlled by different control hardware. However, the different parts may also refer to the same hardware part virtually divided into different parts that can be controlled independently. The different parts of the quantum computer may also be parts of the quantum computer predefined as different parts of the quantum computer that are controlled differently. In one embodiment, the different parts of the quantum computer refer to a second sub-operational part configured to utilize the quantum mechanical states of the quantum elements to form qubits that can be manipulated by operations performed on the quantum elements, and a first sub-operational part configured to couple boson fields to the quantum elements. For example, the control signal referring to the first operation may be executed by the first sub-operational part by manipulating the coupling of boson fields to the quantum elements that form the qubits, and optionally, an expression that refers to the boson fields themselves. A second operation may then be performed by a second sub-operational portion of the quantum computer by manipulating the states of quantum elements, or qubits, on the quantum computer.

[0015] Preferably, the control signal providing unit is configured to generate control signals for controlling a quantum computer, in particular an operating unit of a quantum computer configured to manipulate the state of a quantum expression element according to a determined sequence of operations. However, if the quantum computer itself already provides a control unit adapted to control the operating unit so that the state of the quantum expression element is manipulated, the control signal providing unit of the device can be adapted to provide a control signal to the control unit of the quantum computer. In this case, for example, the control signal may simply refer to an expression of the determined sequence of operations that can be interpreted by the control unit of the quantum computer to provide a respective control signal for controlling the quantum computer's parts accordingly. However, the control signal may also refer to a generally known and interpretable control signal that is converted by the control unit of the quantum computer into a respective dedicated control signal for controlling specific hardware of the quantum computer. Therefore, the control of the control signal providing unit of the device can be direct or indirect depending on the respective implementation of the quantum computer. Therefore, the control signal providing unit of the device, alone or together with the optional control unit of the quantum computer, can be considered to refer to an interface between the quantum computer, in particular the quantum computer's hardware, and software for solving each problem running on a generally known classical computer.

[0016] Furthermore, the control signal providing unit is adapted to control the readout of the quantum computer, in particular the readout of the states of the quantum representation elements, to measure at least one observable of the quantum mechanical state of the prepared representation of the trial state representation, in particular the quantum mechanical state of the quantum representation elements, after application of the determined sequence of quantum operations. In particular, the control signal can be adapted to control the readout of the quantum computer such that one or more observables are measured, i.e. read out, after preparation of the trial state representation is complete. In particular, the control signal providing unit can be adapted to receive the readout of the readout unit and provide the readout to a result determination unit that is, for example, part of the classical computer environment. However, as mentioned above, here too the control signal providing unit can optionally interact with the control unit of the quantum computer to function as an interface between the classical computer environment and the quantum computer.

[0017] In one embodiment of the present invention, the apparatus further comprises an iteration control unit for controlling optimization of the trial state representation using iterations of one or more variational parameters of the trial state representation until the at least one readout observable or a quantity derivable from the at least one readout observable converges, the iterations including adapting and transforming the one or more variational parameters of the trial state representation, providing control signals to prepare the trial state, and providing control signals for readout until the at least one observable or derivable quantity converges to at least one final observable or derivable quantity. The apparatus further comprises a result determination unit for identifying a solution to the problem based on the at least one final observable or derivable quantity.

[0018] Generally, an iteration, or iterative procedure, refers to a series of repetitions of a process until some predetermined condition is met, and in an iteration of a process, the result of a single iteration step generally serves as the starting point for the next iteration step. In this embodiment, an iteration refers to modifying variational parameters of a trial state representation until at least one readout observable or derivable quantity converges, i.e., reaches a predetermined convergence criterion. In some embodiments, the convergence criterion may also refer to the variational parameters converging during an iteration. In particular, an iteration may refer to searching for a minimum or maximum value of one or more readout observable or derivable quantities. The predetermined convergence criterion may then refer to, for example, a residual threshold that determines convergence when the difference between the observable or derivable quantity or variational parameter of the current readout and the observable or derivable quantity or variational parameter of the readout determined during a previous iteration step is below a predetermined residual threshold. However, if convergence is not reached for at least one observable or derivable quantity or variational parameter, for example, due to a failure or error occurring during the iteration, the iteration may be aborted without reaching convergence, for example, based on an alternative abortion criterion. For example, the stopping criterion may refer to a predetermined number of iteration steps after which convergence is assumed not to be possible and the iterations are stopped. In this regard, a derivable quantity refers to a quantity that can be mathematically derived from one or more readout observables. For example, in some embodiments, it may be advantageous to use a convergence criterion that refers to a reduced density matrix, a value for which may be determined based on one or more readout observables.

[0019] Generally, an iteration begins by providing initial variational parameters as a starting point for the iteration. The initial variational parameters can have any value or can be selected based on any known iterative optimization process, e.g., the initial variational parameter values ​​can be selected based on prior knowledge so as to enable a starting point as close as possible to a convergence point of at least one read-out observable or derivable quantity. The iteration then begins by implementing the initial variational parameters into a trial state representation and utilizing a transformation unit and a control signal providing unit to provide control signals that enable preparation of the trial state representation of the initial variational parameters on the quantum computer and read-out of the resulting at least one observable quantity. Based on a known iterative algorithm, the iterative control unit can then be adapted to adapt the variational parameters for the next iteration step, e.g., based on the parameters from the previous iteration and based on at least one previously measured observable quantity. For example, a suitable algorithm for determining the variational parameter values ​​for the next iteration step can be a quasi-Newton method such as the constrained optimization with linear approximation (COBYLA) algorithm or the memory-limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. In general, other gradient-based methods, such as the conjugate gradient (CG) algorithm, can also be used.

[0020] The newly determined variational parameters are then again implemented into the trial state representation, and the steps of converting and providing control signals for preparing this trial state representation and for reading out at least one observable are repeated until a convergence criterion is met, i.e., at least one observable convergence or general abort criterion is met. Such a general abort criterion may, for example, refer to a predetermined number of iteration steps that should not be exceeded, or may refer to some other quantity that indicates an iteration has failed, for example, due to an excessive amount of errors or failures. However, in general, the at least one readout observable will converge after a reasonable amount of iteration steps, and the at least one readout observable determined in the last iteration step is determined as the at least one final readout observable. The at least one final observable then indicates a solution to the problem according to the variational approach, and a result determination unit is adapted to determine a solution to the problem based on the at least one final observable.

[0021] The result determination unit is adapted to determine a solution to the problem based on the one or more retrieved observables. For example, the result determination unit can be adapted to convert the one or more retrieved observables indicative of a solution to the representative quantum mechanical description of the problem into respective solutions in the problem description, e.g., using the same conversion as used to convert the problem description into the representative quantum mechanical description. Additionally and / or alternatively, the result determination unit can be adapted to perform further calculations or operations based on the one or more retrieved observables to determine the solution to the problem. For example, an averaging process, an error correction process, a further optimization process, etc. can be applied based on the one or more retrieved observables to determine the solution to the problem. Generally, the solution to the problem may then be provided to a user via an output unit, e.g., a display, or may be further utilized, e.g., to directly control the production of a product according to respective optimized production parameters.

[0022] In a preferred embodiment, at least one measured observable indicates the energy of a prepared trial state representation, and convergence of the at least one observable indicates energy minimization. In particular, determining a trial state representation such that the measured observable, and thus the observable to be optimized, indicates the energy of the prepared trial state representation, and convergence of the at least one observable indicates energy minimization, makes it possible to solve optimization problems, particularly quantum mechanical many-body problems, which refer to the determination of quantum mechanical systems, such as ground or excited states of quantum mechanical many-body systems, electrons in atoms or molecules, spins in solids, etc. However, this approach can also be advantageous for all other problems, particularly optimization problems, which can be converted to a quantum mechanical description that refers to the determination of ground or excited states of a quantum mechanical system.

[0023] In one embodiment, the control signal providing unit is adapted to provide a control signal for controlling the quantum computer to prepare a predetermined initial state representation on the quantum computer before applying the determined sequence of operations to prepare a trial state representation. Preferably, this state includes overlap with the converged solution of the problem, or the state satisfies the same symmetries, e.g., the same number of particles, as the ideal solution state. Such an initial state may be, for example, a ground state of a non-interacting quantum mechanical system or a simplified model such as a Hartree-Fock ground state, or may be selected to span a significant portion of the computational space. Preparing a first predetermined initial state representation, i.e., preparing a transformation of the quantum computer's quantum representation elements to the initial state as a specific state, ensures that the preparation of the trial state representation on the quantum computer can always start from the same starting point, i.e., the preparation of the trial state representation can always be determined based on knowledge of the initial state. This allows for more effective control and more accurate results for the preparation of the trial state representation. This leads to more accurately identifying the results of the quantum mechanical calculation and fewer iterative steps on the quantum computer to find a solution to the problem. In some embodiments, the initial state refers to the ground state of the mean-field representation of the problem or the Hartree-Fock state of the first part of the problem. Preferably, the initial state refers to the Hartree-Fock reference state of the fermionic part of the problem for the quantum elements, the mean-field state of the spin part of the problem for the quantum elements, and the mean-field state of the bosonic part of the problem for the bosonic elements of the quantum computer, with the interactions between these parts set to zero in the initial state. However, other initial states may be prepared that may be advantageous for preparing a particular problem or trial state.

[0024] In a preferred embodiment, the problem statement is expressible by a quantum mechanical description including fermion-fermion interactions, and the apparatus further comprises a transformation unit adapted to transform the problem statement into a problem statement expressible by a quantum mechanical description including boson-fermion interactions as a first part of the problem and non-interacting fermions as a second part of the problem. Furthermore, a representation of the non-interacting boson fields can also be considered as part of the first part of the problem. In general, the transformation is preferably adapted to transform the fermion-fermion interactions of the quantum mechanical description of the problem into a fermion-boson interaction that defines a link between the fermion-fermion interactions, the boson field resonance frequency, and the fermion-boson field coupling strength. Optionally, the transformed quantum mechanical description may further include statically interacting fermions as a third part. For example, the problem statement can be provided directly as a quantum mechanical description of a fermion-fermion interaction problem, or the problem statement can generally be expressed by a quantum mechanical description of a fermion-fermion interaction problem. Preferably, before transforming the problem, the transformation unit is adapted to transform the problem description into a quantum mechanical description that the transformation unit can use to transform the problem according to respective quantum mechanical laws and algorithms. However, the transformation unit may also be adapted to transform the problem description into any other form or notation that clearly describes the problem, where each transformation used may be based on rules inferred from a quantum mechanical transformation into a quantum mechanical description of the problem. In a preferred embodiment, the transformation unit is adapted to transform the problem description that references a quantum mechanical description including fermion-fermion interactions by using the Hubbard-Stratonovich transformation. However, other known transformation algorithms may also be used.

[0025] In one embodiment, the problem description includes at least some portions expressible by a quantum mechanical description that includes static fermion-fermion interactions as a third part of the problem, and the conversion unit is adapted to approximate these portions of the problem by utilizing the restricted random phase approximation (cRPA). This allows for a reduction in the number of fermion states to be simulated during the quantum mechanical calculation of the problem, thereby reducing the number of operations and the number of quantum elements used in the calculation. Therefore, more complex and larger-scale problems, i.e., problems represented by a larger number of fermion states, can be calculated on a quantum computer. In general, cRPA allows for a distinction between fermions that play an active role in solving the problem and fermions that are considered to be a general background for the active fermions. For example, when simulating a reaction between different molecules, only the electrons residing in the outer orbitals, i.e., the valence orbitals, are considered to play an active role in solving the problem, while the electrons residing in the core orbitals of the atoms can be considered to merely provide a background for the electrons residing in the outer orbitals. Another example is transition metal oxide materials, where only narrow d states close to the Fermi energy play an active role in the calculation, while other electronic states are considered as an effective screening background for cRPA. By applying the constrained random phase approximation, in this situation the background fermions, rather than individuals, can be described as charge clouds interacting with the active fermions, providing a screening effect for the active fermions in particular.

[0026] In one embodiment, the problem description refers to a quantum mechanical description, and the transformation unit is adapted to transform the quantum mechanical description of the problem into a rotating reference frame, in particular by applying a rotating wave approximation, before transformation into the representative computational description. Preferably, the transformation unit is adapted to further apply a rotating wave approximation to the quantum mechanical description in the rotating reference frame. The use of a rotating reference frame and a rotating wave approximation in the quantum mechanical description simplifies different time scales that result from different parts of the hardware operating on these different time scales. For example, the second sub-computing unit may operate on a different time scale than the first sub-computing unit, depending on the actual realization of the quantum computer. The rotating reference frame and the rotating wave approximation allow these different time scales to be more easily synchronized during the quantum mechanical calculation of the problem.

[0027] In a further aspect of the invention, there is presented a system for processing a problem, the problem comprising a first part and a second part, the first part comprising quantities describing the problem that interact with each other and the second part comprising quantities describing the problem that do not interact with each other, the system comprising i) the above-mentioned apparatus for providing control signals for controlling a quantum computer, and ii) a quantum computer adapted to process the provided control signals so as to perform a quantum mechanical calculation. Preferably, the first part is convertible into a quantum mechanical description referring to fermion-boson interactions or spin-boson interactions and the second part is convertible into a quantum mechanical description referring to non-interacting fermions or non-interacting spins, respectively.

[0028] In a preferred embodiment, the quantum computer comprises: i) a second sub-operation unit configured to utilize quantum mechanical states of the quantum elements to form qubits that are manipulable by operations performed on the quantum elements, the operations being associated with the second part of problem; ii) a first sub-operation unit configured to couple boson fields to the quantum elements, the coupling of the boson fields to the quantum elements being manipulable by operations associated with the first part of problem; iii) an operation unit configured to a) operate the second sub-operation unit such that the states of the quantum elements are manipulated based on control signals indicative of the operations associated with the second part of problem, and b) operate the first sub-operation unit such that the coupling of the boson fields to the quantum elements is manipulated based on control signals indicative of the operations associated with the first part of problem; and iv) a readout unit configured to measure at least one observable of a) the quantum mechanical state of each quantum element that represents the state of the respective qubit and b) the boson field after manipulation of the quantum elements and the boson coupling to perform the quantum mechanical computation.

[0029] Because quantum computers are configured such that different parts of a problem can be solved by different parts of the quantum computer, the existence of different dedicated parts of the quantum computer results in more reliable solutions. In particular, because each interacting part of the problem does not need to be simulated by the same part of the problem as the non-interacting quantities, e.g., because quantum elements do not need to be utilized solely to perform the calculations for the interacting parts, the calculations use fewer resources in hardware, i.e., fewer entanglement operations that require sophisticated control of the quantum mechanical system.

[0030] Furthermore, the readout unit is configured to measure not only one observable of the quantum mechanical state of each quantum element representing each qubit state, but also the state of the boson fields, specifically the representation of the boson fields in the quantum computer coupled to each quantum element, thereby providing additional information about the interacting quantities of the problem. This increases the degrees of freedom for solving problems on the quantum computer. Furthermore, because boson fields are generally easier to implement and offer simpler control concepts in hardware implementations, quantum mechanical calculations are less prone to error and therefore more reliable. Thus, more sophisticated problems can be solved with greater precision.

[0031] Generally, a quantum computer can be realized in any known manner, and the following embodiments describe a preferred manner. For example, a quantum computer may be based on superconducting elements, quantum dots, neutral atoms in an optical lattice, nitrogen-vacancy centers in diamond, Bose-Einstein condensates, trapped ions, etc. Because there are multiple different manners, different parts of a quantum computer can also be realized in multiple different manners. For example, in a superconducting quantum computer, the boson field can be represented by an electromagnetic resonator, while in a trapped-ion quantum computer, the boson field can be represented as the vibrational mode of a trapped ion. Preferably, the quantum computer refers to a quantum computer based on quantum gates.

[0032] Quantum computers are generally adapted to perform quantum operations based on control signals that determine a solution to a problem. A quantum operation may refer to an operation performed directly or indirectly on a quantum computer's elements that realize a quantum mechanical description of a problem, i.e., that can be described in terms of quantum mechanical laws instead of classical physics. However, while a quantum computer's elements can be used to realize a quantum mechanical description of a problem, i.e., that can be described according to quantum mechanical laws, the elements themselves do not necessarily correspond to quantum mechanical systems, e.g., atoms or ions. For example, in some embodiments, electromagnetic resonators are used to represent bosonic fields in a quantum computer that generally obey the laws of classical physics, but these resonators can also be described as quantum mechanical quantities in the context of a quantum computer. Preferably, quantum operations include all operations that can directly or indirectly affect quantum elements, i.e., qubit states of a quantum computer. For example, an operation performed on a bosonic field representation also affects the quantum elements through the coupling between the bosonic field and the quantum elements. Thus, an operation performed on a bosonic field representation may also refer to a quantum operation. Quantum operations therefore include direct operations on quantum elements, and hence qubits, on boson fields, and on the coupling of boson fields and quantum elements.

[0033] The control signals underlying the operations performed by the quantum computer are provided by apparatus according to the above-described embodiments of the apparatus.

[0034] The second sub-operational unit, i.e., the fermion or spin operation unit, is configured to utilize the quantum mechanical states of the quantum elements to form qubits that can be manipulated by operations performed on the quantum elements. In general, the second sub-operational unit can refer to any hardware of a quantum computer that enables operations to be performed on quantum elements. For example, the second sub-operational unit may include not only quantum elements themselves, but also elements that can be used to perform operations on quantum elements. However, the second sub-operational unit may refer only to hardware portions of a quantum computer that are adapted to perform operations on quantum elements. In this regard, the second sub-operational unit is adapted to enable operations to be performed on quantum elements related to a second portion of a problem to be solved during quantum computer computation of the problem. Thus, the second sub-operational unit enables operations to be performed on quantum elements related to non-interacting quantities of the problem. For example, if the problem is described in a quantum mechanical description, the second sub-operational unit is preferably adapted to enable operations to be performed on quantum elements related to non-interacting fermions and / or non-interacting spins of the quantum mechanical description of the problem.

[0035] In the case where the problem includes a third part that refers to static interactions of the quantities that describe the problem, in this case the first part of the problem refers to dynamic interactions of the quantities that describe the problem, but the second part operation unit can also be configured to perform operations on quantum elements related to the third part of the problem.

[0036] The first sub-operational unit, i.e., the bosonic operation unit, is configured to couple a bosonic field to the quantum element. Generally, the bosonic field corresponds to an entity representing a bosonic mode in the quantum mechanical description of the quantum computer system. In some implementations of quantum computers, the coupling between the bosonic field and the quantum element may correspond to a hardware-inductive coupling between the hardware element representing the bosonic field and the quantum element, i.e., the hardware representation of the bosonic field can affect the quantum element. However, in other implementations of quantum computers, the bosonic field can be represented by a specific controllable state of the quantum element, e.g., a vibrational mode, so that no additional hardware element directly representing the bosonic field is required. Preferably, because bosonic fields are non-interacting in the quantum mechanical description, the representation of the bosonic field can also be configured to be non-interacting. For example, the hardware bosonic elements can be configured to be non-interacting, i.e., not necessarily including any connections or couplings to each other.

[0037] The first sub-operational unit may generally refer to any hardware component that enables the coupling of a boson field to a quantum element, e.g., that enables the execution of operations on the quantum element and / or the boson element. In this regard, it should again be noted that the boson field itself can be realized by a hardware element, but also as a specific state of one or more elements of the quantum computer, e.g., the quantum element itself. The first sub-operational unit may therefore include a boson element adapted to represent the boson field during the quantum computer calculation in question, and may further include hardware necessary to couple the boson element to the quantum element, as well as hardware elements that enable the coupling and, preferably, the manipulation of the boson element. However, in other embodiments, the first sub-operational unit may refer only to hardware adapted to enable the coupling of a boson field to the quantum element, and generally to hardware parts that enable the manipulation of the coupling. For example, if the quantum computer refers to an ion trapping system quantum computer, the boson field can be represented by vibrational modes of the ions forming the quantum element, and the coupling and / or manipulation of the coupling can be performed by a control laser that can irradiate the trapped ions with laser light having a specific wavelength.

[0038] The coupling of the boson fields to the quantum elements can be manipulated by operations on a first part of the problem to be solved during quantum computer computation of the problem. Thus, the operations specifically relate to interacting quantities that describe the problem, particularly dynamically interacting quantities. Thus, the interacting quantities of the problem are represented in a quantum mechanical computation system as boson fields interacting with the quantum elements. When a problem is provided in a quantum mechanical description corresponding to a fermion-boson system, as described above, the interacting quantities can be mapped to boson-fermion interactions. Furthermore, when a problem is provided in a quantum mechanical description referring to a fermion-boson system, the interacting quantities can be mapped to boson-spin interactions. This type of representation of interacting quantities allows for the use of hardware components that are much easier to handle and manipulate than the quantum elements themselves to represent at least some of the problem quantities. Therefore, quantum bit operations that would otherwise require the representation of interactions between quantities can be replaced by quantum operations performed on the couplings and / or boson fields, thereby reducing the number of qubit operations that correspond to performing operations directly on the quantum elements. Since the number of qubit operations performed on a quantum element is related to the accuracy of the solution to a problem, utilizing coupled boson fields to solve problems with interacting quantities can improve the accuracy of each result.

[0039] The manipulation unit is configured to manipulate a) the states of the quantum elements and b) the boson field and quantum element couplings. Generally, the manipulation is based on control signals indicative of an intended operation to be performed on the quantum elements or boson field couplings. Preferably, the quantum elements are manipulated based on control signals indicative of an operation related to a second part of the problem, and the boson field couplings are manipulated based on control signals indicative of an operation related to a first part of the problem. The manipulation unit may generally correspond to any hardware configured to manipulate the states of each of the quantum elements or the boson field couplings based on the control signals. Thus, the manipulation unit may be considered to refer to an interface between a) software and / or hardware components utilized to provide the control signals and b) the second and first sub-operational units of the quantum computer that implement the quantum computer calculations. For example, the manipulation unit may refer to a controller for the second and / or first sub-operational units. If the quantum computer corresponds to an ion trapping device in which operations on ions are performed by a laser, the manipulation unit may be implemented as a laser controller.

[0040] The readout unit is configured to measure at least one observable of the quantum mechanical state of each quantum element representing each qubit state after the quantum mechanical calculation has been performed, and also to measure the boson field, i.e., the state of the representation of the boson field in the quantum mechanical calculation, e.g., the state of the boson element or the specific state of the quantum element representing the boson field. Generally, the one or more observables measured by the readout unit depend on the respective implementation of the quantum computer. For example, if the quantum computer corresponds to an ion trapping device, the observables measured for the quantum elements may correspond to the electronic states of each quantum element, and the observables measured for the boson field may correspond to each vibrational mode of the ion in the ion trap. However, depending on the problem, the energy of each system can also be measured as an observable. Generally, the measurement result of each observable indicates a solution to the problem. In particular, depending on the transformation of the problem into a quantum mechanical description, the results of the measurement can be used in further calculations or can be recovered from the quantum mechanical solution of each "real-world" solution of the problem.

[0041] In one embodiment, the bosonic coupling of the bosonic field to the quantum elements is adapted to represent a specific coupling of the first part of the quantity in question during the quantum computer calculation, and the manipulation unit is further adapted to adapt the coupling. In this context, manipulating the bosonic field coupling to the quantum elements is considered to correspond to the general possibility of determining which bosonic field should be coupled to which quantum element by implementing and controlling such coupling, e.g., using quantum operations, and the possibility of performing operations on the bosonic field coupling and optionally the bosonic field itself. Adapting the bosonic field coupling to the quantum elements provides the possibility of tailoring the effect of the bosonic field to at least one quantum element coupled to the field by performing each operation or, for example, by adapting the hardware settings, e.g., using a switch before or during the quantum mechanical calculation. The manner in which the effect of the bosonic field on the quantum element is determined generally depends on the respective implementation of the quantum computer. For example, in the case of a trapped-ion quantum computer in which the bosonic field is represented by the vibrational modes of an ion, the effect on the quantum element represented by the electronic state of the ion can be controlled by controlling the environment of the ion, e.g., by using a laser to transfer energy from the vibrational mode to the electronic state. However, in other implementations of quantum computers, the effect of the boson field on the quantum elements coupled to it can be controlled in other ways.

[0042] In one embodiment, the first sub-operational unit is configured to couple at least one boson field to each quantum element forming one quantum bit. In a preferred embodiment, the first sub-operational unit is configured to couple two or more boson fields to each quantum element forming one quantum bit, preferably four boson fields to each quantum element. It is even more preferred that the operation unit is configured to couple a boson field to only one quantum element forming one quantum bit. In this way, each quantum element may be coupled to one or more dedicated boson fields, each of which is coupled to only one quantum element. This has the advantage of allowing more precise control of the interaction between the boson fields and the quantum elements so that unintended interactions can be avoided. Such control can improve the accuracy of quantum mechanical calculation results, as unintended interactions can lead to inaccurate or erroneous quantum mechanical calculations.

[0043] In the following, preferred alternative embodiments of the quantum computer and each defined part of the quantum computer defined above are described. In a first preferred alternative, the quantum computer refers to a superconducting quantum computer in which quantum elements are realized as superconducting circuits and the coupling of bosonic fields to the quantum elements is realized by providing electromagnetic resonators, preferably also based on superconducting technology, coupled to the superconducting circuits via electromagnetic fields. Preferably, in this embodiment, the first sub-operation unit includes resonators as bosonic elements, and the electromagnetic fields of the resonators represent the bosonic fields in quantum mechanical calculations. In particular, the electromagnetic resonators coupled to the superconducting circuits correspond to additional electromagnetic resonators dedicated to representing the bosonic fields. In this context, it should be noted that electromagnetic resonators used in a superconducting quantum computer to measure the state of the superconducting quantum elements, i.e., to read out qubits, are considered to be part of the readout unit, for example, and cannot generally be used to represent the bosonic fields. Each readout operation performed on the readout resonator destroys the state of the bosonic field represented by the resonator and the coupling of the bosonic field to the quantum element being readout, making the readout results unreliable. Therefore, the electromagnetic resonator that generates the coupling to the superconducting circuit for coupling the quantum element to the bosonic field does not correspond to the electromagnetic resonator used to read out the superconducting circuit and is therefore an additional electromagnetic resonator. In this embodiment, the bosonic coupling portion may include or utilize a microwave source for manipulating the electromagnetic field generated by the resonator and thus for expressing the bosonic field. Furthermore, a microwave source may be used to manipulate the coupling between the electromagnetic field generated by the resonator and the superconducting circuit forming the quantum element.

[0044] In a second alternative preferred embodiment, the quantum computer refers to a trapped-ion quantum computer, the quantum elements are realized as ions trapped in an ion trapping device, and the boson field coupling to the quantum elements is realized as coupling of vibrational modes of the trapped ions to electronic states of the trapped ions, forming qubits. In this embodiment, the first sub-operational unit can include or utilize a laser that manipulates the coupling between the ion's electronic states, i.e., modes, and vibrational modes. For example, laser light having a frequency and amplitude at or near resonance with each wavelength, i.e., mode, can be used to turn the coupling on or off or manipulate the strength of the coupling. In particular, the coupling between electronic and vibrational modes refers to the transfer of energy between these modes. Thus, in the absence of coupling, substantially no energy is transferred between the modes, but in the presence of coupling, the amount of energy transferred determines the strength of the coupling. Preferably, the laser is tunable, and in particular, the laser can be tuned to the resonance frequency of the quantum mechanical problem description, i.e., the resonance frequency of the trapped ion quantum elements. Resonance as used in this context preferably refers to the carrier-transfer resonance, the red sideband resonance, and the blue sideband resonance. The carrier transition resonance corresponds to the transition frequency of the trapped ion between electronic states used in quantum computing calculations without initiating energy transfer to or from the vibrational modes of the ion. The red sideband transition resonance corresponds to a frequency that allows energy transfer from an electronic state of the ion to a vibrational mode of the ion within the ion trap, or vice versa. The blue sideband transition resonance corresponds to a frequency that allows simultaneous excitation of a lower energy electronic state of the ion to a higher energy electronic state and increased excitation of a vibrational mode, or simultaneous transition of a higher energy electronic state of the ion to a lower energy electronic state and decreased excitation of a vibrational mode, thereby allowing both to be manipulated simultaneously.

[0045] In a third alternative preferred embodiment, the quantum computer may refer to any type of quantum computer, in which case the bosonic coupling is achieved by performing additional coupling operations on quantum elements that form qubits representing bosonic fields and their coupling to quantum elements. In this embodiment, the quantum elements used to represent the bosonic fields are preferably coupled to each other so that two-qubit operations can be applied, and at least one of the quantum elements representing each bosonic field is preferably coupled to a quantum element representing a fermion that interacts with each bosonic field so as to represent the interacting fermion, i.e., the first portion. Using such a coupling configuration can reduce the control and operation requirements for the quantum computer hardware compared to, for example, fully interacting fermion calculations without bosonic fields. Furthermore, this configuration can reduce the depth of the circuitry required to perform the quantum mechanical calculation of interest, i.e., reduce the number of quantum operations required to simulate a bosonic field compared to simulations of the problem using other coupling configurations.

[0046] In a further aspect of the present invention, a method is presented for determining control signals for generating a solution to a problem translatable into a quantum mechanical description using a quantum computer, the method comprising: i) providing a problem description indicating a problem to be solved, the problem description indicating a first part and a second part of the problem, the first part including quantities describing the problem that interact with each other, and the second part including quantities describing the problem that do not interact with each other; ii) determining a trial state representation of the problem description based on a variational technique, the trial state representation including one or more variational parameters, the trial state representation including first and second parts representing the first and second parts, respectively; and iii) computing the trial state representation for particular values ​​of the one or more variational parameters on the quantum computer to prepare a representation of the trial state representation on the quantum computer. the quantum computer is provided with a control signal for controlling the application of the determined sequence of quantum operations to quantum representation elements of the trial state representation, the control signal being provided for the first operation and a control signal being provided for the second operation to be executed by different parts of the quantum computer; and v) after application of the determined sequence of quantum operations, providing a control signal for controlling the readout of the quantum computer to measure at least one observable of a quantum mechanical state of the prepared representation of the trial state representation.

[0047] In a further aspect of the present invention there is provided a computer program product for solving quantum mechanical problems, comprising program code means for causing the above-mentioned apparatus to carry out the above-mentioned method.

[0048] In a further aspect of the invention, the use of the above described apparatus is presented for solving problems referring to electronic structure problems, spin problems, and / or optimization problems.

[0049] In a further aspect of the invention, the use of the above-described system is presented for solving problems that refer to electronic structure problems, spin problems, and / or optimization problems.

[0050] In a further aspect of the invention, the use of the computer program product as described above is presented for solving problems referring to electronic structure problems, spin problems, and / or optimization problems.

[0051] Electronic structure problems may be particularly directed to molecular and condensed-system problems. Preferably, molecular problems include problems related to at least one of organometallic compounds containing transition metals, including lanthanides and actinides, metal-interacting chelators, catalysts, biomolecules with active centers, polymeric systems, and transition metal compounds embedded in solution or in an environment. Preferably, condensed-system problems include problems related to at least one of transition metal oxides and rare earth elements, such as perovskites used in solid oxide fuel cells, oxide-based battery cathodes, hard magnets for electric engines, catalysts for fuel cells, transition metal heterostructures for sensors, magnetic semiconductor sandwich structures for spintronics, and high-temperature superconductors.

[0052] It is to be understood that an apparatus as described above, a system including an apparatus as described above, a method as described above and a computer program product as described above have similar and / or identical preferred embodiments, in particular as defined in the dependent claims.

[0053] It is to be understood that a preferred embodiment of the invention can also be any combination of the dependent claims or the above embodiments with the respective independent claim.

[0054] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter. [Brief explanation of the drawings]

[0055] [Figure 1]1 illustrates a qubit state representation used in quantum computing devices. [Figure 2] 1 shows a schematic example of a quantum computing device that uses a quantum bit as a computation unit. [Figure 3] 1 shows a schematic example of a method for generating control signals to process measurement signals from a quantum computing device to perform an operation on the quantum computing device. [Figure 4] 1 shows a schematic example of a hybrid system including classical and quantum computing devices. [Figure 5] 1 shows a schematic example of a quantum computing device based on a superconductor. [Figure 6] 1 shows a schematic example of a trapped ion-based quantum computing device. [Figure 7] 1 illustrates, in a schematic and exemplary manner, one embodiment of a system for determining a solution to a problem. [Figure 8] 1 shows, by way of example only, a flow diagram of a method for determining a solution to a problem. [Figure 9] 1 shows, in a schematic and illustrative manner, an example of a series of operations that can be applied to perform quantum mechanical calculations. DETAILED DESCRIPTION OF THE INVENTION

[0056] Detailed Description of the Drawings Below, we first briefly introduce the general principles of quantum computing and its computational performance. Furthermore, the general principles can also be found in "Quantum Computation and Quantum Information: 10th Anniversary Edition," MA Nielsen and IL Chuang (2010).

[0057] Classical computing devices use transistor-based processors. Each transistor has two controllable states, 1 or 0, which represent digital binary, or bits. To execute operations on a classical computing device, human-readable program code is converted into machine-readable instructions through a compiler. The machine-readable instructions are control signals for each transistor, such as voltage settings. The representation of the machine-readable instructions includes binary or hexadecimal representations. Based on these machine-readable instructions, operations are executed by the processor of the classical computing device.

[0058] Quantum computing is a relatively new method of computing that uses quantum effects such as superposition and entanglement to perform certain calculations more efficiently than classical digital computers. In contrast to digital computers, which represent information in the form of bits (e.g., "1" or "0") as described above, quantum computing devices, or quantum computers, use qubits, or quantum bits, to represent information. Quantum computing devices are based on quantum elements that obey the physical laws of quantum mechanics, such as superconductors, ions, atoms, quantum dots, photons, particle spins, and bosons. These quantum elements can be manipulated in a controlled manner to perform operations.

[0059] Qubits and their operations can be described in terms of their mathematical properties, and each such qubit may be implemented in any of a variety of different ways into physical quantum elements, examples of which include superconducting materials, trapped ions, photons, optical cavities, individual electrons trapped in quantum dots, point defects in solids (e.g., phosphorus donors in silicon or nitrogen-vacancy centers in diamond), molecules (e.g., alanine, vanadium complexes), or any medium that exhibits qubit behavior, including quantum states and transitions between them that can be controllably induced or detected.

[0060] In general, for any given physical quantum element that implements a qubit, any of a variety of properties of that physical unit may be selected to implement the qubit. For example, if an electron is selected to implement the qubit, the x, y, or z component of the electron's spin degree of freedom may be selected as the electron's property to represent the qubit state. For any particular degree of freedom, the physical quantum element can be controllably placed into a superposition or entanglement state, and measurements can then be made at the selected degree of freedom to read out the qubit value.

[0061] In contrast to transistors in classical computing devices, each quantum element in a quantum computing device can be in not only a basis state |1> or |0>, but also any superposition of such basis states, such as the state |X>. The state of each quantum element is represented by a quantum bit, or qubit, state, as shown in a simplified two-dimensional diagram in Figure 1. To represent such states, Dirac notation is commonly used in quantum mechanics. In Dirac notation, states in an n-dimensional complex vector space, such as Hilbert space, are represented by bracket notation, e.g., |X>. In conventional terminology, a superposition of "0" and "1" states in a quantum computing device can be represented by α|0> + β|1>. The states "0" and "1" or bits in a classical computing device are analogous to the basis states |0> and |1> or qubits, respectively, of a quantum computing device. The value |α| 2 represents the probability that the qubit is measured in the |0> state, and the value |β| 2 represents the probability that a qubit is measured in the |1> state. When there are two or more qubits, they may be entangled. Entanglement means that the state of one qubit depends on the state of at least one other qubit and vice versa, and furthermore, in the entangled state, each qubit cannot be identified as an individual qubit. In general, a register of N qubits in a quantum computer can be in a superposition of multiple basis states at once, whereas N classical bits can only be in one basis state at a time. Thus, in contrast to classical computing devices, quantum computing devices can Nbasis states can be manipulated and processed simultaneously, essentially allowing exponential parallel processing.

[0062] To perform operations on a quantum computing device, a computational method for solving a given problem can be converted into qubit operations, which may be converted into control signals that manipulate qubits. The representation of the machine-readable instructions may include a general quantum mechanical representation of operations in Hilbert space. Depending on the specific implementation of the quantum computer, different representations of qubit states may be selected. Setting any state in the quantum computing device can be expressed by operations that act on the qubit states. The operations can be converted into control signals that control parts of the quantum computer, which signals depend on the type of quantum computing device used. In this way, operations can be performed on a quantum equivalent of a classical processor as part of a quantum computing device based on operations that act on the qubit states.

[0063] Operations that operate on qubit states are generally single- or multi-qubit operations. A single-qubit operation may change the state of one qubit into a particular superposition, corresponding to, for example, a rotation of the vector |X>, as shown in Figure 1. For example, in a superconducting quantum computer, this may be achieved by a microwave pulse, or in a trapped-ion quantum computer, by irradiating ions with a laser beam. A multi-qubit operation may create entanglement between two or more qubits. For example, in a superconducting quantum computer, this may be achieved by connecting the qubits through an intermediate electrical coupling circuit, or in a trapped-ion quantum computer, by controlling the collective oscillations of trapped ions.

[0064] Generally, to prepare an operation to solve a given problem, each quantum mechanical representation of the problem is converted into a qubit operation, which is then executed to prepare a predetermined solution. After preparing the predetermined solution, i.e., after applying the operation to the qubits of a quantum computer, projected measurements of the individual qubits are performed, returning either a 0 or a 1 for each qubit. In a quantum computing device, this measurement is achieved by applying a hardware-specific readout protocol of a series of readout operations including control pulses and monitoring the response to the control pulses. For example, a superconducting qubit may be coupled to a hardware resonator. The measured shift in the resonator frequency depends on the coupled qubit state, and therefore the qubit state can be determined. For example, in the case of a trapped ion, an optical readout can be used; if the ion emits light, the qubit state is 1; if it does not emit light, the qubit state is 0, or vice versa. In this way, qubits can be used to implement logic circuits and gates similar to classical computing devices.

[0065] FIG. 2 shows a schematic example of a quantum computer. The quantum computing device 100 shown in FIG. 2 includes a quantum register 104 configured to perform a quantum computing calculation, an operation unit 106 configured to operate quantum elements forming the quantum register, particularly qubits, and a readout unit 108 configured to collect measurement signals from the quantum register 104 to read out the qubits after a quantum mechanical calculation. The operation unit 106 provides, among other things, operation signals for operating the quantum register, which are generated based on received control signals determined based on respective operations to be performed on the qubits. In some embodiments, a feedback loop can be provided between the operation unit 106 and the measurement unit 108. In contrast to classical computing, in which a single measurement cycle is used to obtain the state of a transistor, quantum computing involves performing multiple measurement cycles to obtain probability densities or probabilities of qubit states.

[0066] The quantum register 104 may be based on different quantum elements that represent qubits. In some embodiments, the qubits may be implemented as quantum elements using photons. Such an optical quantum computing device may include a laser that generates photons that are sent down a waveguide. A beam splitter may be provided to manipulate the photon state based on a manipulation signal, such as a mechanical rotation applied to a mirror. The measurement unit 108 may be a photon detector in such an embodiment, and the measurement signal may be a photon.

[0067] In other embodiments, the qubits can be implemented by the electronic states of ions confined in a magnetic field. The manipulation unit 106 can then utilize a laser, and the manipulation signal can provide a control laser pulse. Furthermore, in this case, the readout unit 108 can be a photon detector combined with a readout laser pulse, and the measurement signal 102 can be a photon. Other qubit implementations can be based on superconductors as quantum elements, semiconductor materials with anyons as quantum elements, etc.

[0068] 3 is a schematic diagram illustrating an exemplary method for generating control signals for performing operations on a quantum computing device and processing measurement signals from a quantum computing device. In most embodiments of quantum computing devices known today, the control signals for the quantum computing device are provided by a classical computing device, and the measurement signals provided by the quantum computing device are further processed by a classical computing device. However, other embodiments are possible as quantum computing devices mature.

[0069] In step S10, a problem to be solved with the assistance of the quantum computing device is provided, preferably in a mathematical description, to generate control signals for performing an operation on the quantum computing device. Such a problem may, for example, involve determining material properties based on a mathematical description of the material's electronic structure. Other problems may include optimization problems and associated objective functions. Based on the problem to be solved, an operational description of the problem or subproblem may be generated in step S12, the operational description including operations to be applied to the quantum computer's qubits to solve the problem through quantum mechanical calculations. Furthermore, the operational description may include reference states that allow for generating a representation of an initial qubit state in the quantum computer, after which further operations are applied in the quantum computer by manipulating the qubit states. Based on the operational description, control signals for controlling the quantum computer can be generated in step S14, for example, by providing control signals to an operator, which can then operate the qubits based on the control signals. In step S16, the operator then applies the operation operations to individual or multiple qubits in the quantum computer, causing the qubits to perform a quantum mechanical calculation based on the operation operations. After the operation, a measurement signal can be generated in step S18 that determines the result of the quantum mechanical calculation. This step may include reading out, or measuring, the qubit states after applying a manipulation operation to the initial qubit states. The measurement signal is then converted to a measurand in a classical computer in step S20 and, in the case of a subproblem, fed back into the problem to be solved. Finally, the results of the problem computation, including quantum mechanical computations, may be provided to a classical computing device in step S22.

[0070] FIG. 4 shows a schematic example of a hybrid system including a classical computing device and a quantum computing device. As described with respect to the method shown in FIG. 3, quantum computing devices are often used in conjunction with classical computing devices. As shown in FIG. 4, the problem preparation system can be implemented as a classical computing device 110, for example, performing steps S10, S12, S20, and S22 of the method shown in FIG. 3. A control unit can then be provided to interface the classical computing device 110 with the quantum computer 100, and the control unit can also be a classical computing device, for example, performing step S14. The control unit can then be communicatively coupled to an operator 106, which can control a manipulator on the quantum computing device. The operator 106 can also be implemented as classical control hardware that controls specific hardware elements of a classical computing device, for example, a quantum computer, that perform operations on qubits. However, because the operator 106 directly affects the quantum register, it is generally considered part of the quantum computer. The quantum computing device 100 is specifically adapted to perform quantum operation S16 by manipulating qubits in the quantum register. The measurement unit 108, which is also generally considered to be part of the quantum computing device, can then perform step S18 by utilizing classical hardware. The measurement unit 108 can then be communicatively coupled to a configuration system 110 for further processing of the measurement signal.

[0071] FIG. 5 shows a schematic example of a superconductor-based quantum computing device. Superconducting quantum computing devices are a type of solid-state quantum computing technology. Here, quantum register 104 may include Josephson junction-based superconducting circuits 520, 522, and 524. A qubit may then correspond to, for example, a charge, flux, transmon, or phase qubit, depending on the quantity of superconducting circuitry selected to represent the qubit. FIG. 5 shows a simplified diagram of a superconducting quantum computer utilizing charge qubits. For charge qubits, different qubit states are represented by an integer number of Cooper pairs in the superconducting islands. Quantum operations can then be performed by manipulating the qubits via microwave pulses. Resonators 512, 514, and 516 can be used to manipulate the qubit states by applying microwaves or to read out the qubit states by measuring the microwaves, with different resonators typically used for manipulating the qubit states and reading out the qubits. Additionally, resonator 518 can be used to apply microwaves that entangle the qubits. However, entanglement can also be achieved by inductive or capacitive coupling of a superconducting circuit rather than by a resonator 518, or by providing another qubit, here a superconducting circuit, between the qubits to be entangled.

[0072] Such systems are maintained at extremely low temperatures, e.g., tens of millikelvins (mK), at the computational level. Extreme cooling of the system helps keep the superconducting material below its critical temperature and avoid unwanted state transitions. To maintain such low temperatures, quantum information processing systems may operate in cryostats, such as dilution refrigerators. In some implementations, control signals are generated in a hotter environment and transmitted to the quantum computer using shielded, impedance-controlled, gigahertz-capable transmission lines, such as coaxial cables. In some implementations, superconducting qubit state measurements are achieved using a distributed detection scheme. To read out or detect the state of any qubit, a probing signal, e.g., a traveling microwave, can be excited along a readout transmission line coupled to the qubit via each readout resonator. The frequency of the probing signal can be near the resonant frequency of the readout resonator. Depending on the internal quantum mechanical state of the qubit, the intensity or phase of the probing signal transmitted along the readout transmission line can change due to changes in the reflectivity of the readout resonator coupled to the qubit. This enables qubit state detection, where the qubit state collapses, i.e., is projected into one of the basis states, with each probability, during readout. Each probability can be determined by performing multiple quantum mechanical calculations and readouts. Further details of superconducting quantum devices are described in documents such as EP 3830867 A1, EP 3449427 A1, US 2020272925 A1, CN 212061223U, and US 2019019099 A1.

[0073] Figure 6 shows a schematic example of a quantum computing device based on ions in an ion trap. Similar to neutral atom traps, ion traps using, for example, positively charged calcium ions can also be used to implement quantum computing devices. Here, ions 626 are trapped in an oscillating electromagnetic field 624 in a high or ultra-high vacuum. The ions 626 are laser cooled and held in the oscillating electric field 624. Laser light 628 of different frequencies may be used for qubit operations such as superposition or entanglement.

[0074] Generally, gate-model computations can be performed on quantum computer hardware architectures based on the above-described quantum computer implementation methods. Gate-model computations are based on quantum gates. In contrast to classical gates, there are an infinite number of one-qubit quantum gates that can transform the qubit state vector. Changing the state of a qubit state vector is typically called a one-qubit rotation, also referred to herein as a state change or one-qubit quantum gate operation. A rotation, state change, or one-qubit quantum gate operation can be mathematically expressed as a unitary 2×2 matrix with complex elements. A rotation corresponds to the rotation of a qubit state in Hilbert space, which can be conceptualized as the rotation of a vector on the Bloch sphere, commonly known as a geometric representation of the space of pure qubit states. A multi-qubit gate changes the quantum state of a collection of qubits. For example, a two-qubit gate rotates two qubit states as a rotation in the four-dimensional Hilbert space of two qubits. As commonly known, Hilbert space is an abstract vector space with a dot-product structure where length and angle are measurable. Furthermore, Hilbert spaces are complete, meaning that there are limits in the space that allow the use of calculus techniques.

[0075] Hereinafter, the term "operational description" refers to a representation of a problem that includes a sequence of quantum operations to be applied during a quantum mechanical computation of the problem. In the context of the present invention, the term "quantum operation" may include all types of quantum gates mentioned above. Furthermore, the term may also include operations performed on elements of a quantum computer that represent couplings between quantum elements and boson fields that form qubits, and, optionally, elements that represent the boson fields themselves. These operations refer to any kind of change in the state of the couplings or boson fields that represent the elements, such as switching a coupling on or off or changing the frequency of the field. Furthermore, in some applications, quantum operations may also include measurement operations. This allows algorithms to be implemented using measurement feedback. For example, in such algorithms, a quantum computer may execute a quantum gate defined by a sequence of quantum operations, then measure only a subset, i.e., not all, of the other computational elements, such as qubits or boson field states, within the quantum computer, and then determine which further quantum operations to perform next based on the results of one or more measurements. Measurement feedback is particularly useful for, but is not limited to, performing quantum error correction.

[0076] Below, embodiments of the present invention are described, some of which may be adapted to utilize the generally known quantum computer devices described above.

[0077] 7 shows a schematic and exemplary embodiment of a system 700 for processing problems, e.g., electronic structure problems, in quantum computing. The system is specifically adapted for solving problems including first and second parts, where the first part includes quantities that describe the problem interacting with each other and the second part includes quantities that describe the problem without interacting with each other. Preferably, the problem can be expressed in a quantum mechanical description including fermion-boson interactions and, optionally, boson fields that interact with the fermions but do not interact with each other as the first part, and non-interacting fermions as the second part. Furthermore, the problem may include a third part corresponding only to statically interacting quantities, which can be expressed in a quantum mechanical description preferably as static fermion-fermion interactions.

[0078] The system includes a quantum computer 710 and an apparatus 720. Optionally, the system may further include a control unit 730 as an interface between the apparatus 720 and the quantum computer 710. However, an explicit control unit 730 may also be omitted or may be a dedicated part of the quantum computer 710, for example. The quantum computer 710 of the system may refer to any known quantum computer solution relating to the known quantum computer architectures already mentioned above. However, in a preferred embodiment, the quantum computer 710 is dedicated to the calculation of the problem involving the first and second parts, and in particular, it is preferred that the quantum computer 710 includes respective hardware structures that enable highly efficient processing of each problem. Preferably, the quantum computer refers to a modified quantum computer as described below.

[0079] Quantum computer 710 includes a second sub-operational unit 711 configured to utilize the quantum mechanical states of quantum elements to form qubits. For example, the second sub-operational unit may utilize, and optionally include, quantum registers, such as those described with respect to Figure 2. In general, the quantum elements that form qubits are manipulable by quantum gate operations performed on the quantum elements.

[0080] Furthermore, quantum computer 710 preferably includes a first sub-operational unit 712 in addition to second sub-operational unit 711, which differs from commonly known quantum computers such as those illustrated in FIG. 2. First sub-operational unit 712 is configured to couple bosonic fields to quantum elements, such that the coupling of the bosonic fields to the quantum elements, and optionally the bosonic fields themselves, can be manipulated by quantum operations performed on the bosonic fields and / or their coupling. Thus, as indicated by the double-headed arrows, second sub-operational unit 711 and first sub-operational unit 712 interact with each other through the coupling of bosonic fields to quantum elements utilized by second sub-operational unit 711. In general, bosonic operation unit 712 can be implemented in a number of different ways depending on the construction principle on which quantum computer 710 is based. For example, if quantum computer 710 refers to a superconducting quantum computer in which quantum elements are realized as superconducting circuits, as already mentioned above, first sub-operational unit 712 can utilize, and optionally include, additional resonators, i.e., resonators not used for readout or entanglement of the quantum elements, as bosonic elements representing bosonic fields, which resonators are coupled to the quantum elements for coupling of the bosonic fields to the quantum elements. Thus, in such exemplary embodiments, the bosonic fields are represented by electromagnetic fields generated by the resonators, and the coupling is represented by the interaction of each electromagnetic field with the superconducting circuits forming the quantum elements. A more detailed description of this embodiment and further exemplary embodiments of the implementation of the first sub-operational unit will be discussed in relation to more detailed embodiments of the present invention.

[0081] Preferably, the second sub-operation unit 711 is adapted to allow manipulation of the quantum elements by operations on a second part of the problem, including quantities that describe the problem without interacting with each other. In contrast, the first sub-operation unit 712 is specifically configured to allow manipulation by operations on a first part of the problem, which refer to quantities that describe the problem while interacting with each other. Thus, structuring the quantum computer 710 to include the second sub-operation unit 711 and additionally the first sub-operation unit 712, as opposed to the quantum computer described in FIG. 2, allows the representation, i.e., simulation, of the interacting quantities of the problem to be moved to the interaction of different parts of the quantum computer 710, for example, the interaction of additional resonators with independently controllable superconducting circuits. Furthermore, due to the separation of the two parts of the problem, representing the first sub-operation unit 712 by a system constructed to be controlled in a technically different way from the quantum elements allows a reduction in the number of quantum gate operations that need to be explicitly performed on the qubits to solve a given problem. This not only allows for better control, improving the accuracy of the calculations, but also reduces the required qubit resources, allowing more complex problems to be calculated with a given qubit resource.

[0082] Furthermore, quantum computer 710 preferably includes a manipulation unit 713 configured to manipulate a) second sub-operation unit 711 and b) first sub-operation unit 712. In particular, manipulation unit 713 is configured to manipulate second sub-operation unit 711 such that the states of the quantum elements are manipulated based on control signals that are particularly indicative of an operation related to the second portion of the problem, as described above. Furthermore, manipulation unit 713 is configured to manipulate first sub-operation unit 712 such that the coupling of the bosonic fields, and optionally the bosonic fields themselves, are manipulated based on control signals that are indicative of an operation related to the first portion of the problem, as described above. For example, manipulation unit 713 can be considered to be part of second sub-operation unit 712 and can be considered to be a controller of a laser that enables the manipulation of quantum elements, i.e., qubits, in a quantum computer implemented as an ion trapping device. Alternatively, manipulation unit 713 may correspond to a controller of a microwave source used to manipulate qubits and / or bosonic fields in a quantum computer implemented as a superconducting quantum computer. In this way, the operation unit 713 is provided with control signals from the control unit 730 indicating the operations to be performed by, for example, the second sub-operation unit 711 and the second sub-operation unit 712, and uses these control signals to control each part of the quantum computer accordingly.

[0083] Furthermore, the quantum computer 710 preferably includes a readout unit 714 configured to read out the quantum elements utilized by the second sub-operation unit 711 and the boson fields utilized by the first sub-operation unit 712. Generally, reading out the quantum elements and boson fields refers to measuring at least one observable of the quantum mechanical state of each quantum element utilized by the second sub-operation unit 711 and measuring the state of the representation of the boson field utilized by the first sub-operation unit 712. Measuring the boson field may refer to measuring, for example, an observable or signal provided by the boson element representing the boson field. For example, if the quantum computer is a superconducting computer in which the boson field is represented as a resonator, the readout unit can be adapted to measure the electromagnetic field provided by the resonator or changes in the electromagnetic field. Alternatively, if the quantum computer refers to a trapped-ion quantum computer in which the boson field is represented by the vibrational modes of the trapped ion, the measurement unit can be adapted to measure the frequency of the vibrational modes of the trapped ion. The measurement results of the readout unit 714 indicate a solution to the calculated problem.

[0084] Optionally, the functionality of quantum computer 710 can be controlled by control unit 730. Control unit 730 is adapted to provide control signals to operator 713 indicative of desired operations to be performed by second sub-operational unit 711 and first sub-operational unit 712, which then performs each operation, for example by controlling a laser source or a microwave source of second sub-operational unit 711 or first sub-operational unit 712, respectively. Furthermore, control unit 730 can also be adapted to control readout unit 714 to read out each result of the quantum mechanical calculation after the operation has been performed. In particular, readout unit 714 can then be adapted to provide a signal indicative of the measurement result to control unit 730. Thus, optionally, control unit 730 can be part of quantum computer 710. Furthermore, control unit 730 can also be implemented as software and / or hardware together with operator 713, for example as part of a laser or microwave source controller. However, control unit 730 may also be separate from operation unit 713 and may be provided in the form of separate software and / or hardware that controls quantum computer 710 .

[0085] If control unit 730 is provided, for example, as part of quantum computer 710, control unit 730 preferably receives control signals from device 720. Control unit 730 can then generate control signals for controlling operator 713 based on the control signals received from device 720. For example, control unit 730 can convert control signals received from device 720 into control signals that can be understood by the particular hardware and / or software of a particular operator 713 of quantum computer 710. Such conversion may be useful when the control signals provided by device 720 are in a different format or follow a different protocol than the control signals used to control operator 713. However, the control signals provided by device 720 may also already be in the correct format or protocol so that no conversion is necessary, in which case control unit 730 may be omitted or adapted to simply provide the received control signals to operator 713 and / or readout 714 without conversion.

[0086] In particular, control unit 730 is preferably configured to provide control signals that control manipulator 713 such that manipulator 713 operates second sub-operational unit 711 such that the states of the quantum elements are manipulated based on an operation relating to a second part of the problem. Furthermore, control unit 730 is preferably configured to provide control signals that control manipulator 713 such that it operates first sub-operational unit 712 such that the coupling of bosonic fields to the quantum elements is manipulated based on an operation relating to a first part of the problem. In this way, control unit 730 is particularly adapted to control manipulator 713 according to the principle of providing operations relating to different parts of quantum computer 710 with operations.

[0087] In the following, an embodiment of the apparatus 720, which optionally provides control signals to the quantum computer 710 via the control unit 730, is described in more detail. The apparatus 720 includes a problem providing unit 721 adapted to provide a problem description indicating a problem to be solved, comprising a first and a second part. Preferably, the problem description refers to a quantum mechanical description of the problem, e.g., a quantum mechanical description of an electronic structure problem. However, the problem description may refer to any other problem notation that unambiguously describes the problem to be solved, in which case the problem providing unit 721 is adapted to convert the provided problem description into a quantum mechanical description that can be solved by the quantum computer 710. The problem description may, for example, be stored in a storage unit and then provided by the problem providing unit 721, or may be received by the problem providing unit 721 via an input unit, e.g., through which a user provides input of the problem description. Thus, in a preferred embodiment, the problem providing unit 721 corresponds to a user interface that enables a user to define the problem to be solved, such that the problem description can be provided to the trial state determination unit 722.

[0088] Next, the trial state determination unit 722 is adapted to determine a trial state representation of the problem statement based on a variational approach. Preferably, the trial state determination unit is adapted to utilize a distributed Hamiltonian hypothesis or a unitary coupled cluster hypothesis to determine the trial state representation. The trial state representation generally includes one or more variational parameters, and the trial state representation is optimizable with respect to the variational parameters. In particular, the trial state representation is determined such that, for at least one optimal value of each of the one or more variational parameters, the trial state representation is an optimal state, i.e., at least one observable quantity of the trial state representation is in a minimum or maximum state. Furthermore, the trial state representation is determined such that at least one observable quantity referring to the optimized state of the trial state representation indicates a solution to the problem to be solved. According to the principles of the present invention, the trial state determination unit is adapted to determine the trial state representation such that it also includes portions referring to the first and second portions of the problem, i.e., such that the trial state representation includes a first portion that refers to or can be converted into fermion-boson interactions or spin-boson interactions, respectively, and a second portion that refers to or can be converted into non-interacting fermions or non-interacting spins, respectively. Thus, the trial state representation also still includes a problem structure similar to that of the original problem. The trial state determination unit 722 then provides the determined trial state representation to the conversion unit 723.

[0089] The transformation unit 723 is generally adapted to transform the trial state representation for a particular value of one or more variational parameters into an operational trial state description. The operational trial state description includes a series of quantum operations applied to the quantum representation elements 711, 712 of the quantum computer 710 to prepare a trial state representation, i.e., a representation of the trial state, on the quantum computer 710. For example, the quantum operations may refer to quantum gates applied to the quantum elements forming the qubits of the quantum computer 710 and / or bosonic operations applied to the coupling between the bosonic fields and the quantum elements, or the bosonic field representation itself. In particular, the series of operations includes a) a second operation determined based on the second part of the trial state representation and b) a first operation determined based on the first part of the trial state representation. Thus, the principle of dividing the problem into two parts that are processed differently is maintained while transforming the trial state representation into quantum operations. The operational trial state description including the series of quantum operations is then provided by the transformation unit 723 to the control signal providing unit 724.

[0090] The control signal providing unit 724 is adapted to provide, optionally via the control unit 730, control signals to the quantum computer 710 for controlling the application of the determined sequence of quantum operations. For example, the control unit 730 may be utilized to convert the control signals provided by the control signal providing unit 724 into a format interpretable by the quantum computer 710, e.g., by the operation unit 713. However, the control signal providing unit 724 may also be adapted to provide the control signals already in a format that can be directly utilized by the quantum computer 710, in which case the control unit 730 may be omitted. The control signals provided by the control signal providing unit 724 are generally provided such that a control signal referring to a first operation and a control signal referring to a second operation are performed by different parts of the quantum computer. For example, when the term "quantum computer" refers to a commonly known quantum computer, the control signal referring to the first operation may be performed on a given set of quantum elements forming a qubit, and the control signal referring to the second operation may be performed on a different set of quantum elements forming the qubit. However, the term "quantum computer" preferably refers to a quantum computer specifically modified to provide the second sub-operation unit 711 and the first sub-operation unit 712, as described above. In this case, a control signal referring to the first operation can be provided to the operation unit 713 such that the first operation is applied to the first sub-operation part 712 and the second operation is applied to the second sub-operation part 711. This makes it possible to prepare each state of the trial state representation on hardware dedicated to these respective parts of the trial state representation for easier control and also to reach higher accuracy.

[0091] Optionally, in a preferred embodiment, the apparatus 720 further comprises an iteration control unit 725 adapted to control the iterations utilized to optimize the trial state representation to determine optimized observables for the trial state representation. In particular, the iteration control unit 725 may be adapted to determine values ​​of variational parameters at each iteration step. For example, first predetermined initial variational parameters may be utilized for the first iteration, and then for all subsequent iteration steps, the variational parameters may be adapted, for example, according to a known algorithm based on the variational parameters and at least one measured observable of the previous iteration step. During each iteration step, the iteration control unit 725 may be adapted, for example, to control the transformation unit 723 to transform the trial state representation for the particular value of the variational parameter for the current iteration step, and further to control the control signal providing unit 724 to again provide a control signal enabling preparation of the trial state representation for the particular value of the variational parameter for the current iteration step. Furthermore, the iteration control unit 725 may be adapted to provide a control signal for the readout of each at least one observable after preparation of the trial state representation on the quantum computer, and further to control the control signal providing unit 724 to determine whether a respective interruption criterion for the at least one measured observable has been reached, e.g., whether the at least one measured observable has already converged, or, e.g., whether a predetermined maximum number of iteration steps has already been reached. If none of these interruption criteria is met, the iteration control unit 725 is adapted to re-adapt the variational parameters and start a new iteration step with the newly determined variational parameters. However, if it is determined that the at least one observable has converged, e.g., if it is determined that the difference between the currently measured observable and the observable measured in the previous step is below a predetermined convergence criterion, the iteration control unit 725 may be adapted to determine that the observable measured in the last iteration step refers to the at least one final observable.

[0092] The at least one final observable may then be provided by the iteration control unit 725 to an also optional result determination unit 726, which may then be adapted to determine a solution to the problem from the at least one final observable. For example, if the problem refers to identifying the energy of the ground state of an electronic structure system, the at least one observable may refer to the energy of a trial state representation prepared on a quantum computer, and thus the optimized energy may directly refer to the solution to the problem, i.e., the energy of the ground state of the electronic structure system. However, the result determination unit may also be adapted to further process the at least one final observable to determine a solution to the problem, for example, to convert the at least one final observable back into the format of the respectively provided problem description, or to utilize the at least one final observable in a further algorithm to determine a solution to the problem.

[0093] 8 shows, in a schematic and exemplary manner, a flow diagram of a method 800 for determining control signals for generating a solution to a problem, as already mentioned above. The method comprises, in a first step 810, providing a problem description indicating the problem to be solved. In particular, as explained in more detail above, the problem description comprises a first part that can be converted into a quantum mechanical description referring to fermion-boson interactions or spin-boson interactions, respectively, and a second part that can be converted into a quantum mechanical description referring to non-interacting fermions or non-interacting spins. In a further step 820, a trial state representation of the problem description is determined based on a variational approach, according to the principles already described above with respect to the trial state determination unit 722. After determining the trial state representation in step 820, in step 830 the trial state representation is converted into an operational trial state description comprising a sequence of quantum operations for specific values ​​of one or more variational parameters. In particular, the sequence of quantum operations includes first and second operations, e.g., as already described above with respect to transformation unit 723, where the first operation is determined based on a portion of the trial state representation that refers to fermion-boson or spin-boson interactions, and the second operation is determined based on a portion of the trial state representation that refers to non-interacting fermions or non-interacting spins, respectively. In step 840, control signals for controlling the application of the determined sequence of quantum operations are provided to the quantum computer. In particular, the control signals are provided such that the first operation and the second operation are provided to different portions of the quantum computer, preferably the first sub-operation unit and the second sub-operation unit, respectively. In step 850, control signals for reading the quantum computer are then provided to the quantum computer to measure at least one observable quantity of the quantum mechanical state of the prepared trial state representation after application of the determined sequence of quantum operations, i.e., after preparing the trial state representation on the quantum computer.

[0094] In a preferred embodiment, method 800 further includes iterating the trial state representation to optimize at least one observable of the trial state representation, the iterations being represented in FIG. 8 by arrows and step 851. In particular, after measuring the at least one observable in step 850, it may be determined in step 851 whether a predetermined convergence criterion has already been met, e.g., whether at least one read observable has already converged, or whether a rejection criterion has been met. If not, method 800 may include determining new values ​​for one or more variational parameters to be utilized in the next iteration step in step 851. Steps 830, 840, and 850 are then again performed using the newly determined specific values ​​for the one or more variational parameters. This iteration 851 is then performed until it is indeed determined after step 850 that the convergence criterion is met, in particular until it is determined that at least one observable has converged. In this case, the last at least one measured observable may be determined as the at least one final observable. The at least one final observable is then optionally utilized in step 860 to determine a solution to the problem.

[0095] In the following, a more detailed example of an embodiment of the invention is described with respect to a particular problem. In this example, the problem is convertible into a quantum mechanical description including fermion-fermion interactions. Thus, for example, molecules and solids can be described. Preferably, for such problems, the apparatus further comprises a transformation unit adapted to transform the problem description into a problem description expressible by a quantum mechanical description including boson-fermion interactions and non-interacting fermions. Such coupled fermion-boson systems can be more easily simulated on existing quantum computing architectures and, as will also be described below, can be even more advantageously simulated if quantum computing hardware is adapted in some cases. In particular, the number of quantum gate operations required is O(N 4 ) to O(N 2), where N is a measure of the problem size, e.g., the number of orbitals or the system size. This reduces the computational time and complexity, potentially enabling the simulation of larger systems than currently anticipated on near-term quantum computers. Furthermore, simulating physical fermion-boson interactions, such as electron-photon and electron-phonon interactions, is important for understanding phenomena such as UV / Vis spectra or vibrational transitions in molecules, and for the engineering of transport phenomena in solids or, optionally, quantum sensors. To solve problems in this regard, it is often advisable to prepare the ground state of a fermion-boson Hamiltonian in the form of a quantum computer.

[0096]

number

[0097]

number

[0098] is the creation operator of the fermion in state i, which adds a fermion to the state, and c i is the annihilation operator that removes a fermion from state i. h ij describes non-interacting fermions moving from, for example, atomic nuclei or electromagnetic fields to an external potential, which may be time-dependent, for example, in an oscillating electromagnetic field, or static. ijkl describes general fermionic interactions, e.g., Coulomb repulsion for electrons. The operator b r is the boson annihilation operator that removes one boson from mode r,

[0099]

number

[0100] is the creation operator that adds bosonic excitations to the mode r. g ij,rdescribes the coupling strength between the bosonic mode r and the fermionic states i and j. r is the natural frequency of the boson mode.

[0101] In the case of superconducting quantum computing hardware, boson modes, i.e., boson fields, can be represented, for example, by additional hardware resonators, while fermion modes remain represented by existing quantum elements forming qubits, for example, in the quantum register described above. However, particularly when utilizing such quantum computer hardware to solve the above-mentioned problems, in commonly known ways, this leads to two different time scales that must be matched during the calculation: the simulated time evolution of the qubits and the actual physical time evolution of the resonators. In addition, since the frequency of the resonators is often fixed within a specific threshold given by the respective hardware configuration, it can be difficult to find a respective quantum computer that includes a resonator with the desired frequency for a particular problem. Neither problem exists in standard qubit-only fermion simulations. The present invention makes it possible to solve these problems by utilizing superconducting quantum computers, for example, as described above with respect to the present device, when the problem is to be solved on specific hardware that uses boson-field coupling. However, the present invention also has other advantages, as already described above.

[0102] The following describes in more detail quantum mechanical hardware that is preferably used in conjunction with the above-described apparatus to perform quantum mechanical calculations, such as preparing trial state representations.

[0103] In a first preferred embodiment, the quantum computer used refers to a superconducting quantum computer. In this case, bosonic modes, i.e., bosonic fields, can be represented by providing additional hardware resonators, e.g., LC circuits, as bosonic elements, since, for example, a readout resonator cannot be used to both readout and represent bosonic modes. Therefore, it is preferred that O(N) additional resonators are disposed on a chip containing the superconducting circuits forming the qubits. In particular, it is preferred that two to four resonators are provided per qubit, i.e., quantum element, and are arranged to be coupleable to each qubit. For example, if the conversion unit is adapted to apply a restricted random phase approximation to the quantum mechanical description of the problem, the resulting single frequency-dependent interaction part can be converted into a quantum operation to be applied to two to four hardware resonators. In another example, if the quantum mechanical description of the problem includes a four-exponential interaction term, such as exists in a molecular Hamiltonian, then O(N) additional resonators can be disposed on a chip containing the superconducting circuits forming the qubits. 2 ) additional resonators are preferably provided. Since it is difficult to place this amount of resonators on a chip, the transformation unit is preferably adapted to apply a low-rank decomposition to the quantum mechanical description of the problem to reduce the O(N) or O(NlogN) resonator requirement.

[0104] In some hardware implementations, the resonator frequency is often fixed within a certain threshold due to the fixed resonator length and superconducting gap, which can make it difficult to provide a resonator with the desired frequency for a particular problem. In particular, if the quantum mechanical description of the problem includes static fermion interactions, the resonator must provide a high frequency. In this case, it is preferable that the transformation unit of the device is adapted to transform the quantum mechanical problem description into the rotating reference frame of the resonator, for example, using the rotating wave approximation. Because this approach can still lead to complex effective time evolutions of the hardware elements, in a further preferred embodiment, the first sub-operational unit can be adapted to utilize oscillating driving fields for coupling and / or bosonic field manipulation. However, one advantage of using the above-mentioned variational approach to solve problems is that it allows avoiding these problems in most cases, or at least strongly reducing their impact. Therefore, for example, utilizing oscillating driving fields is optional in this approach.

[0105] An exemplary series of quantum operations that can be utilized in preparing a trial state representation on a quantum computer is discussed below with respect to Figure 9. In general, the implementation of the phase quantum operations that are part of the exemplary series of operations shown in Figure 9 may depend on the hardware utilized. For example, in a trapped-ion quantum computer, the phase quantum operations may correspond directly to the manipulation of laser light used to manipulate bonds, while in other hardware implementations, the phase quantum operations may correspond to modified standard quantum gates applied to qubits.

[0106] In general, it is preferred that the transformation unit is adapted to utilize such phase operations to transform a first part of the problem, which corresponds to a fermion-boson or spin-boson interaction in the quantum mechanical description, into an operational description. In particular, the phase operations may correspond to specially modified standard quantum gates available in the hardware implementation of the respective quantum computer device. In general, pure fermion-fermion interactions can be expressed by standard one-qubit and two-qubit gates, but the inclusion of bosonic modes preferably leads to quantum operations that also implement a phase that depends on the state of a bosonic field, e.g., represented by an electromagnetic field in a resonator. In particular, the phase operation may refer to an additional quantum gate operation and subsequent latency while the qubit, i.e., quantum element, and the bosonic field representation interact in the real world.

[0107] An example of such a phase operation is described below with reference to a variant of the well-known FSWAP algorithm that can be used to implement the effective time evolution of quantum mechanical systems. With regard to boson-fermion interactions, the FSWAP gate needs to additionally account for the phase shift due to the bosonic modes. As already mentioned above, this is achieved by introducing a waiting time into the sequence of FSWAP gates, i.e., a time during which the representations of the boson field and each quantum element can interact. The unitary matrix representation of the FSWAP gate is given by

[0108]

number

[0109] where b is the boson annihilation operator, b †is the boson creation operator, g describes the coupling strength of the fermion or quantum element to the bosonic mode, and t is a parameter describing the gate. An example of a corresponding gate sequence is shown in Figure 9. The top two rows of boxes represent gate operations performed on each of the two qubits, and the boxes in the third row represent operations performed on the bosonic field or the coupling of the bosonic field to the qubit. Within these boxes is shown each mathematical operator to which the operation corresponds in the quantum mechanical description of the problem. In this example, we have a controlled Z (CZ), a SWAP gate, a single-qubit gate, and a U of an FSWAP gate with a phase shift due to the bosonic mode. phys The decomposition into (1) is shown. Boson gates, which take into account the phase shift, can also be considered as phase operations in this case, corresponding to the latency during which the interaction between the qubit and the boson field occurs. In general, such a decomposition, i.e., a series of quantum operations, can be provided as appropriate for each hardware implementation of the quantum computer. The measurement, i.e., readout, of the Hamiltonian and other observables of the quantum mechanical system preferably also includes measurement of the boson field, e.g., measurement of one or more observables of the electromagnetic field generated by the resonator. Therefore, it is preferable that the readout unit is adapted accordingly. Since the qubit operator and the boson operator communicate, the readout unit can be adapted to measure the observables of the quantum element and the observables of the boson field simultaneously or sequentially. Standard Hamiltonian averaging of the measurements can be used in the following processing of the measurement results.

[0110] Preferably, the coupling between the quantum element and the resonator is configured to be digitally switchable and adjustable. In particular, the first sub-operational unit can allow manipulation of the coupling strength. However, in general, the coupling may be physically constrained; for example, for transmon qubits, the transverse coupling may be stronger than the longitudinal coupling, while for flux qubits, the transverse and longitudinal coupling strengths may be equal. Furthermore, the coupling energy may be physically limited to about 10% of the transmon qubit-level splitting energy. Preferably, a coupling energy of about 1% is used for coupling.

[0111] When using a resonator to represent a boson field, two different time scales need to be synchronized during quantum mechanical calculations. In particular, the simulated, e.g., Trotterized, time evolution of a qubit and the real, i.e., physical, time evolution of the resonator need to be synchronized. By using the variational approach of the present invention, it is possible to omit an additional synchronization method due to the nature of the approach. However, in some cases, it may be advantageous to use an additional synchronization method. Preferably, the conversion unit is adapted to convert the quantum mechanical description of the problem into quantum operations, such that the simulated time is less than or equal to the real time, and by using a wait operation corresponding to the wait time. During the wait operation, no further operations are performed, allowing the boson field to interact with the quantum elements.

[0112] An advantage of such a superconducting quantum computer is that it can generally apply quantum operations, and in particular quantum gates, in parallel. This also allows the transformation unit to take parallelism into account when generating a sequence of quantum operations, for example by determining a sequence of quantum operations that can be applied simultaneously. A further advantage is that the resonators can apply broadening of the Boson peak to increase the broadening, for example via a measurable external magnetic field or via coupling of the Boson field to an ancilla qubit. Furthermore, it is advantageous to measure the Boson field directly, for example by measuring the field characteristics generated by each resonator. A further advantage of this hardware, particularly with respect to the approach used by the above-described apparatus according to the invention, is that the superconducting quantum computer can measure the quantum mechanical observables † + b〉 term can be measured directly. In particular when solving problems related to determining the ground or excited states of quantum mechanical systems, e.g., quantum mechanical many-body systems, electrons in atoms or molecules, spins in solids, etc., this allows for a technically simpler realization of the readout of the respective observable.

[0113] In a more preferred embodiment, the quantum computer utilized refers to trapped-ion quantum hardware. In particular, in this case, the vibrational modes of the trapped ions can be used to represent boson modes, i.e., boson fields. In this embodiment, it is not necessary to provide hardware boson elements to represent the boson fields. Instead, the first sub-operational unit can be configured to manipulate the already existing vibrational modes of the trapped ions to interact with, i.e., couple with, the electronic states of the trapped ions that form the qubit. Because the boson fields in this case are represented by vibrational modes, the number of boson fields is naturally limited by the number of ions, to approximately 3N boson fields.

[0114] In general, it is preferred that the first sub-operational unit allows for manipulation of the frequency of the boson field to provide energy to each vibrational mode of the trapped ions in order to transfer energy from the vibrational modes to the electronic modes or vice versa. In the case of a trapped ion quantum computer, manipulation of the frequency of the boson field can be achieved by manipulating the distance between the trapped ions, for example, by manipulating the electromagnetic field that traps the ions in the ion trapping device, by manipulating the frequency of the laser used to manipulate the quantum elements, or by using a rotating frame. This allows for very simple manipulation of the coupling and / or the boson field itself. Again, the transformation unit is adapted to transform the quantum mechanical problem description into a rotating reference frame, which can be more flexibly selected since a laser can be used to manipulate the vibrational modes. Furthermore, it is preferred that the transformation unit is adapted to provide an operational description of the problem including quantum operations that tune a laser to resonate with the frequency of the fermionic and / or boson modes so that complex time evolution effects are suppressed. In general, in contrast to the superconducting quantum computer realizations mentioned above, in trapped ion realizations the time scales of the qubit and boson field evolutions are identical since both are realized by the same quantum mechanical system.

[0115] In contrast to superconducting hardware, the coupling of the bosonic field to the quantum element can be seen as occurring naturally via the possibility of transferring energy from vibrational modes to the electronic states of the trapped ion and / or from the electronic states of the trapped ion to the vibrational modes, and the first sub-operational unit is therefore preferably configured to enable said coupling by controlling the coupling via laser pulses.

[0116] In trapped-ion quantum computers, quantum gates can generally only be applied serially. Therefore, in this embodiment, the transformation unit is preferably adapted to take this into account by providing an operation description such that each sequence of quantum operations corresponds only to quantum operations that are applied serially. However, if solutions are found that allow for the parallel application of quantum operations in trapped-ion quantum computers, the transformation unit can also take these new solutions into account.

[0117] Again, the transformation unit can be adapted to utilize quantum operations that result in broadening of the Boson peak, such as those that correspond to coupling of an external field to the Boson field, or to increased broadening by utilizing measurable ancilla qubits.

[0118] Preferably, the transformation unit is in this case particularly adapted to apply the restricted random phase approximation to the quantum mechanical description of the problem while deriving the effective electron-electron interactions, the hardware described above being particularly useful for such interactions provided by the problem.

[0119] In a further preferred embodiment, the bosonic degrees of freedom can be implemented in quantum elements using dedicated qubit gates, rather than as superconducting resonator lines or using vibrational modes of trapped ion hardware. In this case, the first sub-operation unit is adapted to utilize the overhead of the number of quantum elements forming the qubits representing the bosonic field and the coupling of the bosonic field with quantum elements representing other quantities of interest. Therefore, in this embodiment, it is preferred that the operation unit provides specific quantum operations for encoding the coupling and the bosonic field with the overhead qubits. In this case, it is preferred that the operation unit defines a cutoff threshold for the number of qubits available to represent the bosonic field, thereby limiting the number of excitations in the bosonic mode that can be simulated. The threshold can be defined using phenomenological methods.

[0120] In this embodiment, bosonic coupling is also performed using quantum elements that form qubits, but because the bosonic fields themselves do not interact and the time evolution can be applied in parallel to all bosonic fields as with fermionic quantum elements, the set of quantum operations for a given problem also does not necessarily contain substantially more quantum operations as with either of the above implementation approaches. Furthermore, the overhead quantum elements preferably have a lower probability of interacting than quantum elements dedicated to representing non-interacting fermions. This has the advantage that this embodiment allows for improved control at low excitation levels of bosonic modes.

[0121] Furthermore, other quantum computer architectures can also be modified to provide a first sub-operational unit that represents bosonic fields and allows coupling of bosonic fields with quantum elements. For example, ultra-cold / Rydberg atomic quantum hardware architectures can also be utilized and modified according to the principles described above.

[0122] Below, examples of solving problems according to the present invention are described in terms of utilizing a superconducting quantum computer with an additional digitally switchable resonator to represent the boson field. Such a resonator offers more flexibility and is easier to implement in the quantum computer hardware. However, the general principles described can be applied to any of the additional quantum computer realizations mentioned above. The following functions can be performed, for example, by functional parts of the device to provide control signals for quantum operations that solve problems on the quantum computer:

[0123] The main principle of the present invention for solving the above-mentioned problems, for example when using superconducting quantum computers, refers to the use of variational methods. In particular, these methods make it possible to prepare a good approximation of the ground state of a coupled fermion-boson system on a quantum computer. These methods generally involve: U=exp(-iH フェルミオン-ボソン t) Although it is more limited in its application to specific problems than directly simulating the unitary time evolution of fermionic systems with bosonic resonators via

[10] , it also has less stringent requirements on the quantum mechanical hardware; for example, the two different time scales mentioned above do not necessarily have to coincide.

[0124] The advantage of using variational techniques is that instead of preparing a full-time decomposition simulation of the problem, only the preparation of a trial state representation needs to be performed on the quantum computer as a function of a set of variational parameters. Preferably, the trial state determination unit is adapted to use a variational Hamiltonian hypothesis (VHA) for determining the trial state representation. In this case, the preparation, i.e., the application of a series of quantum operations, involves applying a partial time evolution of the original problem to the initial state. However, the preparation of the trial state representation does not need to have any connection with the physical time evolution. Therefore, the problems related to the complete physical time evolution as mentioned above can be avoided.

[0125] In general, in this example, and particularly for fermion-boson quantum mechanical descriptions, the goal of using variational techniques such as those described with respect to the above apparatus is to prepare a set of correlated qubit-resonator states on a quantum computer, where the qubits represent the fermionic degrees of freedom of the problem and the resonators represent the bosonic degrees of freedom, then measure the energy of the simulated states represented by the qubit-resonator states and minimize the energy over the variational parameters of the trial states. However, in other examples, hardware elements other than resonators can be used to represent bosonic degrees of freedom, or even additional qubits, without departing from the respective principles of preparing representations of trial state representations in different parts of the quantum computer. Furthermore, in other examples, observables other than the energy of the prepared trial state representations can also be selected for optimization, depending on the respective problem.

[0126] In this principle, the prepared representation of the trial state representation is measured only at one point in time, so in general the physical properties of the boson field representation, e.g. the resonator, do not have to correspond exactly to the properties of the simulated boson mode, just as the energy partitioning of a qubit does not generally correspond to the on-site energy of a fermionic model.

[0127] Preferably, the trial state determination unit is adapted to utilize a boson field representation, e.g., a frequency of a physical resonator, when determining the trial state representation, which is convenient for the respective implementation of the boson field. Furthermore, the variational parameters are preferably selected such that the time evolution of the first and second parts of the trial state representation are implemented with different times that can be used as variational parameters. For example, preferably, t refers to fermion hopping, fermion interaction, fermion-boson coupling, and waiting time, respectively. hop , t tint , t coupl , τ wait is chosen as a variational parameter by the trial state representation unit, which can lead the above Hamiltonian example to the unitary evolution operator in the quantum mechanical description below.

[0128]

number

[0129] Preferably, the control signal providing unit is adapted to provide a control signal for controlling the quantum computer to prepare a predetermined initial state representation on the quantum representation element of the quantum computer. The unitary evolution operator U can then be converted into a series of operations for preparing a representation of the trial state representation on the quantum computer. For example, the above time evolution can then be applied to the initial state representation defined by the trial state representation.

[0130]

number

[0131] Ω r is the physical boson frequency, e.g., the physical resonator frequency, and |ψ0> フェルミオン is the fermion initial state, e.g., the Hartree-Fock reference state, |00000…> ボソン is the initial state of the collective bosons, which may be the ground state. In some embodiments, the trial state determination unit determines the four-exponential fermion interaction U, e.g., by applying a low-rank decomposition. ijkl by density-density fermion interactions. Examples of such low-rank decompositions can be found, for example, in the paper "Low rank representations for quantum simulation of electronic structure", M. Motta, et. al., npj Quantum INF 7, 83 (2021). Alternatively, in some instances, depending on the problem, for example, the trial state representation unit can be adapted to apply the Fermi-Hubbard model to reduce complexity. In both cases,

[0132]

number

[0133] teeth

[0134]

number

[0135] where n j is the particle number operator for the fermion state J. This modification can also be applied directly to the quantum mechanical description of the problem, e.g., the Hamiltonian above, or directly to the trial state representation, e.g., the equation above.

[0136] In the above formula, we distinguish between simulated time, using the Latin lowercase letter t, and simulated time, i.e., elapsed time in the laboratory, using τ. int , τ coupl , and τ hop is the time used to implement the corresponding fermion term on a quantum computer, and τ wait can be used as an additional variational parameter. The simulated time t can be used as a variational parameter. For accuracy, the number of layers n layer can be increased to use more variational parameters τ(s) and t(s).

[0137] In the above example,

[0138]

number

[0139] This leads to a trial state representation where the expectation value of is measured as an observable. Then, the expectation value of the Hamiltonian as a cost function of the variational optimization, i.e., the energy of the trial state representation, is given by r Instead, the selected boson frequency ω rIn this particular example of the variational approach, the utilized hardware of the quantum computer is the resonator excitation level.

[0140]

number

[0141] It is necessary to be able to measure In general, following the above principles, instead of problems that can be transformed into a quantum mechanical description involving fermion-boson interactions, problems that can be transformed into a quantum mechanical description involving spin-boson interactions can also be treated, for example, by replacing all the fermion operators mentioned above by spin operators, e.g., Pauli matrices.

[0142] In the following we provide a more detailed example of a method for dealing with the above mentioned problems, which can be performed by each unit of the apparatus, for example as described with respect to FIG.

[0143] In a first step of the method, performed for example by a problem providing unit, a respective problem that can be transformed into a quantum mechanical description comprising a first and a second part, e.g., as described in more detail above, is provided. Typically, this step is performed on a classical computer. For example, the problem description may be expressed as a function of the Hamiltonian H フェルミオン-ボソン For example, in the next step performed by the trial state determination unit, the trial state representation of the problem is determined by a unitary evolution operator U(t hop ,t int ,t coupl ,τ wait ) is determined. In this step, which may also utilize, for example, a trial state determination unit and / or a transformation unit, the initial state representation, in particular the fermion initial state |ψ0> フェルミオン Furthermore, we can determine the set of quantum operations to prepare the coupling strength g ij,r and integral hij and U ijkl The quantities present in the trial state representation, in particular the operator U, such as , can also be determined in this step on a classical computer, for example by using a Hartree-Fock calculation. Furthermore, in a next step, the transformation unit transforms the fermion operators U(t hop ,t int ,t coupl ,τ wait ) in the iterative control unit. In this step, the iterative control unit determines the initial values ​​of the variational parameters, e.g., the different time parameters t and τ wait The method may be adapted to select an initial value of .

[0144] In the next step, the sequence of operations that refer to the trial state representation operation description is first performed by the qubit register, i.e., the quantum element is |ψ0> フェルミオン and the boson modes are initialized according to, for example, |00000…> ボソン and transmits it to the quantum computer by, for example, a control signal providing unit. Second, the control signal based on a series of operations is converted into an entangled fermion-boson trial state representation |ψ according to the above example trial state representation by applying, for example, a sequence representing a unitary operator U. 試行 > are provided so that trial state representations are prepared on the quantum computer by creating a >. In some embodiments, prior to preparation, each trial state representation can be determined using an FSIM network algorithm or a CZ algorithm using low-rank decomposition.

[0145] Each observable for which the trial state representation is optimized is then measured. For example, in the example problem above, the energy of the prepared trial state representation is calculated on a quantum computer using the Hamiltonian, E=<ψ 試行 │H フェルミオン-ボソン │ψ 試行For this purpose,

[0146]

number

[0147] The expected value of is measured, for example, using the readout unit. The repetition control unit then calculates the expected value of the physical frequency Ω r Instead, the model boson frequency ω r Using H フェルミオン-ボソン In general, if an observable, e.g., the energy E, has not yet converged, the iterative control unit may be adapted to iteratively iterate all variational parameters, e.g., t and τ, on a classical computer to optimize the observable, e.g., to minimize the energy. wait and may be adapted to initiate the next iteration step by initiating the iterative portion of the iteration by determining a set of quantum operations for new variational parameters. For example, COBYLA, L-BFGS, or CG optimization methods may be utilized to determine the new variational parameters. When the observables have converged with respect to a predetermined convergence criterion, a final observable, e.g., a final energy E, is determined and used by a result determination unit, e.g., as a component for further post-processing on, e.g., a classical computer, and application to each specific molecule, solid, material, etc., to identify a solution to the problem.

[0148] In general, the above-described inventions, e.g., devices and methods, can be applied to multiple problems. Preferred applications are described below. For example, the method can be used to simulate physical fermion-boson systems. One example refers to the simulation of electronic structure systems, including both molecular and condensed matter systems interacting with bosons. It can also solve electron-phonon systems, e.g., vibronic absorption and emission spectra and electron-vibration coupling in molecules, and polarons in condensed matter systems, to calculate Franck-Condon factors, IR spectra, etc. Furthermore, it can handle problems in the field of electron-photon systems, e.g., the interaction of molecules with electromagnetic fields resulting in electronic transitions relevant to UV / Vis spectroscopy, e.g., absorption, emission such as fluorescence and phosphorescence, and photoelectron spectroscopy. Furthermore, the present invention can handle electron-exciton systems in metals, semiconductors, thermoelectrics, or superconductors, electron-phonon coupling to calculate, optionally, quantum, thermal, and electrical transport properties in sensors, light-matter interactions, i.e., electron-photon interactions, and electron spin coupling to calculate transport properties in magnetic materials, e.g., the Kondo effect.

[0149] Furthermore, the method and apparatus can be used to simulate physical spin-boson systems, such as nuclear spins or electron spins interacting with photons associated with NMR and ESR. With respect to physical fermion-boson systems, the present application is not limited to systems in which the fermions are electrons, but can also be used to simulate other physical fermion-boson systems, including those in which the fermions are other elementary particles, such as muons, neutrinos, quarks, or composite particles, such as protons and neutrons, and the bosons are gauge bosons, such as photons, W and Z bosons, gluons, or quasiparticles, such as magnons and plasmons.

[0150] Furthermore, the method can also be used to simulate coupled fermion-boson systems obtained by the Hubbard-Stratonovich transformation of pure fermion systems. Coupled fermion-boson systems also arise, for example, when calculating electron screening, which provides effective frequency-dependent interactions of electrons that are not part of the active space calculation. Preferably, for such systems, the restricted random phase approximation (cRPA) can be utilized.

[0151] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

[0152] For the processes and methods disclosed herein, the operations performed in the processes and methods may be implemented in a different order. Furthermore, the outlined operations are provided only as examples, and some of the operations are optional and may be combined into fewer steps and operations, supplemented with further operations, or expanded into additional operations without detracting from the essence of the embodiments of the present disclosure.

[0153] In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality.

[0154] A single unit or device may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0155] The steps performed by one or more functional units or devices, such as providing a problem, transforming a problem, generating a control signal, etc., may be performed by any number of other functional units or devices. These steps may be implemented as program code means of a computer program and / or as dedicated hardware.

[0156] The computer program product may be stored / distributed on any suitable medium, such as an optical storage medium or a solid-state medium, may be supplied together with or as part of other hardware, or may be distributed in other forms, for example via the Internet or other wired or wireless telecommunications systems.

[0157] Any of the functional units described herein may be a processing unit that is part of a classical computing system. The processing unit may include a general-purpose processor, a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or any other dedicated circuitry. Any memory may be physical system memory, which may be volatile, nonvolatile, or a combination of both. The term "memory" may include any computer-readable storage medium, such as non-volatile mass storage. If the computing system is distributed, processing and / or storage capacity may also be distributed. A computing system may include multiple structures as "executable elements." The term "executable element" is a structure well understood in the computing arts that may be software, hardware, or a combination thereof. For example, when implemented in software, those skilled in the art will understand that the structure of an executable element may include software objects, routines, methods, etc. that can be executed on the computing system. This may include both executable elements in the computing system's heap or executable elements on a computer-readable storage medium. The structure of the executable elements may reside on a computer-readable medium that, when interpreted by one or more processors of a computing system, e.g., by processor threads, causes the computing system to perform functions. Such structure may be directly computer-readable by a processor, e.g., where the executable elements are binary, or may be interpretably structured and / or compiled, e.g., in a single or multiple steps to generate binary that is directly interpretable by a processor. In other examples, the structure may be hard-coded or hard-wired logic gates that are implemented exclusively or nearly exclusively in hardware, e.g., in a field programmable gate array (FPGA), application specific integrated circuit (ASIC), or other dedicated circuitry.

[0158] Thus, the term “executable component” is a term for a structure well understood by those skilled in the art of computing, whether implemented in software, hardware, or a combination. Any embodiments herein are described with reference to operations performed by one or more processing units of a computing system. When such operations are implemented in software, one or more processors direct the operations of the computing system in response to execution of the computer-executable instructions that make up the executable component. A computing system may also include communications channels that enable the computing system to communicate with other computing systems, for example, over a network. A “network” is defined as one or more data links that enable the transmission of electronic data between computing systems and / or modules and / or other electronic devices. When information is transferred or provided to a computing system via a network or another communications connection, e.g., either hardwired, wireless, or a combination of hardwired and wireless, the computing system properly considers the connection to be a carrier medium. A carrier medium may include a network and / or data link that can be used to carry desired program code means in the form of computer-executable instructions or data structures and that can be accessed by a general-purpose computing system or a special-purpose computing system, or a combination thereof. Although not all computing systems require a user interface, in some embodiments a computing system includes a user interface system for use in interfacing with a user. The user interface serves as an input or output mechanism to the user, for example, via a display.

[0159] Those skilled in the art will appreciate that at least portions of the present invention may be implemented in networked computing environments having many types of computing system configurations, including personal computers, desktop computers, laptop computers, message processors, handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, cellular phones, PDAs, pagers, routers, switches, data centers, wearable devices such as eyeglasses, etc. The present invention may also be practiced in distributed system environments where tasks are performed together by local and remote computing systems that are linked, for example, through a network, by either hardwired data links, wireless data links, or a combination of hardwired and wireless data links. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

[0160] Those skilled in the art will also understand that at least a portion of the present invention may be implemented in a cloud computing environment. A cloud computing environment may be distributed, but this is not required. If distributed, a cloud computing environment may be distributed internationally within an organization and / or have components held across multiple organizations. For purposes of this specification and the claims that follow, "cloud computing" is defined as a model that enables on-demand network access to a shared pool of configurable computing resources, such as networks, servers, storage, applications, and services. The definition of "cloud computing" is not limited to any of the many other advantages that may be obtained when such a model is deployed. The computing systems in the figures, as described, include various components or functional blocks that may implement various embodiments disclosed herein. The various components or functional blocks may be implemented on a local computing system or on a distributed computing system that includes elements that reside in the cloud or implement aspects of cloud computing. The various components or functional blocks may be implemented as software, hardware, or a combination of software and hardware. The computing systems shown in the figures may include more or fewer components than those shown in the figures, and some of the components may be combined where circumstances permit.

[0161] Any reference signs in the claims should not be construed as limiting the scope.

Claims

1. 1. An apparatus for determining control signals for generating a solution to a problem translatable into a quantum mechanical description using a quantum computer, the apparatus (720) comprising: a problem provision unit (721) for providing a problem description indicating the problem to be solved, the problem description indicating a first part and a second part of the problem, the first part including quantities describing the problem that interact with each other, and the second part including quantities describing the problem that do not interact with each other; a trial state determination unit (722) for determining a trial state representation of the problem description based on a variational approach, the trial state representation including one or more variational parameters, the trial state representation including a first part and a second part representing the first part and the second part of the problem, respectively; a transformation unit (723) for transforming the trial state representation for a particular value of the one or more variational parameters into an operational trial state description comprising a series of quantum operations applied to quantum representation elements of the quantum computer (710) to prepare a representation of the trial state representation on the quantum computer (710), the series of operations comprising: a) a second operation determined based on the second part of the trial state representation; and b) a first operation determined based on the first part of the trial state representation; a control signal providing unit (724) for providing control signals for controlling application of the determined sequence of quantum operations on the quantum computer (710) so that the representation of the trial state representation is prepared, and for controlling readout of the quantum computer (710) to measure at least one observable quantity of the quantum mechanical state of the prepared representation of the trial state representation after application of the determined sequence of quantum operations, wherein the control signals are provided such that a control signal referring to the first operation and a control signal referring to the second operation are performed by different parts of the quantum computer (710); An apparatus comprising:

2. 2. The apparatus of claim 1, further comprising: an iteration control unit for controlling optimization of the trial state representation using iterations of the one or more variational parameters of the trial state representation until the at least one readout observable or a quantity derivable from the at least one readout observable converges, the iteration comprising adapting the one or more variational parameters of the trial state representation, repeating the transformation, providing control signals to prepare the trial state, and providing control signals for the readout until the at least one observable or derivable quantity converges to at least one final observable or derivable quantity; and a result determination unit for identifying a solution to the problem based on the at least one final observable or derivable quantity.

3. The apparatus of claim 2 , wherein the at least one measured observable indicates an energy of the prepared trial state representation, and convergence of the at least one observable refers to minimizing the energy.

4. 10. The apparatus of claim 9, wherein the control signal providing unit (724) is adapted to provide a control signal for controlling the quantum computer (710) to prepare a predetermined initial state representation on the quantum computer (710) before applying the determined sequence of operations to prepare the trial state representation.

5. The apparatus of claim 4 , wherein the initial state refers to a ground state of a mean-field representation of the problem or a Hartree-Fock state of the first part of the problem.

6. 10. The apparatus of claim 1, wherein transforming the trial state representation of the particular variational parameters into a representative operational trial state representation is based on a Jordan-Wigner or a Blavi-Kitaev transformation.

7. 10. The apparatus of claim 9, wherein the problem providing unit (721) is adapted to provide a problem description expressed as a quantum mechanical problem description including fermion-fermion interactions, and the apparatus (720) further comprises a conversion unit adapted to convert the problem description into a problem description expressed by a quantum mechanical description including boson-fermion interactions as a first part of the problem and non-interacting fermions as a second part of the problem.

8. 8. The apparatus of claim 7, wherein a Hubbard-Stratonovich transformation is utilized to transform the problem statement into a problem statement expressible as a quantum mechanical problem statement including boson-fermion interacting and non-interacting fermions.

9. 9. The apparatus of claim 7, wherein the problem description comprises at least a plurality of parts representable by a quantum mechanical description that includes static fermion-fermion interactions as a third part of the problem, and the transformation unit is adapted to approximate these parts of the problem by utilizing a restricted random phase approximation.

10. 10. The apparatus of any one of the preceding claims, wherein the variational approach refers to the variational Hamiltonian hypothesis or the unitary coupled cluster hypothesis.

11. 1. A system for processing a problem, the problem comprising a first portion and a second portion, the first portion comprising quantities that interact with each other to describe the problem, and the second portion comprising quantities that do not interact with each other to describe the problem, the system comprising: An apparatus (720) according to any one of the preceding claims for providing a control signal for controlling a quantum computer; a quantum computer (710) adapted to process the provided control signals to perform the quantum mechanical calculation.

12. The quantum computer (710) a second sub-operational unit (711) configured to utilize the quantum mechanical states of quantum elements to form qubits that can be manipulated by operations performed on the quantum elements, the operations relating to the second portion of the problem that is processed during quantum computer computation of the problem; a first sub-operational unit (712) configured to couple boson fields to the quantum elements, the coupling of the boson fields to the quantum elements being manipulable by operations on the first portion of the problem to be processed during the quantum computer computation of the problem; an operation unit (713) configured to: a) operate the second sub-operation unit (711) such that the states of the quantum elements are manipulated based on control signals indicative of operations on the second portion of the problem to be processed during the quantum computer calculation of the problem; and b) operate the first sub-operation unit such that the couplings of the boson fields to the quantum elements are manipulated based on control signals indicative of operations on the first portion of the problem to be processed so that a quantum mechanical calculation of the problem is performed; a readout (714) configured to measure at least one observable of a) the quantum mechanical state of each quantum element representing the state of each qubit and b) the boson field after manipulating the quantum elements and the boson couplings to perform the quantum mechanical calculation; The system of claim 11 , comprising:

13. 1. A computer-implemented method (800) for determining control signals to generate a solution to a problem translatable to a quantum mechanical description using a quantum computer, comprising: providing (810) a problem description describing the problem to be solved, the problem description describing a first portion and a second portion of the problem, the first portion including quantities describing the problem that interact with each other, and the second portion including quantities describing the problem that do not interact with each other; determining (820) a trial state representation of the problem statement based on a variational approach, the trial state representation including one or more variational parameters, the trial state representation including a first part and a second part representing the first part and the second part of the problem, respectively; converting (830) the trial state representation for a particular value of the one or more variational parameters into an operation trial state description including a series of quantum operations to be applied to quantum representation elements of the quantum computer to prepare a representation of the trial state representation on the quantum computer, the series of operations including: a) a second operation determined based on the second part of the trial state representation; and b) a first operation determined based on the first part of the trial state representation; providing (840) control signals for controlling application of the determined sequence of quantum operations on the quantum computer such that a representation of the trial state representation is prepared, the control signals being provided such that a control signal referring to the first operation and a control signal referring to the second operation are performed by different parts of the quantum computer; providing (850) a control signal for controlling a readout of the quantum computer to measure at least one observable of the quantum mechanical state of the prepared representation of the trial state representation after application of the determined sequence of quantum operations; 20. A computer-implemented method comprising:

14. A computer program product for solving quantum mechanical problems, said computer program product comprising program code means for causing an apparatus (720) according to any one of claims 1 to 10 to perform the method (800) according to claim 13.

15. Use of the apparatus (720) of any one of claims 1 to 10 for solving problems referring to electronic structure problems, spin problems and / or optimization problems.

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