Apparatus for providing control signal for controlling quantum computer

Abstract

The invention relates to an apparatus (720) for determining a signal for generating a solution to a problem using a quantum computer. A providing unit (721) provides a question description indicating a first portion and a second portion of the question. A determination unit (722) determines a heuristic representation based on a variational method. The heuristic representation includes a first portion and a second portion representing the first portion and the second portion, respectively. A conversion unit (723) converts the heuristic representation into an operational heuristic description comprising a) a second operation determined based on the second portion and b) a first operation determined based on the first portion. A providing unit (724) provides signals for controlling the quantum computer to prepare a representation of the heuristic representation. The signal relating to the first operation and the signal relating to the second operation are executed by different portions of the quantum computer.

Description

Technical Field

[0001] The present invention relates to an apparatus, a method and a computer program product for providing a control signal for controlling a quantum computer to solve a problem. Furthermore, the present invention relates to a system for determining a solution to a problem comprising the apparatus. Background Art

[0002] A quantum computer is a fundamentally new computing system that exploits the unique behavior of quantum mechanical systems to perform computations that, under the right circumstances, conventional computers cannot perform within any reasonable time or with reasonable resource and energy consumption. Furthermore, quantum computers have been shown to be particularly well-suited for solving problems related to the quantum mechanical world—that is, problems that can be translated into quantum mechanical descriptions. These problems include, for example, electronic structure problems, molecular problems, and condensed matter problems. However, problems outside the description of physical quantum mechanical systems can also be translated into quantum mechanical descriptions. For example, known encoding and decoding problems, complex analytical problems, and optimization problems can all be translated into quantum mechanical descriptions that can be processed by quantum computers. Examples of such problem translations can be found, for example, in the literature “Quantum algorithms: an overview,” by Montanaro, A., npj Quantum Inf 2, 15023 (2016). However, currently available quantum computers often exhibit inherent sensitivity to errors due to relaxation and decoherence, as well as imperfect control of the quantum mechanical systems at their core or due to readout errors. These difficulties in the accuracy of quantum mechanical calculations are directly related to the number of qubits (i.e., quantum mechanical elements consisting of at least two states) used and the duration of the quantum mechanical calculation, and are also directly related to the number of qubit operations performed on the quantum mechanical system. Therefore, to date, the problems that can be solved on quantum mechanical computers have often been limited by the quantum mechanical computational effort required. Therefore, it would be advantageous if solutions could be provided that reduce the demands on the quantum resources of quantum computers and allow more complex problems to be calculated on quantum computers. Summary of the Invention

[0003] The object of the present invention is to provide an apparatus, a system, a method and a computer program product which allow reducing the requirements on the quantum resources of a quantum computer, thereby allowing problems of increasing complexity to be solved. Furthermore, with the present invention, a wider variety of problems can be solved on a quantum computer. In particular, problems involving frequency-dependent dynamic interactions of the quantities in the problem, such as those resulting from perturbation theory applied to the problem, for example using constrained random phase approximation (cRPA), can be solved on a quantum computer.

[0004] In a first aspect of the present invention, a device for determining control signals for generating a solution to a problem convertible into a quantum mechanical description using a quantum computer is provided, wherein the device comprises: i) a problem providing unit for providing a problem description indicating the problem to be solved, wherein the problem description indicates a first part and a second part of the problem, wherein the first part includes mutually interacting quantities describing the problem, and the second part includes mutually non-interacting quantities describing the problem, ii) a trial state determining unit for determining a trial state representation of the problem description based on a variational method, wherein the trial state representation includes one or more variational parameters, and wherein the trial state representation includes a first part and a second part representing the first part and the second part of the problem, respectively, iii) a conversion unit for converting the trial state representation into an operational state for a specific value of the one or more variational parameters. A quantum computer is provided for performing a trial state description, the trial state description comprising a sequence 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, wherein the sequence of operations comprises a) a second operation determined based on a 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 application of the determined sequence of quantum operations on the quantum computer to prepare the representation of the trial state representation; and further for controlling a readout of the quantum computer to measure at least one observable value of a 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 control signals relating to the first operations and control signals relating to the second operations are performed by different parts of the quantum computer.

[0005] Because the trial state representation includes a first part and a second part representing a first part and a second part of the problem, and because the conversion unit is adapted to convert the trial state representation into a representative quantum trial state description comprising a sequence of quantum operations for a specific value of one or more variational parameters, the sequence of quantum operations comprising 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, wherein the control signal providing unit is adapted to provide control signals for controlling the application of the determined sequence of quantum operations on the quantum computer such that the control signals related to the first operations and the control signals related to the second operations are executed on different parts of the quantum computer, the control and the necessary quantum resources can be specifically adapted to the corresponding parts of the problem. In particular, the first part, for example, involving fermion-boson interactions or spin-boson interactions, can be implemented by utilizing specifically adapted control signals and quantum computing resources. This allows for a reduction in the general requirements for quantum mechanical resources, in particular, for quantum mechanical hardware. Furthermore, by splitting the problem into a first part and a second part that are processed differently, for example, the first part of the problem can be implemented on a component of the quantum computer's quantum mechanical hardware that is easier to control than quantum elements. This allows for more efficient control of the quantum mechanical resources of the quantum computer. Consequently, the quantum resources required to solve the problem can generally be reduced, allowing for the solution of more complex problems.

[0006] Furthermore, since variational methods are chosen in this context, the complex time evolution caused by the coupling of bosonic modes with fermionic or spin modes in the first part of the problem can be avoided with the help of variational optimization methods. For example, this allows the introduction of optimization parameters that can be adjusted on a classical computer. Consequently, the complexity of the quantum mechanical calculations can be reduced, allowing for a reduction in the quantum computer resources required to solve the problem, thereby directly enabling easier and less complex control of the quantum mechanical components of the quantum computer. Since the error rate of a quantum computer is directly related to the calculation time and, therefore, the amount of quantum computing resources used, not only does the control become more efficient, but the reliability of the results of the quantum mechanical calculations can also be further improved.

[0007] Typically, the device can be implemented in the form of software or hardware or a combination thereof, wherein hardware can refer to any known dedicated or general-purpose classical computer hardware. For example, the device can be implemented as any known computing device, such as a PC. However, the device can also be implemented as a cloud environment, a computing network, etc., so that at least a part of the device can also be implemented as a network solution, which can be distributed on multiple computing devices. The device is adapted to provide control signals that can be provided to any known quantum computer hardware architecture (i.e., can be interpreted by it). However, in a preferred embodiment, the quantum computer used for the quantum mechanical calculation of the problem (the device provides control signals to the quantum computer) is specially modified and dedicated to solving the problem comprising the first part and the second part.

[0008] The problem to be solved by a quantum computer is a problem comprising a first part and a second part, wherein the first part comprises interacting quantities describing the problem, and the second part comprises non-interacting quantities describing the problem. In embodiments, the first part may consist solely of interacting quantities describing the problem, and / or the second part may consist solely of non-interacting quantities describing the problem. Preferably, the problem can be provided in the form of a quantum mechanical description or can be converted into a quantum mechanical description, wherein, in this specification, preferably, the first part is represented by bosonic fields interacting with fermions or spins and thus describes the interacting quantities of the problem, and the second part is represented by non-interacting fermions or spins and thus describes the non-interacting quantities of the problem. Preferably, the interaction of the quantities describing the problem in the first part refers to dynamic interaction, i.e., frequency- or time-dependent interaction of the interacting quantities, wherein the interaction may also be lagging or leading interaction. Furthermore, the problem may include a third part, wherein the third part also comprises interacting quantities describing the problem, in particular, statically interacting quantities, i.e., interacting such that the interaction between the interacting quantities has no time or frequency dependence. The third part of the problem is also preferably processed by the second operational part of the quantum computer. Thus, in some embodiments, the third part of the problem can be considered as part of the second part of the problem, which is also processed by the second part of the operation of the quantum computer. If the problem is provided in a quantum mechanical description, the third part of the problem can refer to, for example, statically interacting fermions, for example, to density-density interactions of fermions.

[0009] The problem providing unit is adapted to provide a problem description that indicates that the problem is convertible into a quantum mechanical description, wherein the quantum mechanical description indicates or includes a first part and a second part to be solved, and in particular indicates or includes a fermion-boson interaction or a spin-boson interaction. In particular, the problem providing unit may be a storage unit having the problem description already stored thereon. However, the problem providing unit may also include an input unit, for example, by which a user can provide the problem description of the problem to the problem providing unit. The problem description may be any form of problem description that allows the determination of quantities describing the problem and the form of the interaction between these quantities. Preferably, the problem description is a mathematical description of the problem. However, the problem description may also refer to any other unambiguous symbolic form of the problem. In a preferred embodiment, the problem description is provided in the form of a quantum mechanical description, wherein the quantum mechanical description represents the problem in terms of quantities that obey the rules of quantum mechanics, i.e., a representation of the problem in the quantum mechanical world. However, the problem description may also be provided in any other form, in which case it is preferred that the providing unit is 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, wherein in this case the trial state determination unit and the conversion unit are preferably adapted to process the corresponding form of the problem description accordingly, for example by utilizing principles derived from the processing of the problem description in the form of a quantum mechanical description.

[0010] The tentative state determination unit is adapted to determine a tentative state representation of the problem description based on a variational method. In particular, the tentative state representation can be optimized with respect to one or more variational parameters, wherein the optimized state of the tentative state representation indicates the solution to the problem. Generally, a variational method refers to solving a problem using a calculus of variations, which refers to finding functions that provide solutions to the problem when optimized with respect to optimization parameters (also called variational parameters). Generally, the tentative state representation of the problem description involves a function that provides an indication of the solution to the problem in an optimized state, wherein the tentative state representation is optimized with respect to one or more variational parameters. The tentative state determination unit can be adapted to determine a tentative state representation of the corresponding problem description using any known method in the context of a variational method. Some exemplary methods and principles for variational methods and finding a tentative state representation of a given problem description can be found, for example, in the following article: “Variational quantum algorithms”, Cerezo, M. et al., Nat Rev Phys 3, 625–644 (2021). Preferably, the variational method refers to a variational Hamiltonian hypothesis or a variational quantum eigensolver. Typically, the trial state determination unit can be adapted to determine a trial state representation by determining a unitary evolution operator, which is applied to a predetermined initial state of the quantum mechanical system described by the problem, thereby generating a trial state representation. The unitary evolution operator can be any operator that transforms the predetermined initial state into the determined trial state representation. This determination of the trial state representation can be directly regarded as a representation of a calculation performed on a quantum computer, wherein in this calculation, a sequence of quantum operations is applied to the initial state of the quantum representation elements of the quantum computer.

[0011] Variational parameters are typically abstract parameters that are only defined such that they allow the optimization of the trial state representation. Therefore, the variational parameters do not necessarily refer to specific physical quantities or problem-related quantities. Since the problem to be solved comprises a first part and a second part, the trial state determination unit is adapted to determine the trial state representation such that the trial state representation comprises 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 preferably refers to a fermion-boson interaction or a spin-boson interaction, and the second part of the trial state representation is preferably convertible into a quantum mechanical description that refers to non-interacting fermions or non-interacting spins, respectively. Therefore, the general structure of the problem as described above is maintained during the conversion into the trial state representation.

[0012] The conversion unit is adapted to convert the trial state representation into a representative operational trial state description for a specific value of one or more variational parameters. In particular, the conversion unit is adapted to determine a representative operational trial state description based on the problem description, such that the representative operational trial state description includes a sequence of operations to be performed by the quantum computer to prepare a representation of the trial state representation on the quantum computer. Typically, operations are performed by the quantum computer by manipulating the states of quantum representation elements of the quantum computer. Quantum representation elements refer to elements of the quantum computer used to simulate the problem. For example, quantum representation elements can refer to quantum elements forming qubits, but can also refer to bosonic fields representing bosonic modes during computation of the problem. The conversion unit is adapted to convert the trial state representation into a representative operational trial state description, such that the sequence of quantum operations includes a) a second operation determined based on a second portion of the trial state representation and b) a first operation determined based on a first portion of the trial state representation. Thus, also during this determination of the sequence of operations, the problem is divided into two distinct parts that can be specifically adapted for application to different parts of the quantum computer. Preferably, as will be described below, the first operation is determined so that it can be performed by a first operational portion of the quantum computer, and the second operation is specifically adapted to be performed by a second operational portion of the specially modified quantum computer. Thus, to prepare a trial state on the quantum computer, the portion of the quantum mechanical description of the trial state representation involving boson-fermion interactions or boson-spin interactions can be implemented on the first operational portion of the quantum computer, and the portion of the trial state representation involving non-interacting fermions or spins, or optionally statically interacting fermions or spins, can be prepared on the second operational portion of the quantum computer. Preferably, the conversion of the trial state representation into a representative operational trial state representation for a particular variational parameter is based on a Jordan-Wigner transform or a Bravyi-Kitaev transform. In particular, these transforms are applied to the fermion portion of the trial state representation, wherein other known transforms can be utilized for the boson portion or the spin portion.In particular, for the spin part, the transformation can be omitted, and for the bosonic part, if a well-known quantum computer is used, in particular if the bosonic part is represented by quantum elements of the quantum computer, standard binary coding, Gray coding and / or unary coding can be used, for example, as described in the following article: "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. However, if the quantum computer used includes a first part operating part that is specifically adapted to represent the bosonic part, in particular the bosonic elements, the transformation can also be omitted. If 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, then the sequence of operations for determining the representative operational trial state representation 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 the quantum representation elements in the representative initial state, thereby preparing a representation of the trial state representation (i.e., a trial state) on the quantum computer. However, in some cases, the initial state may be predetermined so that the initial state is automatically prepared on the quantum computer at the beginning of the computation. In this case, the sequence of operations may also include only a sequence of operations for applying the representation of the unitary evolution operator to the quantum representation elements in the representative initial state, thereby preparing a representation of the trial state representation (i.e., a trial state) on the quantum computer.

[0013] In the event that the problem description is not provided in the form of a quantum mechanical description, the conversion unit is preferably further adapted to convert the problem description accordingly, for example, to map the problem description to a description of a quantum mechanical system that can typically be simulated by a correspondingly selected quantum computer, for example, by mapping the problem description to the Hamiltonian of the quantum mechanical system, which Hamiltonian defines the relationship between and influences on quantities similar to the problem. Thus, for example, an optimization problem in the field of optimizing production parameters (such as temperature, pressure, flow rate, etc.) for producing a product can be converted into a quantum mechanical description representing the problem in the quantum mechanical world of a quantum computer. In this case, for example, the Ising model can be used for this conversion. However, if the problem already involves a quantum mechanical problem, such as an electronic structure problem, this specific step of converting the problem into a quantum mechanical description can be omitted. Generally, the conversion unit can be adapted to convert the problem description based on predetermined rules or predetermined models for a specific problem class, or can be adapted to convert the problem description during an interactive process based on user input. In the case of an interactive process, for example, a user interface may be provided to the user, which 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 to select a corresponding set of rules or models to be applied to transform the provided problem. However, the user interface may also facilitate other interactions to transform the problem. Furthermore, in order to transform the provided problem, the transformation unit may also be adapted to access a storage device on which transformations for a particular problem are already stored, e.g., for a problem that has been previously solved, e.g., with different parameters.

[0014] The control signal providing unit is configured to provide control signals for controlling the execution of the determined sequence of quantum operations on the quantum computer, thereby preparing a representation of a trial state representation. In particular, the control signals are provided so that the control signals related to the first operation and the control signals related to the 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 can be different hardware parts controlled by different control hardware. However, the different parts can also refer to the same hardware part that is virtually divided into different parts (these different parts can be controlled independently). The different parts of the quantum computer can also be the following parts of the quantum computer: these parts are predefined as different parts of the quantum computer to be controlled differently. In an embodiment, the different parts refer to the quantum computer, the second partial operation part, and the first partial operation part, the second partial operation part being configured to utilize the quantum mechanical state of the quantum element to form a quantum bit that can be manipulated by the operation performed on the quantum element, and the first partial operation part being configured to couple the bosonic field to the quantum element. For example, a control signal related to a first operation can be performed by a first portion of the operation by manipulating the coupling of a bosonic field to a quantum element forming a qubit, and optionally manipulating a representation related to the bosonic field itself. Then, a second operation can be performed by a second portion of the operation of the quantum computer by manipulating the state of the quantum element (i.e., qubit) on the quantum computer.

[0015] Preferably, the control signal providing unit is configured to generate control signals for controlling the quantum computer, in particular, a manipulation portion of the quantum computer, which is configured to manipulate the states of the quantum representation elements according to the determined sequence of operations. However, if the quantum computer itself already provides a control unit adapted to control the manipulation portion so as to manipulate the states of the quantum representation elements, the control signal providing unit of the device may be adapted to provide control signals to the control unit of the quantum computer. In this case, for example, the control signal may simply refer to a representation of the determined sequence of operations, which can be interpreted by the control unit of the quantum computer to provide corresponding control signals to control the various components of the quantum computer accordingly. However, in this case, the control signal may also refer to a well-known and interpretable control signal that is converted by the control unit of the quantum computer into a corresponding dedicated control signal for controlling the specific hardware of the quantum computer. Therefore, the control by the control signal providing unit of the device may be direct or indirect, depending on the respective implementation of the quantum computer. Therefore, the control signal providing unit of the device, alone or in conjunction with the optional control unit of the quantum computer, can be considered to represent the interface between the quantum computer (in particular, the hardware of the quantum computer) and the software running on a well-known classical computer for solving the corresponding problem.

[0016] Furthermore, the control signal providing unit is adapted to control a readout of the quantum computer, in particular a readout of the state of the quantum representation element, to measure at least one observable value of the quantum mechanical state of the representation of the prepared trial state representation (in particular the quantum mechanical state of the quantum representation element) after applying the determined sequence of quantum operations. In particular, the control signal can be adapted to control the readout part of the quantum computer so that one or more observable values ​​are measured (i.e. readout) after the preparation of the trial state representation is completed. In particular, the control signal providing unit can be adapted to receive a reading of the readout part and provide the reading to, for example, a result determination unit, which is part of the classical computing environment. However, as mentioned above, here, the control signal providing unit can also optionally interact with a control unit of the quantum computer to act as an interface between the classical computing environment and the quantum computer.

[0017] In an embodiment of the present invention, the apparatus further includes an iterative control unit configured to control optimization of the tentative state representation using iterations of one or more variational parameters of the tentative state representation until at least one observable value read out or a quantity derivable from the at least one observable value read out converges, wherein the iterations include adjusting the one or more variational parameters of the tentative state representation and repeating the transformation, providing a control signal for preparing the tentative state representation, and providing a control signal for the readout until the at least one observable value or derivable quantity has converged to at least one final observable value or final derivable quantity. The apparatus further includes a result determination unit configured to determine a solution to the problem based on the at least one final observable value.

[0018] Typically, an iteration (i.e., an iterative process) refers to a series of repetitions of a process until a predetermined condition is satisfied, wherein the result of a single iterative step in the repetition of the process is typically the starting point for the next iterative step. In this embodiment, the iteration involves changing the variational parameters represented by the tentative state until at least one observable value or derivable quantity read out converges, i.e., reaches a predetermined convergence criterion. In some embodiments, the convergence criterion may also involve the variational parameters that converge during the iteration. In particular, the iteration may involve searching for a minimum or maximum value for one or more observable values ​​or derivable quantities read out. The predetermined convergence criterion may then involve, for example, a residual threshold value that determines if the difference between the currently read observable value, derivable quantity, or variational parameter and the observable value, derivable quantity, or variational parameter read out during the previous iterative step is below the predetermined residual threshold value, then convergence is achieved. However, if at least one observable value, derivable quantity, or variational parameter does not reach convergence, for example due to a failure or error occurring during the iteration, the iteration may also be terminated without reaching convergence, for example based on an alternative termination criterion. For example, the termination criterion may involve a predetermined number of iteration steps, after which convergence is assumed to be impossible and the iteration is terminated. In this context, 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 involving a reduced density matrix, the value of which can be determined based on one or more readout observables.

[0019] Typically, an iteration begins by providing an initial variational parameter as a starting point for the iteration, wherein the initial variational parameter can have an arbitrary value or can be selected based on any known iterative optimization process, for example, it can be selected based on a priori knowledge so that the initial variational parameter value allows the starting point to be as close as possible to the convergence point of at least one readout observable value or derivable quantity. Then, the iteration begins by implementing the initial variational parameter into a trial state representation and using a conversion unit and a control signal providing unit to provide control signals that allow the trial state representation of the initial variational parameter to be prepared on the quantum computer and the at least one observable value generated to be read out. Then, based on a known iterative algorithm, the iteration control unit can be adapted to adjust the variational parameter of the next iteration step, for example, based on the previous iteration parameter and based on at least one previously measured observable value. For example, a suitable algorithm for determining the variational parameter value of the next iteration step can be a linear approximation constrained optimization (COBYLA) algorithm or a quasi-Newton method, such as a finite memory 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] Then, the newly determined variational parameters are again implemented into the tentative state representation, and the steps of converting and providing control signals for preparing the tentative state representation and for reading out the at least one observable are repeated until a convergence criterion is met (i.e., the at least one observable converges) or a general termination criterion is met. Such a general termination criterion may involve, for example, a predetermined number of iteration steps that should not be exceeded, or may involve other quantities that indicate that the iterations failed (e.g., due to too large an amount of error or due to interference). However, typically, the at least one observable read out will converge after a reasonable number of iteration steps, and the at least one observable read out determined for the last iteration step is determined as the at least one final observable read out. Then, according to the variational method, the at least one final observable indicates a solution to the problem, and the result determination unit is adapted to determine the solution to the problem based on the at least one final observable.

[0021] The result determination unit is then adapted to determine the solution to the problem based on the at least one final observable value. For example, the result determination unit can be adapted to convert at least one final observable value indicating the solution of the representative quantum mechanical description of the problem into a corresponding solution in the problem description, for example, using the same conversion method 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 manipulations based on the at least one final observable value 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 at least one final observable value to determine the solution to the problem. Typically, the solution to the problem can then be provided to a user, for example, via an output unit (such as a display), or can be further used to directly control the production of the product, for example, via corresponding optimized production parameters.

[0022] In a preferred embodiment, at least one measured observable value indicates the energy of the prepared trial state representation, and the convergence of the at least one observable value is the minimization of this energy. In particular, the trial state representation is determined such that the measured observable value, and therefore the observable value to be optimized, is related to the energy of the prepared trial state representation (wherein the convergence of the at least one observable value is the minimization of this energy), which allows, for example, solving optimization problems, in particular quantum mechanical many-body problems involving the determination of a ground state or an excited state of a quantum mechanical system, such as, for example, a quantum mechanical many-body system, electrons in atoms or molecules, spins in a solid, etc. However, this approach can also be advantageous for all other problems (in particular optimization problems) that can be converted into a quantum mechanical description involving the determination of a ground state or an excited state of a quantum mechanical system.

[0023] In an embodiment, the control signal providing unit is adapted to provide control signals for controlling the quantum computer to prepare a predetermined initial state representation on the quantum computer and then apply the determined sequence of operations to prepare a trial state representation. Preferably, the state includes an overlap with a converged solution to the problem, or the state satisfies the same symmetry as the ideal solution state, such as the same number of particles. This initial state can, for example, be the ground state or Hartree-Fock ground state of a simplified model (such as a non-interacting quantum mechanical system), or can be selected to span a large portion of the computational space. Preparing the first predetermined initial state representation (i.e., an initial state that is converted into a specific state that serves as a quantum representation element of the quantum computer) ensures that the preparation of the trial state representation on the quantum computer can always start from the same starting point, that is, the preparation of the trial state representation can always be determined based on knowledge of the initial state. Therefore, control can be more efficient, and the results of the preparation of the trial state representation can be more accurate. This allows for more accurate determination of the results of the quantum mechanical calculation and for finding the solution to the problem on the quantum computer with fewer iterative steps. In an embodiment, 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 fermion part of the quantum element problem, the mean field state of the spin part of the quantum element problem, and the mean field state of the bosonic part of the bosonic element problem of the quantum computer, wherein the interaction between these parts is set to zero in the initial state. However, other initial states that may be beneficial for a particular problem or trial state preparation may also be prepared.

[0024] In a preferred embodiment, the problem description can be represented by a quantum mechanical description including fermion-fermion interactions, wherein the apparatus further comprises a transformation unit adapted to transform the problem description into a problem description that can be represented by a quantum mechanical description including bosonic-fermion interactions as a first part of the problem and non-interacting fermions as a second part of the problem. Furthermore, the representation of the non-interacting bosonic field can also be considered as part of the first part of the problem. Typically, the transformation is preferably adapted to transform the fermion-fermion interactions of the quantum mechanical description of the problem into fermion-bosonic interactions, thereby defining the connection between the fermion-fermion interactions, the bosonic field resonant frequency, and the fermion-bosonic field coupling strength. Optionally, the transformed quantum mechanical description can further include statically interacting fermions as a third part. For example, the problem description can be directly provided as a quantum mechanical description related to the fermion-fermion interaction problem, or the problem description can generally be represented using a quantum mechanical description related to the fermion-fermion interaction problem. Preferably, before the transformation unit transforms the problem, the transformation unit is adapted to convert the problem description into a quantum mechanical description, so that the transformation unit can be adapted to transform the problem according to corresponding quantum mechanical rules and algorithms. However, the transformation unit can also be adapted to transform the problem description in any other form or notation that explicitly describes the problem, wherein, in this case, the corresponding transformation utilized can be based on rules that have been derived from quantum mechanical transformations of the problem in the quantum mechanical description. In a preferred embodiment, the transformation unit is adapted to transform the problem description involving a quantum mechanical description including fermion-fermion interactions by utilizing a Hubbard-Stratonovich transformation. However, other known transformation algorithms can also be utilized.

[0025] In an embodiment, the problem description includes at least a portion that can be represented by a quantum mechanical description that includes static fermion-fermion interactions as a third part of the problem, and wherein the transformation unit is adapted to approximate these portions of the problem by utilizing constrained random phase approximation (cRPA). This allows reducing the number of fermion states that must be simulated during quantum mechanical calculations of the problem, thereby also allowing reducing the number of operations and the number of quantum elements used in the calculation. As a result, even more complex and larger problems, i.e., problems represented by a greater number of fermion states, can be calculated on a quantum computer. In general, cRPA allows distinguishing between fermions that actively participate in the problem solution and fermions that can be considered as a general background of actively participating fermions. For example, if a reaction between different molecules is to be simulated in the problem, only electrons in outer orbitals (i.e., valence orbitals) can be considered as actively participating in the problem solution, while electrons in the inner orbitals of atoms can be considered as providing only background for the electrons in the outer orbitals. Another example is transition metal oxide materials, where only narrow d states close to the Fermi level participate in the active part of the calculation, while other electronic states are considered by cRPA to be an effective screening background. In such a context, applying the constrained random phase approximation allows describing the background fermions (rather than single fermions) as charge clouds that interact with (and, in particular, provide screening effects for) the active fermions.

[0026] In an embodiment, the problem description refers to a quantum mechanical description, and the conversion unit is adapted to transform the quantum mechanical description of the problem into a rotating reference frame before converting into a representative operational description, in particular by applying a rotating wave approximation. Preferably, the conversion unit is adapted to further apply the 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 for the quantum mechanical description allows to simplify these different time scales that arise from different parts of the hardware acting on different time scales. For example, depending on the actual implementation of the quantum computer, the second part of the operational part defined below may act on a different time scale than the first part of the operational part defined below. The rotating reference frame and the rotating wave approximation allow to more easily synchronize these different time scales during the quantum mechanical calculation of the problem.

[0027] In another aspect of the invention, a system for processing a problem is proposed, wherein the problem comprises a first part and a second part, wherein the first part comprises quantities describing the problem that interact with one another, and the second part comprises quantities describing the problem that do not interact with one another, wherein the system comprises: i) a device as described above for providing a control signal for controlling a quantum computer, and ii) a quantum computer adapted to process the provided control signal in order to perform a quantum mechanical calculation. Preferably, the first part is convertible into a quantum mechanical description involving fermion-boson interactions or spin-boson interactions, and the second part is convertible into a quantum mechanical description involving non-interacting fermions or non-interacting spins, respectively.

[0028] In a preferred embodiment, the quantum computer includes: i) a second partial operating portion configured to utilize quantum mechanical states of quantum elements to form qubits that are manipulable by operations performed on the quantum elements, wherein the operations are related to the second part of the problem, ii) a first partial operating portion configured to couple bosonic fields to the quantum elements, wherein the couplings of the bosonic fields to the quantum elements are manipulable by operations related to the first part of the problem, iii) a manipulation portion configured to manipulate a) the second partial operating portion so that the states of the quantum elements are manipulated based on control signals indicative of operations related to the second part of the problem, and b) the first partial operating portion so that the couplings of the bosonic fields to the quantum elements are manipulated based on control signals indicative of operations related to the first part of the problem, and iv) a readout portion configured to measure a) the quantum mechanical state of each quantum element representing the state of the corresponding qubit and b) at least one observable in the bosonic field after manipulating the quantum elements and the bosonic couplings to perform the quantum mechanical computation.

[0029] Because a quantum computer is configured so that different parts of a problem can be solved by different parts of the quantum computer, the different specialized parts of the quantum computer can achieve more reliable solutions. In particular, since the interacting parts of the problem do not have to be simulated on the same part as the non-interacting quantities of the problem, for example, the calculations for the interacting parts do not have to be performed using separate quantum elements, the calculations become less resource-intensive in terms of hardware, i.e., fewer entanglement operations are required, which require a high degree of control over the quantum mechanical system.

[0030] Furthermore, because the readout section is configured to measure not only one observable value of the quantum mechanical state of each quantum element representing the state of the corresponding quantum bit, but also the bosonic field, particularly the state of the bosonic field coupled to the corresponding quantum element in the quantum computer, additional information about the interaction quantity of the problem can be provided. This provides an additional degree of freedom for solving problems on the quantum computer. Furthermore, because bosonic fields are generally easier to implement and provide simpler control concepts in hardware implementation, quantum mechanical calculations become less error-prone and thus more reliable. As a result, more complex problems can be solved with higher accuracy.

[0031] In general, a quantum computer may refer to any known implementation of a quantum computer, wherein preferred implementations will be described in the following embodiments. For example, a quantum computer may be based on superconducting elements, quantum dots, neutral atoms in optical lattices, nitrogen-vacancy centers in diamond, Bose-Einstein condensates, trapped ions, etc. Due to the variety of possible implementations, different parts of a quantum computer may also be implemented in a variety of different ways. For example, in a superconducting quantum computer, the bosonic field may be represented by an electromagnetic resonator, while in an ion trap quantum computer, the bosonic field may be represented by the vibrational modes of trapped ions. Preferably, a quantum computer refers to a quantum computer based on quantum gates.

[0032] Quantum computers are typically adapted to perform quantum operations based on control signals to determine the solution to a problem. A quantum operation may refer to any operation performed directly or indirectly on an element of a quantum computer that implements a quantum mechanical description of a problem (i.e., can be described according to the rules of quantum mechanics rather than classical physics). However, although a certain element of a quantum computer can be used to implement a quantum mechanical description of a problem, i.e., can be described using the rules of quantum mechanics, the element itself does not necessarily have to refer to a quantum mechanical system, such as an atom or an ion. For example, although in some embodiments, electromagnetic resonators are used to represent bosonic fields that typically follow the rules of classical physics in quantum computers, 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 the state of a quantum element (i.e., a quantum bit) of a quantum computer. For example, through the coupling between the bosonic field and the quantum element, the operation performed on the representation of the bosonic field will also affect the quantum element. Therefore, the operation performed on the representation of the bosonic field can also refer to a quantum operation. Quantum operations can therefore include operations performed directly on quantum elements, and therefore also on qubits, on bosonic fields, and on couplings between bosonic fields and quantum elements.

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

[0034] The second part operation part (i.e., the fermion operation part or the spin operation part) is configured to utilize the quantum mechanical state of the quantum element to form a quantum bit that can be manipulated by the operation performed on the quantum element. Generally, the second part operation part can refer to any hardware in the quantum computer that allows the operation to be performed on the quantum element. For example, the second part operation part can include the quantum element itself and the components that can be used to perform operations on the quantum element. However, the second part operation part can also refer only to the hardware part in the quantum computer that is adapted to perform operations on the quantum element. In this context, the second part operation part is adapted to make it possible to perform operations related to the second part of the problem to be solved during the quantum calculation of the problem on the quantum element. Therefore, the second part operation part allows the quantum element to perform operations related to the non-interacting amount of the problem. For example, if the problem is described in a quantum mechanical way, the second part operation part is preferably adapted to allow the quantum element to perform operations related to the non-interacting fermions or non-interacting spins of the quantum mechanical description of the problem.

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

[0036] The first operation part (i.e., the bosonic operation part) is configured to couple the bosonic field to the quantum element. Generally, the bosonic field refers to an entity that represents a bosonic mode in the quantum mechanical description of a quantum computer system. In some implementations of the quantum computer, the coupling between the bosonic field and the quantum element may refer to a hardware inductive coupling between a hardware element representing the bosonic field and the quantum element, so that the bosonic element (i.e., the hardware representation of the bosonic field) can affect the quantum element. However, in other implementations of the quantum computer, the bosonic field can be represented by a controllable specific state of the quantum element (e.g., a vibration mode), so that no additional hardware components are required to directly represent the bosonic field. Preferably, the bosonic field is non-interactive in the quantum mechanical description, so that the representation of the bosonic field can also be configured as non-interactive. For example, hardware bosonic elements can be configured as non-interactive, that is, they do not have to include connections or couplings with each other.

[0037] The first part of the operational part may generally refer to any hardware component that allows coupling the bosonic field to the quantum element, for example, allowing operations to be performed on the quantum element and / or optionally on the bosonic element, thereby coupling the bosonic field to the quantum element. In this context, it is again noted that the bosonic field itself can be implemented by a hardware element, but can also be implemented as a specific state of one or more elements of the quantum computer (for example, the quantum element itself). Therefore, the first part of the operational part may include the bosonic element adapted to represent the bosonic field during the quantum calculation of the problem, and further include the hardware required to couple the bosonic element to the quantum element and the hardware elements that allow manipulation of the coupling (preferably manipulation of the coupling of the bosonic element). However, in other embodiments, the first part of the operational part may also refer only to the hardware adapted to allow coupling the bosonic field to the quantum element and generally to the hardware part that allows manipulation of the coupling. For example, if the quantum computer refers to an ion trap system quantum computer, the bosonic field can be represented by the vibration modes of the ions forming the quantum elements, and the coupling and / or the manipulation of the coupling can be provided by control lasers that can provide laser light with a specific wavelength to the trapped ions.

[0038] The couplings between bosonic fields and quantum elements can be manipulated via operations related to the first part of the problem to be solved during quantum computation. Specifically, these operations relate to the interaction quantities that describe the problem, particularly the dynamically interacting quantities that describe the problem. Therefore, the interaction quantities of the problem are represented in the quantum mechanical computation system as bosonic fields interacting with the quantum elements. If the problem is presented in a quantum mechanical description involving a fermion-boson system as described above, the interaction quantities can be mapped to the interactions between bosons and fermions. Furthermore, if the problem is presented in a quantum mechanical description involving a spin-boson system, the interaction quantities can be mapped to the interactions between bosons and spins. This representation of interaction quantities allows at least a portion of the problem quantities to be represented using hardware components that are easier to handle and manipulate than the quantum elements themselves. Consequently, the qubit operations involved in performing operations directly on the quantum elements can be reduced, as the qubit operations that would otherwise be required to represent the interactions between quantities can be replaced with quantum operations performed on the couplings and / or bosonic fields. Since the number of qubit operations performed on quantum elements is related to the accuracy of the solution to a problem, solving problems with interacting quantities using coupled bosonic fields can improve the accuracy of the corresponding results.

[0039] The manipulation part is configured to a) manipulate the state of the quantum element and b) couple the bosonic field to the quantum element. Typically, the manipulation is based on control signals that indicate the operations intended to be performed on the quantum element or the coupling of the bosonic field. Preferably, the quantum element is manipulated based on the control signals indicating the operations related to the second part of the problem, and the coupling of the bosonic field is manipulated based on the control signals indicating the operations related to the first part of the problem. The manipulation part can generally refer to any hardware configured to manipulate the individual states of the quantum element or the coupling of the bosonic field based on the control signals. Therefore, the manipulation part can be regarded as referring to a) software and / or hardware components for providing control signals and b) the interface between the second part operation part and the first part operation part of the quantum computer that implements the quantum computation. For example, the manipulation part can refer to a controller of the second part operation part and / or the first part operation part. In the case where the quantum computer is an ion trap in which operations are performed on ions by a laser, the manipulation part can be implemented as a controller of the laser.

[0040] The readout portion is configured to measure at least one observable value of the quantum mechanical state of each quantum element representing the state of the corresponding quantum bit after the quantum mechanical calculation is performed, and further measure the bosonic field, that is, measure the state of the representation of the bosonic field in the quantum mechanical calculation, for example, the state of the bosonic element or the specific state of the quantum element representing the bosonic field. Generally, the one or more observable values ​​measured by the readout portion depend on the corresponding implementation of the quantum computer. For example, if the quantum computer is an ion trap, the observable value measured for the quantum element may refer to the electronic state of the corresponding quantum element, while the observable value for the bosonic field may refer to the corresponding 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 value. Generally, the measurement result of the corresponding observable value indicates the solution to the problem. In particular, depending on the conversion of the problem into a quantum mechanical description, the measurement result can be used in further calculations or can be converted from the quantum mechanical solution back to the corresponding "real world" solution of the problem.

[0041] In an embodiment, the bosonic coupling of a bosonic field to a quantum element is configured to be adaptable to a specific coupling of a quantity representing a first part of a problem during a quantum computation, wherein the manipulation part is further configured to adapt the coupling. In this context, manipulation of the coupling of a bosonic field to a quantum element is taken to mean the general possibility of providing and controlling such coupling, for example, by the possibility of determining which bosonic fields should be coupled to which quantum elements by utilizing quantum operations, as well as the possibility of performing operations on the coupling of the bosonic fields and, optionally, on the bosonic fields themselves. Adaptation of the coupling of a bosonic field to a quantum element refers to the possibility of specifically adapting the influence of a bosonic field on at least one quantum element to which it is coupled, for example, by performing corresponding operations or by adapting hardware settings (e.g., by utilizing switches) before or during a quantum mechanical computation. How the influence of the bosonic field on the quantum element is determined typically depends on the respective implementation of the quantum computer. For example, in the case of a trapped ion quantum computer, where the bosonic field is represented by the vibrational modes of the ions, the influence on the quantum elements, represented by the electronic states of the ions, can be controlled by controlling the environment of the ions, for example, by utilizing lasers, so that the energy transfer from the vibrational modes to the electronic states can be tailored. However, in other implementations of quantum computers, the influence of the bosonic field on the quantum elements to which it is coupled can be controlled in other ways.

[0042] In an embodiment, the first partial operating portion is configured to couple at least one bosonic field to each quantum element forming a quantum bit. In a preferred embodiment, the first partial operating portion is configured to couple more than one bosonic field to each quantum element forming a quantum bit, preferably, to couple four bosonic fields to each quantum element. Further preferably, the operating portion is configured to couple the bosonic field to only one quantum element forming a quantum bit. Thus, each quantum element can be coupled to one or more dedicated bosonic fields that are coupled to only one quantum element. This has the advantage that the interaction between the bosonic field and the quantum element can be more accurately controlled, so that unintentional interactions can be avoided. Since unintentional interactions can lead to inaccuracies or errors in quantum mechanical calculations, this allows the accuracy of the results of quantum mechanical calculations to be improved.

[0043] In the following, preferred alternative embodiments of the quantum computer and the various defined parts of the quantum computer as defined above will be described. In a first preferred alternative, the quantum computer refers to a superconducting quantum computer, wherein the quantum elements are implemented as superconducting circuits, and the bosonic field is coupled to these quantum elements by providing electromagnetic resonators, which are preferably also based on superconducting technology and are coupled to these superconducting circuits via electromagnetic fields. Preferably, in this embodiment, the first part of the operating part includes a resonator as a bosonic element, wherein the electromagnetic field of the resonator represents the bosonic field during quantum mechanical calculations. In particular, the electromagnetic resonator coupled to the superconducting circuit refers to an additional electromagnetic resonator specifically provided for representing the bosonic field. In this context, it should be noted that the electromagnetic resonator (for example, regarded as part of the readout unit) used to measure the state of the superconducting quantum element (i.e., for reading out the quantum bit) in the superconducting quantum computer cannot generally be used to represent the bosonic field. Each readout operation performed on the readout resonator will destroy the state of the bosonic field represented by the resonator and the coupling of the bosonic field to the quantum element during readout, thereby making the readout result unreliable. Therefore, the electromagnetic resonator that provides coupling with the superconducting circuit to couple the bosonic field to the quantum element is not the electromagnetic resonator used to read out the superconducting circuit, and is therefore an additional electromagnetic resonator. In this embodiment, the bosonic coupling portion can include or utilize a microwave source to manipulate the electromagnetic field generated by the resonator to represent the bosonic field. In addition, the microwave source can also 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 is an ion trap quantum computer, wherein the quantum elements are implemented as ions trapped in an ion trap, and the coupling of the bosonic field to these quantum elements is implemented as the coupling of the vibrational modes of these trapped ions with the electronic states of these trapped ions forming the quantum bits. In this embodiment, the first operating portion may include or utilize a laser to manipulate the coupling between the electronic states (i.e., modes) of the ions and the vibrational modes. For example, using a laser having a corresponding wavelength (i.e., frequency) and amplitude that is in resonance or near resonance with the modes, the coupling can be turned on or off, or the strength of the coupling can be manipulated. In particular, the coupling of electronic and vibrational modes refers to the transfer of energy between these modes. Therefore, if there is no coupling, there is essentially no energy transfer between the modes, and if there is coupling, the amount of energy transferred determines the strength of the coupling. Preferably, the laser is adapted to be tunable, in particular, the laser can be tuned to the resonant frequency of the quantum mechanical problem description, i.e., the resonant frequency of the quantum elements of the ion trap. The resonance used in this context preferably refers to carrier transition resonance, red sideband resonance and blue sideband resonance. Carrier transition resonance refers to the transition frequency between the electronic states of trapped ions used in quantum computer calculations without initiating energy transfer between the vibrational modes of the ions. Red sideband transition resonance refers to the frequency that allows energy to be transferred from the electronic state of the ion to the vibrational mode of the ion in the ion trap (and vice versa). Blue sideband transition resonance refers to a frequency that allows simultaneous excitation from the lower energy electronic state of the ion to the higher energy electronic state of the ion and increases the excitation in the vibrational mode, or allows simultaneous transition from the higher energy electronic state of the ion to the lower energy electronic state of the ion and reduces the excitation in the vibrational mode, so that both can be manipulated simultaneously.

[0045] In a third alternative preferred embodiment, a quantum computer can refer to any type of quantum computer, and in this case, bosonic coupling is achieved by performing additional coupling operations on quantum elements representing bosonic fields that form qubits, and coupling the bosonic fields to the quantum elements. In this embodiment, the quantum elements representing the bosonic fields are preferably coupled to each other to enable two-qubit operations, and at least one of the quantum elements representing the respective bosonic fields is coupled to a quantum element representing interacting fermions, i.e., the fermions interact with the respective bosonic fields to enable representation of the first component. Utilizing this coupling configuration allows for reduced control and manipulation requirements for the quantum computer's hardware compared to, for example, fully interacting fermionic computations without bosonic fields. Furthermore, in this configuration, the circuit depth required to perform quantum mechanical computations on a problem can be reduced compared to simulating the problem using other coupling configurations, i.e., the number of quantum operations required to simulate the bosonic fields can be reduced.

[0046] In another aspect of the present invention, a method for determining control signals for generating a solution to a problem convertible into a quantum mechanical description using a quantum computer is provided, wherein the method comprises: i) providing a problem description indicative of the problem to be solved, wherein the problem description indicates a first part and a second part of the problem, wherein the first part comprises mutually interacting quantities describing the problem and the second part comprises mutually non-interacting quantities describing the problem, ii) determining a tentative state representation of the problem description based on a variational method, wherein the tentative state representation comprises one or more variational parameters, and wherein the trial state representation comprises the first part and the second part representing the first part and the second part, respectively, of the problem, iii) converting the trial state representation into a representative operational trial state description for specific values ​​of the one or more variational parameters, the representative operational trial state description comprising a sequence 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, wherein the sequence of operations comprises a) a second operation determined based on a second portion of the trial state representation, and b) a first operation determined based on the first portion of the trial state representation, iv) providing control signals for controlling the application of the determined sequence of quantum operations to the quantum computer to prepare the representation of the trial state representation, wherein the providing of the control signals causes control signals relating to the first operations and control signals relating to the second operations to be performed by different portions of the quantum computer, and v) providing control signals for controlling a readout of the quantum computer to measure at least one observable value of a quantum mechanical state of the prepared representation of the trial state representation after application of the determined sequence of quantum operations.

[0047] In another aspect of the present invention, a computer program product for solving quantum mechanics problems is provided, wherein the computer program product comprises program code means for causing the apparatus described above to execute the method described above.

[0048] In another aspect of the invention, the use of a device as described above for solving problems involving electronic structure problems, spin problems and / or optimization problems is proposed.

[0049] In another aspect of the invention, the use of a system as described above for solving problems involving electronic structure problems, spin problems and / or optimization problems is proposed.

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

[0051] In particular, electronic structure problems may refer to molecular problems and condensed matter problems. Preferably, these molecular problems include problems involving at least one of the following: organometallic compounds containing transition metals (including lanthanides and actinides), chelating agents that interact with metals, catalysts, biomolecules with active centers, macromolecular systems, and transition metal compounds in solution or embedded in an environment. Preferably, condensed matter problems include problems involving at least one of the following: transition metal oxides and rare earth elements (e.g., perovskites, e.g., for solid oxide fuel cells), oxide-based battery cathodes, hard magnets for electric motors, catalysts for fuel cells, transition metal heterostructures for sensors, magnetic semiconductor sandwich structures for spintronics, and high-temperature superconductors.

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

[0053] It shall be understood that a preferred embodiment of the present invention may also be any combination of the dependent claims or the above-described embodiments with the respective independent claim.

[0054] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In the attached figure:

[0056] Figure 1 Demonstrates the state representation of qubits used in quantum computing devices,

[0057] Figure 2 A schematic example of a quantum computing device using qubits as computing units is shown.

[0058] Figure 3 Illustrative example methods for generating control signals to perform operations on a quantum computing device and for processing measurement signals from a quantum computing device are presented.

[0059] Figure 4 A schematic example of a hybrid system comprising classical and quantum computing devices is shown,

[0060] Figure 5 A schematic example of a quantum computing device based on superconductors is shown,

[0061] Figure 6 A schematic example of a quantum computing device based on trapped ions is shown.

[0062] Figure 7An embodiment of a system for determining a solution to a problem is shown schematically and exemplarily,

[0063] Figure 8 A flow chart schematically and exemplarily showing a method for determining a solution to a problem, and

[0064] Figure 9 An example of a sequence of operations suitable for performing quantum mechanical calculations is shown schematically and exemplarily. DETAILED DESCRIPTION

[0065] The following article first briefly introduces the general basic principles of quantum computers and the computing performance of quantum computers. Further general principles can also be found in the following literature: "Quantum Computation and Quantum Information: 10 th Quantum Computation and Quantum Information: Anniversary Edition, MA Nielsen and ILChuang (2010).

[0066] Classical computing devices use transistor-based processors. Each transistor has two controllable states, 1 or 0, representing a binary number or bit. To execute operations on a classical computing device, a compiler converts human-readable program code into machine-readable instructions. The machine-readable instructions are control signals for each transistor, such as voltage settings. The representation of the machine-readable instructions can include binary or hexadecimal representation. Based on these machine-readable instructions, operations are executed on the processor of the classical computing device.

[0067] Quantum computing is a relatively new computing method that uses quantum effects (such as superposition and entanglement) to perform certain calculations more efficiently than classical digital computers. Compared to digital computers that represent information in the form of bits (e.g., "1" or "0") as described above, quantum computing devices (i.e., quantum computers) use quantum bits (qubits / quantum bits) to represent information. Quantum computing devices are based on quantum elements that follow quantum mechanical physics, such as superconductors, ions, atoms, quantum dots, photons, particle spins, bosons, etc. These quantum elements can be manipulated in a controlled manner to perform operations.

[0068] Although qubits and their manipulation can be described in terms of their mathematical properties, each such qubit can be implemented in any of a variety of different ways in physical quantum elements. Examples of such quantum elements include superconducting materials, trapped ions, photons, optical cavities, single electrons trapped within 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 sensed or detected.

[0069] In general, for any given physical quantum element that implements a qubit, any of a variety of properties of that physical element can be selected to implement the qubit. For example, if an electron is chosen to implement a qubit, the x, y, or z component of the electron's spin degree of freedom can be selected as the property of that electron to represent the state of that qubit. For any particular degree of freedom, the physical quantum element can be controllably placed into a superposition or entangled state, and measurements can then be performed on the selected degree of freedom to obtain a readout of the qubit's value.

[0070] Compared to transistors in classical computing devices, each quantum element in a quantum computing device can adopt not only the ground state |1> or |0>, but also any superposition of such ground states, such as the state |X>. The state of each quantum element is represented by the state of a quantum bit (qubit), such as Figure 1 This is shown in the two-dimensional simplification of . To represent this state, Dirac notation is commonly used in quantum mechanics. In Dirac notation, a state in an n-dimensional complex vector space (such as Hilbert space) is represented by a braket symbol, for example, |X>. According to conventional terminology, the superposition of the "0" and "1" states in a quantum computing device can be represented as α|0>+β|1>. The states "0" and "1" or bits of a classical computing device are similar to the ground states |0> and |1> or qubits of a quantum computing device, respectively. The value |α| 2 represents the probability that the qubit will be measured in the |0> state, while the value |β| 2 represents the probability that a qubit will be measured in the |1> state. If there is more than one qubit, two or more qubits may be entangled. Entanglement means that the state of one qubit depends on the state of at least one other qubit, and vice versa, wherein, further, in the entangled state, the individual qubits can no longer be considered as separate qubits. In general, a register of N qubits in a quantum computer can be in a superposition of ground states at the same time, while a register of N classical bits can only be in a single ground state at the same time. Therefore, compared to classical computing devices on quantum computing devices, 2 Nbasis states, thus achieving exponential inherent parallelism.

[0071] To perform operations on a quantum computing device, the computational method used to solve a given problem can be converted into qubit operations, which can be converted into control signals for manipulating the qubits. The representation of machine-readable instructions can include common quantum mechanical representations of operations in Hilbert space. Depending on the specific implementation of the quantum computer, different representations of qubit states can be selected. Any state preparation on a quantum computing device can be represented by an operation acting on the qubit state. The operation can be converted into control signals to control the corresponding part of the quantum computer, depending on the type of quantum computing device used. In this way, based on the operations acting on the qubit state, the operation can be performed on the quantum equivalent of the classical processor (as part of the quantum computing device).

[0072] An operation on a qubit state can typically be one or more qubit operations. A qubit operation can change the state of a qubit, for example, to Figure 1 The displayed rotation of the vector |X> corresponds to a specific superposition. For example, in a superconducting quantum computer, this can be achieved using microwave pulses, or in a trapped ion quantum computer, by irradiating ions with a laser beam. Multi-qubit operations can generate entanglement between two or more qubits. For example, in a superconducting quantum computer, this can be achieved by connecting the qubits via an intermediate electrical coupling circuit, or in a trapped ion quantum computer, by controlling the collective vibrations of the trapped ions.

[0073] Typically, in order to prepare operations for solving a given problem, the corresponding quantum mechanical representation of the problem can be converted into qubit operations, which are performed to prepare a solution to the given problem. After the predetermined solution is prepared, that is, after the operations are applied to the qubits of the quantum computer, a projection measurement of all individual qubits is performed, returning either 0 or 1 for each qubit. On a quantum computing device, this measurement is achieved by applying a hardware-specific readout protocol (including control pulses) for a series of readout operations and monitoring the response to the control pulses. For example, a superconducting qubit can be coupled to a hardware resonator. Measuring the shift in the resonator frequency allows the state of the qubit to be determined, because the shift depends on the state of the coupled qubit. For example, in the case of trapped ions, optical readout can be used, for example, if the ion emits light, the state of the qubit is 1, and if the ion does not emit light, the state of the qubit is 0, and vice versa. In this way, qubits can be used to implement logic circuits or gates as in classical computing devices.

[0074] exist Figure 2 In , a schematic example of a quantum computer is shown. Figure 2 The quantum computing device 100 shown in FIG. 1 includes a quantum register 104 configured to perform quantum computations, a manipulation section 106 configured to manipulate the quantum register (particularly the quantum elements forming qubits), and a readout section 108 configured to collect measurement signals from the quantum register 104 to read out the qubits after a quantum mechanical computation. In particular, the manipulation section 106 provides manipulation signals for manipulating the quantum register, wherein these manipulation signals are generated based on received control signals, which are determined based on corresponding operations that should be performed on the qubits. In some embodiments, a feedback loop can be provided between the manipulation section 106 and the measurement section 108. In contrast to classical computing, where one measurement cycle provides the state of a transistor, quantum computing involves performing multiple measurement cycles to provide a probability density or probability of the qubit state.

[0075] The quantum register 104 can be based on different quantum elements representing qubits. In some embodiments, the qubits can be implemented as quantum elements using photons. Such an optical quantum computing device can include a laser that generates photons that are provided to a waveguide. A beam splitter can be provided for manipulating the photon state based on a manipulation signal (such as a mechanical rotation applied to a mirror). In such an embodiment, the measurement portion 108 can be a photon detector, and the measurement signal can be a photon.

[0076] In other embodiments, qubits can be implemented as electronic states of ions trapped in a magnetic field. In this case, manipulation section 106 can utilize a laser, and the manipulation signal can provide a control laser pulse. Furthermore, in this case, readout section 108 can be a photon detector combined with the readout laser pulse, and 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, and so on.

[0077] Figure 3 Illustrative exemplary methods for generating control signals for performing operations on a quantum computing device and for processing measurement signals from the quantum computing device are presented. In most embodiments of quantum computing devices known to date, control signals for the quantum computing device are prepared on a classical computing device, and measurement signals provided by the quantum computing device are further processed on the classical computing device. However, as quantum computing devices mature, other embodiments are also conceivable.

[0078] To generate control signals for performing operations on a quantum computing device, in step S10, a problem to be solved using the quantum computing device is preferably provided in the form of a mathematical description. For example, such a problem may include determining material properties based on a mathematical description of the material's electronic structure. Other problems may include optimization problems and associated objective functions. In step S12, an operational description of the problem or subproblem may be generated based on the problem to be solved, wherein the operational description includes the operations to be applied to the qubits of the quantum computer to solve the problem in a quantum mechanical calculation. Furthermore, the operational description may include a reference state that allows for generating a representation of the initial qubit state on the quantum computer, and then applying further operations on the quantum computer by manipulating the qubit state. Then, in step S14, based on the operational description, control signals may be generated to control the quantum computer, for example, by providing these control signals to a manipulation unit, which may then manipulate the qubit state based on these control signals. In step S16, the manipulation unit then applies manipulation operations to one or more qubits of the quantum computer, wherein the qubits perform a quantum mechanical calculation based on these manipulation operations. Following this manipulation, a measurement signal may be generated in step S18 to determine the result of the quantum mechanical calculation. This step may include reading out (i.e., measuring) the qubit state after applying the manipulation operation to the initial qubit state. Then, in step S20, the measurement signal may be converted into a measurement quantity on a classical computer and, in the case of a subproblem, fed back into the problem to be solved. Finally, in step S22, the result of the problem calculation, including the quantum mechanical calculation, may be provided on the classical computing device.

[0079] Figure 4 A schematic example of a hybrid system including classical and quantum computing devices is shown. Figure 3 As described in the methods presented in [1], quantum computing devices are often used in conjunction with classical computing devices. Figure 4 As shown, the question preparation system can be implemented to perform e.g. Figure 3A classical computing device 110 is provided for performing steps S10, S12, S20, and S22 of the illustrated method. A control unit can then be provided as an interface between the classical computing device 110 and the quantum computer 100, wherein the control unit can also be, for example, the classical computing device that performs step S14. The control unit can then be communicatively coupled to a manipulation portion 106, which can control a manipulator of the quantum computing device. Furthermore, manipulation portion 106 can be implemented as a classical computing device, such as classical control hardware for controlling specific hardware components that perform qubit manipulation in a quantum computer. However, manipulation portion 106 is typically considered part of the quantum computer because it directly affects the quantum registers. The quantum computing device 100 is adapted to perform quantum operation S16, specifically by manipulating the qubits of the quantum registers. A measurement portion 108, also typically considered part of the quantum computing device, can then perform step S18 using classical hardware. Measurement portion 108 can then be communicatively coupled to a preparation system 110 for further processing of the measurement signal.

[0080] Figure 5 A schematic example of a superconductor-based quantum computing device is shown. Superconducting quantum computing devices are one of the solid-state quantum computing technologies. Here, quantum register 104 may include superconducting circuits 520, 522, and 524 based on Josephson junctions. Depending on the number of superconducting circuits selected to represent a qubit, the qubit may be, for example, a charge qubit, a flux qubit, a transport qubit, or a phase qubit. Figure 5 A simplified illustration of a superconducting quantum computer using charge qubits. For charge qubits, the different states of the qubit are represented by an integer number of Cooper pairs on a superconducting island. The qubits can then be manipulated by microwave pulses to perform quantum operations. Resonators 512, 514, 516 can be used to manipulate the state of the qubit by applying microwaves, or to read out the state of the qubit by measuring the corresponding microwaves, wherein different resonators are typically used to manipulate the state of the qubit and to read out the qubit. In addition, resonator 518 can be used to apply microwaves that entangle the qubits. However, in addition to resonator 518, entanglement can also be achieved by inductive coupling or capacitive coupling of superconducting circuits or even by providing another qubit (here, a superconducting circuit) between the qubits to be entangled.

[0081] At the operational level, such systems are maintained at extremely low temperatures, for example, tens of mK. The extreme cooling of the system keeps the superconducting material below its critical temperature and helps avoid unnecessary state transitions. To maintain this low temperature, the quantum information processing system can be operated in a cryostat (such as a dilution refrigerator). In some embodiments, the control signal is generated in a higher temperature environment and transmitted to the quantum computer using a shielded impedance-controlled GHz transmission line (such as a coaxial cable). In some embodiments, a dispersion detection scheme is used to achieve state measurement of superconducting qubits. In order to read out or detect the state of any qubit, a probe signal (e.g., a traveling wave microwave) can be excited along a readout transmission line coupled to the qubit via a corresponding readout resonator. The frequency of the probe 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 probe signal transmitted along the readout transmission line can be changed because the reflectivity of the readout resonator coupled to the qubit varies according to the state of the qubit. This allows state detection of the qubit, wherein, during the readout of the qubit state, the state of the qubit collapses, that is, it is projected onto one of the ground states with a corresponding probability. By performing quantum mechanical calculations and reading them out multiple times, the corresponding probabilities can be determined. Further details of superconducting quantum devices are described in, for example, EP 3830867 A1, EP 3449427 A1, US 2020272925 A1, CN 212061223U, and US 2019019099 A1.

[0082] Figure 6 A schematic example of a quantum computing device based on ions in an ion trap is shown. Similar to neutral atom traps, ion traps containing, for example, positively charged calcium ions can be used to implement quantum computing devices. Here, ions 626 are trapped in an oscillating electromagnetic field 624 within a high or ultra-high vacuum. Ions 626 are laser-cooled and held in the oscillating electric field 624. For qubit manipulation (such as superposition or entanglement), lasers 628 of different frequencies can be used.

[0083] Generally, based on the aforementioned quantum computer implementations, gate-model-type computations can be performed on quantum computer hardware architectures. Gate-model-type computations are based on quantum gates. Compared to classical gates, there are an infinite number of possible single-qubit quantum gates that can change the state vector of a qubit. Changing the state of a qubit's state vector is often referred to as a single-qubit rotation and may also be referred to herein as a state change or a single-qubit quantum gate operation. Rotations, state changes, or single-qubit quantum gate operations can be mathematically represented using a unitary 2×2 matrix with complex elements. A rotation corresponds to a rotation of the qubit state within its Hilbert space, which can be conceptualized as a rotation of a vector on the Bloch sphere, which is often referred to as a geometric representation of the space of pure states of a qubit. A multi-qubit gate changes the quantum state of a group of qubits. For example, a two-qubit gate rotates the states of two qubits by rotating the two qubits in four-dimensional Hilbert space. As is well known, Hilbert space is an abstract vector space with an inner product structure that allows for the measurement of lengths and angles. Furthermore, Hilbert space is complete, meaning that sufficient limits exist within the space to allow the use of calculus techniques.

[0084] Hereinafter, the term operational description refers to a representation of a problem, including the sequence of quantum operations that should be applied during quantum mechanical calculations of that problem. In the context of the present invention, the term "quantum operation" can include all types of quantum gates as described above. Furthermore, the term can also include operations performed on components in a quantum computer that represent the coupling between the quantum elements forming qubits and the bosonic field (and optionally, components representing the bosonic field itself). These operations then involve any kind of change in the state of the coupling or bosonic field, such as switching the coupling on and off, or changing the field frequency. Furthermore, in some applications, quantum operations can also include measurement operations. This allows algorithms to be implemented using measurement feedback. For example, in such an algorithm, a quantum computer can execute quantum gates defined by a sequence of quantum operations, then measure only a subset (i.e., less than all) of the qubits or other computational elements (such as the bosonic field state) in the quantum computer, and then decide which further quantum operations to perform based on the results of one or more measurements. In particular, measurement feedback can be used to perform quantum error correction, but is not limited to such use.

[0085] In the following, embodiments of the present invention are described, wherein some embodiments may be adapted to utilize the above-mentioned well-known quantum computer devices.

[0086] Figure 7An embodiment of a system 700 for processing problems (e.g., electronic structure problems) in quantum computing is schematically and exemplarily shown. The system is specifically adapted to solve problems comprising a first part and a second part, wherein the first part comprises quantities that interact with each other describing the problem, and the second part comprises quantities that do not interact with each other describing the problem. Preferably, the problem can be represented by a quantum mechanical description comprising, as a first part, fermion-bosonic interactions, and optionally bosonic fields that interact with fermions but do not interact with each other, and as a second part, non-interacting fermions. In addition, the problem may also comprise a third part involving only statically interacting quantities, wherein the third part may preferably be represented in the quantum mechanical description as a static fermion-fermion interaction.

[0087] The system includes a quantum computer 710 and an apparatus 720. Optionally, the system may further include a control unit 730, which serves as an interface between the apparatus 720 and the quantum computer 710. However, the explicit control unit 730 may also be omitted, or may be, for example, a dedicated part of the quantum computer 710. As described above, the quantum computer 710 of the system may refer to any known quantum computer solution associated with a known quantum computer architecture. However, in a preferred embodiment, the quantum computer 710 is dedicated to computing problems involving the first and second parts. In particular, it is preferred that the quantum computer 710 includes a corresponding hardware structure that allows the corresponding problem to be processed very efficiently. Preferably, the quantum computer refers to a modified quantum computer as described below.

[0088] The quantum computer 710 preferably includes a second partial operation part 711, which is configured to use the quantum mechanical state of the quantum element to form a quantum bit. For example, the second partial operation part can use and optionally also include, for example, reference Figure 2 Typically, the quantum elements that form a qubit can be manipulated by performing quantum gate operations on the quantum elements.

[0089] Furthermore, the quantum computer 710 includes, in addition to the second operating part 711, Figure 2Unlike the well-known quantum computers described, the second partial operating section 711 preferably also includes a first partial operating section 712. The first partial operating section 712 is configured to couple a bosonic field to a quantum element, wherein the coupling of the bosonic field to the quantum element, and optionally the bosonic field itself, can be manipulated via quantum operations performed on the coupling of the bosonic field and / or the bosonic field itself. Thus, as indicated by the double-headed arrows, the second partial operating section 711 and the first partial operating section 712 interact with each other via the coupling of the bosonic field to the quantum element utilized by the second partial operating section 711. In general, depending on the construction principle on which the quantum computer 710 is based, the bosonic operating section 712 can be implemented in a variety of different ways. For example, if the quantum computer 710 refers to a superconducting quantum computer in which the quantum elements are implemented as superconducting circuits, as explained above, the first partial operating portion 712 can be configured to 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, wherein these resonators are coupled to the quantum elements to provide coupling of the bosonic fields to the quantum elements. Thus, in such an exemplary embodiment, the bosonic fields will be represented by the electromagnetic fields provided by the resonators, and the coupling will be represented by the interaction of the corresponding electromagnetic fields with the superconducting circuits forming the quantum elements. A more detailed description of further exemplary embodiments of this embodiment and of the implementation of the first partial operating portion will be discussed with reference to more detailed embodiments of the present invention.

[0090] Preferably, the second part operation section 711 is adapted to allow manipulation of the quantum elements by operations related to the second part of the problem, which second part comprises quantities describing the problem that do not interact with each other. In contrast, the first part operation section 712 is specifically configured to allow manipulation by operations related to the first part of the problem, which first part involves quantities describing the problem that interact with each other. Thus, preferably, by operations related to Figure 2 Compared to constructing a quantum computer 710 to provide a second partial operation portion 711 and an additional first partial operation portion 712, the described quantum computer can transform the representation (i.e., simulation) of the interacting quantities of a problem into the interactions of different parts of quantum computer 710, for example, into the interactions of an additional resonator and a superconducting circuit that can be independently controlled. Furthermore, due to the decoupling of the two parts of the problem, the first partial operation portion 712 can be represented by a system that is configured to be controlled in a technologically different manner from the quantum elements, thereby reducing the number of quantum gate operations that must be explicitly performed on the qubits to solve a given problem. Therefore, not only can better control be provided, allowing for improved computational accuracy, but the necessary qubit resources can also be reduced, allowing for the computation of more complex problems within a given qubit resource.

[0091] Furthermore, quantum computer 710 preferably includes a manipulation section 713 configured to manipulate a) second partial manipulation section 711 and b) first partial manipulation section 712. Specifically, manipulation section 713 is configured to manipulate second partial manipulation section 711 so as to manipulate the state of the quantum element based on a control signal specifically indicative of an operation related to the second part of the problem. Furthermore, manipulation section 713 is configured to manipulate first partial manipulation section 712 so as to manipulate the coupling of the bosonic field and, optionally, the bosonic field itself, based on a control signal indicative of an operation related to the first part of the problem. For example, manipulation section 713 can be considered a controller for a laser, which can be considered part of second partial manipulation section 712 and allows for manipulation of quantum elements, i.e., qubits, in a quantum computer implemented as an ion trap. Alternatively, manipulation section 713 can be a controller for a microwave source used to manipulate qubits and / or bosonic fields in a quantum computer implemented as a superconducting quantum computer. Therefore, the manipulation part 713 is provided with control signals of, for example, the control unit 730, and uses these control signals to control the corresponding parts of the quantum computer accordingly, these control signals indicating the operations that should be performed by the second partial operation part 711 and the first partial operation part 712.

[0092] Furthermore, the quantum computer 710 preferably includes a readout section 714 configured to read out the quantum elements used by the second partial operating section 711 and the bosonic fields used by the first partial operating section 712. Generally, reading out the quantum elements and bosonic fields refers to measuring at least one observable value of the quantum mechanical state of each quantum element used by the second partial operating section 711, as well as measuring the state of the representation of the bosonic field used by the first partial operating section 712. For example, measuring the bosonic field may refer to measuring an observable value or signal provided by the bosonic element representing the bosonic field. For example, if the quantum computer is a superconducting computer in which the bosonic field is represented by a resonator, the readout unit may be adapted to measure the electromagnetic field provided by the resonator or changes in the electromagnetic field. Alternatively, if the quantum computer is an ion trap quantum computer in which the bosonic field is represented by the vibrational modes of trapped ions, the measurement unit may be adapted to measure the frequencies of the vibrational modes of the trapped ions. The measurement results of the readout unit 714 then indicate a solution to the computational problem.

[0093] Optionally, the functions of quantum computer 710 can be controlled by control unit 730. Control unit 730 is adapted to provide control signals to manipulation section 713, these control signals indicating desired operations to be performed by second partial operating section 711 and first partial operating section 712, wherein manipulation section 713 then performs the corresponding manipulations, for example, by controlling the laser or microwave source of second partial operating section 711 or first partial operating section 712, respectively. Furthermore, control unit 730 can also be adapted to control readout unit 714 to read out the corresponding results of quantum mechanical calculations after the operations are performed. In particular, readout section 714 can then be adapted to provide signals indicating the measurement results to control unit 730. Thus, control unit 730 can optionally be part of quantum computer 710. For example, control unit 730 can be implemented together with manipulation section 713 as software and / or hardware, for example, as part of a laser or microwave source controller. However, the control unit 730 may also be separated from the manipulation unit 713 and provided in the form of separate software and / or hardware for controlling the quantum computer 710 .

[0094] For example, if control unit 730 is provided as part of quantum computer 710, it is preferred that control unit 730 receive control signals from device 720. Control unit 730 can then generate control signals for controlling manipulation portion 713 based on the control signals received from device 720. For example, control unit 730 can convert the control signals received from device 720 into control signals that can be understood by the specific hardware and / or software of a specific manipulation portion 713 of quantum computer 710. This conversion can be useful in situations where the control signals provided by device 720 are in a different format or follow a different protocol than the control signals used to control manipulation portion 713. However, the control signals provided by device 720 may also already be in the correct format or protocol, making conversion unnecessary. In this case, control unit 730 can be omitted or adapted to simply provide the received control signals to manipulation portion 713 and / or readout portion 714 without conversion.

[0095] In particular, it is preferred that the control unit 730 is configured to provide control signals to the manipulation portion 713 such that the manipulation portion 713 manipulates the second partial manipulation portion 711, thereby manipulating the state of the quantum element based on the operation associated with the second part of the problem. Furthermore, the control unit 730 is preferably configured to provide control signals to the manipulation portion 713 such that the first partial manipulation portion 712 is manipulated such that the coupling of the bosonic field to the quantum element is manipulated based on the operation associated with the first part of the problem. Thus, the control unit 730 is specifically adapted to control the manipulation portion 713 based on the principle of providing operations to different parts of the quantum computer 710 for different parts of the problem.

[0096] Below, an embodiment of an apparatus 720 for optionally providing a control signal to the quantum computer 710 via the control unit 730 will be 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 part and a second part. Preferably, the problem description refers to a quantum mechanical description of the problem, for example, a quantum mechanical description of an electronic structure problem. However, the problem description may refer to any other problem notation that explicitly describes the problem to be solved, in which case the problem providing unit 721 may be adapted to convert the provided problem description into a quantum mechanical description that can be solved on 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, for example, via an input unit into which a user provides input of the problem description. Therefore, in a preferred embodiment, the problem providing unit 721 refers to a user interface that allows a user to define the problem to be solved, so that the problem description can be provided to the trial state determination unit 722.

[0097] Then, the tentative state determination unit 722 is adapted to determine a tentative state representation of the problem description based on a variational method. Preferably, the tentative state determination unit is adapted to determine the tentative state representation using a variational Hamiltonian assumption or a unitary coupled cluster assumption. The tentative state representation generally includes one or more variational parameters, wherein the tentative state representation can be optimized with respect to the variational parameters. In particular, the tentative state representation is determined so that for at least one optimal value of the corresponding one or more variational parameters, the tentative state representation is in an optimal state, that is, at least one observable value of the tentative state representation is in a minimum or maximum state. In addition, the tentative state representation is determined so that at least one observable value referring to the optimized state of the tentative 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 so that the trial state representation also includes a portion that refers to the first part and the second part of the problem, that is, the trial state representation includes a first portion that refers to or can be converted into a fermion-boson interaction or a spin-boson interaction, and a second portion that refers to or can be converted into a non-interacting fermion or a non-interacting spin. Therefore, the trial state representation still includes a problem structure similar to the structure of the original problem. The trial state determination unit 722 then provides the determined trial state representation to the conversion unit 723.

[0098] The conversion unit 723 is typically adapted to convert the trial state representation into an operational trial state description for a specific value of one or more variational parameters. The operational trial state description includes a sequence of quantum operations to be applied to the quantum representation elements 711, 712 of the quantum computer 710 to prepare a representation of the trial state representation (i.e., a trial state) on the quantum computer 710. For example, quantum operations can refer to quantum gates applied to quantum elements forming qubits of the quantum computer 710, and / or to bosonic operations applied to the coupling between a bosonic field and a quantum element or to the bosonic field representation itself. In particular, the operation sequence includes a) a second operation determined based on a second part of the trial state representation and b) a first operation determined based on a first part of the trial state representation. Therefore, also during the conversion of the trial state representation into quantum operations, the principle of splitting the problem into two parts that are processed in different ways is maintained. The conversion unit 723 then provides the operational trial state description including the sequence of quantum operations to the control signal providing unit 724.

[0099] Control signal providing unit 724 is adapted to provide control signals for controlling the application of the determined sequence of quantum operations to quantum computer 710, optionally via control unit 730. For example, control unit 730 may be configured to convert the control signals provided by control signal providing unit 724 into a format interpretable by quantum computer 710 (e.g., by manipulation section 713). However, control signal providing unit 724 may also be adapted to provide control signals in a format that can be used directly with quantum computer 710, in which case control unit 730 may be omitted. The control signals provided by control signal providing unit 724 are typically provided so that the control signals related to the first operation and the control signals related to the second operation are performed by different parts of the quantum computer. For example, if the quantum computer is a well-known quantum computer, the control signals related to the first operation may be performed with respect to a predetermined set of quantum elements forming a qubit, while the control signals related to the second operation may be performed with respect to a different set of quantum elements forming a qubit. However, preferably, the quantum computer is a quantum computer specifically modified to provide the second partial operation section 711 and the first partial operation section 712 as described above. In this case, a control signal relating to the first operation may be provided to the manipulation unit 713 so that the first operation is applied to the first partial operation portion 712 and the second operation is applied to the second partial operation portion 711. This allows the respective states of the tentative state representation to be prepared on hardware dedicated to these respective portions of the tentative state representation, making it possible to achieve easier control and even greater accuracy.

[0100] Optionally, in a preferred embodiment, the apparatus 720 further comprises an iteration control unit 725 adapted to control iterations for optimizing the tentative state representation in order to determine an optimized observable value of the tentative state representation. In particular, the iteration control unit 725 can be adapted to determine the value of the variational parameter in each iteration step. For example, a first predetermined initial variational parameter can be used for the first iteration, and then, for all subsequent iteration steps, the variational parameter can be adjusted according to a known algorithm based on the variational parameter of the previous iteration step and at least one measured observable value. During each iteration step, the iteration control unit 725 can be adapted to control, for example, the conversion unit 723 to convert the tentative state representation for the specific value of the variational parameter for the current iteration step, and further adapted to control the control signal providing unit 724 to again provide control signals that allow the preparation of a tentative state representation for the specific value of the variational parameter for the current iteration step. Furthermore, the iteration control unit 725 can be adapted to control the control signal providing unit 724 to provide a control signal for reading out the corresponding at least one observable value after preparing the trial state representation on the quantum computer, and further adapted to determine whether a corresponding termination criterion with respect to the at least one observable value measured is met, for example, whether the at least one observable value measured has converged, or, for example, whether a predetermined maximum number of iteration steps has been reached. If none of these termination criteria are met, the iteration control unit 725 is adapted to adjust the variational parameters again and start a new iteration step with the newly determined variational parameters. However, if it is determined that the at least one observable value has converged, for example, the difference between the currently measured observable value and the observable value measured in the previous step is below a predetermined convergence criterion, the iteration control unit 725 can be adapted to determine that the observable value measured for the last iteration step refers to the at least one final observable value.

[0101] The iterative control unit 725 can then provide the at least one final observable value to a (also optional) result determination unit 726, which can then be adapted to determine the solution to the problem based on the at least one final observable value. For example, if the problem involves determining the energy of the ground state of the electronic structure system, the at least one observable value can refer to the energy of the trial state representation prepared on the quantum computer, and therefore, the optimized energy can directly refer to the solution to the problem, that is, the energy of the ground state of the electronic structure system. However, the result determination unit can also be adapted to further process the at least one final observable value to determine the solution to the problem, for example, to convert the at least one final observable value back into the form of the corresponding provided problem description, or to use the at least one final observable value in another algorithm to determine the solution to the problem.

[0102] Figure 8A flow chart of a method 800 for determining a control signal for generating a solution to a problem as described above is shown schematically and exemplarily. The method comprises, in a first step 810, providing a problem description indicating the problem to be solved. In particular, as described in more detail above, the problem description comprises a first part and a second part, the first part being convertible into a quantum mechanical description involving fermion-boson interactions or spin-boson interactions, respectively, and the second part being convertible into a quantum mechanical description involving non-interacting fermions or non-interacting spins. In a further step 820, a tentative 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 the trial state representation is determined 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, as already described above, for example, with respect to conversion unit 723, the sequence of quantum operations includes a first operation and a second operation, wherein the first operation is determined based on a portion of the trial state representation involving fermion-boson interactions or spin-boson interactions, and wherein the second operation is determined based on a portion of the trial state representation involving non-interacting fermions or non-interacting spins. In step 840, control signals for controlling the application of the determined sequence of quantum operations are provided to the quantum computer. In particular, these control signals are provided such that the first operation and the second operation are applied to different portions of the quantum computer, preferably to a first partial operation portion and a second partial operation portion, respectively. Then, in step 850, control signals for reading out the quantum computer are provided to the quantum computer to measure at least one observable value of the quantum mechanical state of the prepared trial state representation after applying the determined sequence of quantum operations (i.e., after preparing the trial state representation on the quantum computer).

[0103] In a preferred embodiment, method 800 further includes iterating the tentative state representation to optimize at least one observable value of the tentative state representation, wherein the iteration is performed at Figure 8851. In particular, after measuring at least one observable value in step 850, it can be determined in step 851 whether a predetermined convergence criterion has been met, for example, whether at least one read-out observable value has converged or whether a failure criterion has been met. If this is not the case, method 800 can include determining, in step 851, new values ​​for one or more variational parameters to be used in the next iterative step. Steps 830, 840, and 850 are then performed again with the newly determined specific values ​​for the one or more variational parameters. This iteration 851 is then performed until it is determined after step 850 that the convergence criterion has been met, in particular until it is determined that at least one observable value has converged. In this case, the last at least one measured observable value can be determined as the at least one final observable value. The at least one final observable value can then optionally be used to determine the solution to the problem in step 860.

[0104] In the following, a more detailed example of an embodiment of the invention will be described with respect to a specific problem. In this example, the problem is transformable into a quantum mechanical description comprising fermion-fermion interactions. For example, molecules and solids can be described accordingly. Preferably, for such a problem, the apparatus further comprises a transformation unit adapted to transform the problem description into a problem description that can be represented by a quantum mechanical description comprising bosonic-fermion interactions and non-interacting fermions. As also described below, such coupled fermion-bosonic systems can be simulated more easily (and in some cases even more advantageously if the quantum computing hardware is adapted accordingly) on existing quantum computing architectures. In particular, the number of required quantum gate operations can be reduced from Reduce to where N is a measure of the problem size, for example the number of orbitals or the size of the system. This reduces computational time and computational complexity and potentially allows the simulation of larger systems than are currently expected to be possible on near-term quantum computers. Furthermore, simulating physical fermion-bosonic interactions (such as electron-photon interactions and electron-phonon interactions) is important for understanding phenomena such as UV / Vis spectroscopy or vibrational transitions in molecules and transport phenomena in solids, or for alternatively the engineering design of quantum sensors. In order to solve problems in this context, it is often wise to prepare on a quantum computer the ground state of a fermion-bosonic Hamiltonian of the form:

[0105]

[0106] operator is the fermion creation operator in state i, which adds fermions to this state, and c i The annihilation operator removes the fermion from state i. h ijDescribes non-interacting fermions that move in an external potential, such as from an atomic nucleus or an electromagnetic field, where the external potential can be time-dependent (such as for an oscillating electromagnetic field) or static. ijkl Describes general fermionic interactions, for example, the Coulomb repulsion of electrons. The operator b r is the boson annihilation operator, which removes a boson from the pattern r, and is a creation operator that adds bosonic excitations to mode r. g ij，r Describes the coupling strength between the bosonic mode r and the fermionic states i and j. ω r is the characteristic frequency of the Bosonic mode.

[0107] For the example of superconducting quantum computing hardware, the bosonic modes (i.e., bosonic fields) can be represented, for example, by additional hardware resonators, while the fermionic modes are still represented by existing quantum elements forming qubits, for example in a quantum register as described above. However, in particular, when using such quantum computer hardware in well-known methods to solve the above problem, this leads to two different time scales that must be matched during the calculation, i.e., the simulated time evolution of the qubits and the real physical time evolution of the resonators. In addition, it may be challenging to find a corresponding quantum computer that includes resonators of the frequencies required for a specific problem, because in most cases the frequencies of the resonators are fixed within certain thresholds given by the corresponding hardware setup. These two problems do not exist in standard qubit-only fermion simulations. As described above, the present invention, for example regarding the device, enables these problems to be solved when using a superconducting quantum computer and trying to use bosonic field coupling to solve problems on specific hardware. However, as described above, the present invention also has other advantages.

[0108] In the following, quantum mechanical hardware that is preferably used together with the above-described apparatus for performing quantum mechanical calculations (eg preparing trial state representations) is described in more detail.

[0109] In a first preferred embodiment, the quantum computer used is a superconducting quantum computer. In this case, the bosonic mode (i.e., the bosonic field) can preferably be represented by providing an additional hardware resonator as a bosonic element (e.g., an LC circuit), because, for example, the readout resonator cannot be used for both the readout and the representation of the bosonic mode. Then, preferably, a chip including the superconducting circuit forming the quantum bit is arranged. Additional resonators. In particular, preferably, two to four additional resonators are provided per qubit (i.e., quantum element), and these additional resonators are arranged so that they can be coupled to the corresponding qubit. For example, if the conversion unit is adapted to apply the constrained random phase approximation to the quantum mechanical description of the problem, then one resulting frequency-dependent interaction part can be converted into a quantum operation to be applied to two to four hardware resonators. In another example, in the case where the quantum mechanical description of the problem includes a 4-index interaction term present in the molecular Hamiltonian, it is preferably provided Since such a number of resonators may be difficult to arrange in one chip, the conversion unit is preferably adapted to apply a low-rank decomposition to the quantum mechanical description of the problem in order to reduce the requirements to or A resonator.

[0110] In some hardware implementations, it may be challenging to provide a resonator with the required frequency for a specific problem, since the frequency of the resonator is typically fixed within certain thresholds due to the fixed resonator length and the superconducting energy gap. In particular, if the quantum mechanical description of the problem includes static fermion interactions, the resonator must provide a high frequency. In this case, preferably, the conversion unit of the device is adapted to convert the quantum mechanical problem description into the rotating reference frame of the resonator, for example using a rotating wave approximation. Since this approach still leads to a complex effective time evolution of the hardware components, in another preferred embodiment, the first partial operation part can be adapted to manipulate the coupling and / or bosonic field using an oscillating drive field. However, one advantage of using the above-mentioned variational method to solve the problem is that in most cases these problems can be circumvented or at least their impact is greatly reduced. Therefore, in this method, the use of, for example, an oscillating drive field is optional.

[0111] In the following, about Figure 9 We discuss exemplary sequences of quantum operations that can be used to prepare trial state representations on a quantum computer. Figure 9 The implementation of the phase quantum operations that form part of the exemplary sequence of operations shown can depend on the hardware being used. For example, in a trapped ion quantum computer, the phase quantum operations can directly manipulate the laser light used to manipulate the coupling, while in other hardware implementations, the phase quantum operations can refer to modified standard quantum gates applied to the qubits.

[0112] Typically, it is preferred that the conversion unit is adapted to utilize such a phase operation to convert the first part of the problem, which involves fermion-bosonic interactions or spin-bosonic interactions in the quantum mechanical description, into an operational description. In particular, the phase operation may refer to a specially modified standard quantum gate available on each quantum computer device hardware implementation. In general, although pure fermion-fermion interactions can be represented by standard single-qubit gates and two-qubit gates, the inclusion of bosonic modes results in the quantum operation preferably also implementing a phase depending on the state of the bosonic field (e.g. represented by the electromagnetic field in the resonator). In particular, the phase operation may refer to an additional quantum gate operation followed by a waiting time during which the representation of the qubit (i.e., quantum element) and the bosonic field interact with each other in the real world.

[0113] An example of such phase manipulation is described below with reference to a modification of the known FSWAP algorithm that can be used to implement the effective time evolution of quantum mechanical systems. With respect to bosonic-fermion interactions, the FSWAP gates need to additionally implement the phase shifts due to the bosonic modes. As already described above, this is achieved by introducing a waiting time in the FSWAP gate sequence (i.e., the time that the representation of the bosonic field and the corresponding quantum element are allowed to interact with each other). The unitary matrix of the FSWAP gate is represented as

[0114]

[0115] where b is the boson annihilation operator, and is the bosonic creation operator, g describes the coupling strength between the fermions or quantum elements and the bosonic mode, and t is a parameter describing the gate. Figure 9 An example of a corresponding gate sequence is shown in . The boxes in the top two rows represent gate operations performed on the two corresponding qubits, while the boxes in the third row represent operations performed on the bosonic field or the coupling of a bosonic field to a qubit. In these boxes, the corresponding mathematical operators involved in the operations in the quantum mechanical description of the problem are shown. In this example, the decomposition of the FSWAP gate with a phase shift due to the bosonic mode into a controlled Z (CZ), a SWAP gate, a single-qubit gate, and a gate denoted as U is shown. physBosonic gates. In this case, the bosonic gates taking into account the phase shift can also be regarded as phase operations and involve waiting times for interactions between the quantum bit and the bosonic field. In general, a decomposition as described above, i.e., a sequence of quantum operations, can be provided for each quantum computer hardware implementation accordingly. Measuring (i.e., reading out) the Hamiltonian and other observables of the quantum mechanical system preferably also includes measuring the bosonic field, for example, measuring one or more observables of the electromagnetic field generated by the resonator. Therefore, preferably, the readout part is adapted accordingly. Since the quantum bits and bosonic operators are interchangeable, the readout part can be adapted to measure the observables of the quantum element and the observables of the bosonic field simultaneously or sequentially. In the subsequent processing of the measurement results, standard Hamiltonian averaging can be used for the measurements.

[0116] Preferably, the coupling between the quantum element and the resonator is configured to be digitally switchable and tunable. In particular, the first manipulation section can allow for manipulation of the coupling strength. However, coupling is often subject to physical limitations. For example, for transport qubits, transverse coupling may be stronger than longitudinal coupling, while for flux qubits, transverse and longitudinal coupling may be equally strong. Furthermore, for transport qubits, the coupling energy can be physically limited to approximately 10% of the qubit-level split energy. Preferably, coupling is performed using a coupling energy of approximately 1%.

[0117] When resonators are utilized to represent bosonic fields, two different time scales must be synchronized during quantum mechanical calculations. In particular, the simulated (e.g. Trotterized time evolution of the qubit) and the real (i.e. physical) resonator time evolution must be synchronized. Due to the nature of the variational method of the present invention, utilizing such an approach allows for omitting additional synchronization methods. However, in some cases it may be advantageous to utilize additional synchronization methods. Preferably, the conversion unit is adapted to convert the quantum mechanical description of the problem into quantum operations such that the simulation time is less than or equal to the real time and utilizes a wait operation involving a wait time. During the wait time operation, no further operations are applied and the bosonic field is allowed to interact with the quantum element.

[0118] An advantage of a superconducting quantum computer as described above is that quantum operations, in particular quantum gates, can generally be applied in parallel. This also allows the conversion unit to take this parallelism into account when generating a sequence of quantum operations, for example, by determining a sequence of quantum operations that can be applied simultaneously. Another advantage is that the resonator allows the application of bosonic peak broadening, for example, via an external field or via coupling of the bosonic field with auxiliary quantum bits that can be measured, to increase the broadening. Further, it is also advantageous to directly measure the bosonic field, for example, by measuring the properties of the field generated by each resonator. In particular for the method used by the above-mentioned device according to the present invention, another advantage of the hardware is that the superconducting quantum computer allows the direct measurement of items As quantum mechanical observables. In particular, when solving problems concerning the determination of the ground state or excited states of a quantum mechanical system (e.g., a quantum mechanical many-body system, electrons in atoms or molecules, spins in solids, etc.), this allows for a technically simpler readout of the corresponding observables.

[0119] In another preferred embodiment, the quantum computer used is trapped ion quantum hardware. In particular, in this case, the vibrational modes of the trapped ions can be used to represent bosonic modes, i.e., bosonic fields. In this embodiment, there is no need to provide hardware bosonic elements to represent the bosonic fields. Instead, the first operating portion can be configured so that the existing vibrational modes of the trapped ions can be manipulated to interact (i.e., couple) with the electronic states of the trapped ions that form the quantum bits. Since the bosonic fields are represented by vibrational modes in this case, the number of bosonic modes is naturally limited by the number of ions, thereby generating approximately 3N bosonic fields.

[0120] Typically, it is preferred that the first operational portion allows manipulation of the frequency of the bosonic field in order to provide energy for the corresponding vibrational modes, thereby transferring energy from the vibrational modes of the trapped ions to the electronic modes or vice versa. In the case of a trapped ion quantum computer, manipulation of the frequency of the bosonic 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 trap, by manipulating the frequency of the laser used to manipulate the quantum elements, or by utilizing a rotating reference frame. This allows for very easy manipulation of the coupling and / or the bosonic field itself. In this case as well, the conversion unit can be adapted to additionally convert the quantum mechanical problem description into a rotating reference frame, wherein the choice of the rotating reference frame is more flexible due to the ability to manipulate the vibrational modes using lasers. Furthermore, it is preferred that the conversion unit is adapted to provide an operational description of the problem, which operational description includes quantum operations that tune the laser to resonate with the frequency of the fermionic and / or bosonic modes, thereby suppressing complex time evolution effects. In general, compared to the above-mentioned implementations of superconducting quantum computers, in ion trap implementations, the time scales of the time evolution of the qubit and the time evolution of the bosonic field are the same, because both are implemented through the same trapped ion quantum mechanical system.

[0121] Compared to superconducting hardware, the coupling of bosonic fields to quantum elements can be seen as naturally implemented through the possibility of transferring energy from vibrational modes of trapped ions to electronic states and / or from electronic states to vibrational modes. Therefore, the first operating section is preferably configured to allow such coupling by controlling the coupling via laser pulses.

[0122] In a trapped ion quantum computer, quantum gates can typically only be applied serially. Therefore, preferably, for this embodiment, the conversion unit is adapted to take this into account by providing an operation description such that the corresponding sequence of quantum operations only refers to quantum operations that are applied serially. However, if solutions are found that allow the application of quantum operations in parallel on the trapped ion quantum computer, the conversion unit can also take these new solutions into account.

[0123] In this case as well, the conversion unit can be adapted to also utilize quantum operations that lead to broadening of the bosonic peak. Such quantum operations can refer, for example, to coupling of an external field to the bosonic field or increasing the broadening by utilizing auxiliary qubits that can be measured.

[0124] Preferably, for this case, the conversion unit is adapted to apply a constrained random phase approximation to the quantum mechanical description of the problem, in particular to derive effective electron-electron interactions. For such interactions provided by the problem, the above hardware is particularly useful.

[0125] In another preferred embodiment, instead of implementing the bosonic degrees of freedom as superconducting resonator lines or using vibrational modes in trapped ion hardware, the bosonic degrees of freedom can also be implemented using specifically determined qubit gates on quantum elements. In this case, the first part of the operation section is adapted to represent the bosonic field and the coupling between the bosonic field and the quantum elements representing other quantities of the problem using the overhead of the number of quantum elements forming the qubit. Therefore, in this embodiment, preferably, the manipulation unit provides specific quantum operations for encoding the coupling and the bosonic field in the overhead qubit. In this case, preferably, the manipulation unit defines a cutoff threshold for the number of qubits that can be used to represent the bosonic field, thereby providing a limit on the number of excitations that can be simulated in the bosonic mode. The threshold can be defined by utilizing a phenomenological approach.

[0126] Although in this embodiment, bosonic coupling is also implemented using quantum elements that form qubits, the sequence of quantum operations for a given problem does not necessarily include substantially more quantum operations as in any of the above-described embodiments, because the bosonic fields themselves do not interact, and the time evolution can be applied in parallel to all bosonic fields and to the fermionic quantum elements. Furthermore, the overhead quantum elements preferably have fewer interaction possibilities than those provided by quantum elements dedicated to representing non-interacting fermions. This has the advantage that this embodiment allows for improved controllability at low excitation energy levels of bosonic modes.

[0127] Furthermore, other quantum computer architectures can also be modified to allow for the representation of bosonic fields and to provide a first portion of the operational components that allow for coupling between bosonic fields and quantum elements. For example, ultracold / Rydberg atom quantum hardware architectures can also be utilized and modified according to the principles described above.

[0128] Below, an example of a problem-solving method according to the present invention will be described using a superconducting quantum computer with an additional digitally switchable resonator for representing a bosonic field. This resonator offers greater flexibility and is easier to implement in the quantum computer's hardware. However, the general principles described can also be applied to any of the other quantum computer implementations described above. For example, the following functions can be performed by respective units of the device to provide corresponding control signals associated with quantum operations for solving a problem on the quantum computer.

[0129] The main principle of the present invention for solving problems such as the above is to use variational methods when using superconducting quantum computers. In particular, these methods allow a good approximation of the ground state of a coupled fermion-bosonic system to be prepared on a quantum computer. Compared to the direct simulation of the unitary time evolution of a fermionic system with the help of a bosonic resonator via the following formula, these methods are generally more limited in their application to specific problems.

[0130] U=exp(-iH 费米子-玻色子 t)

[0131] But these methods also place less stringent demands on quantum mechanical hardware; for example, the two different time scales mentioned above do not necessarily need to match.

[0132] The advantage of using a variational approach is that the preparation of the trial state representation only has to be performed on a quantum computer according to a set of variational parameters, without having to prepare a full-time analytical simulation of the problem. Preferably, the trial state determination unit is adapted to determine the trial state representation using a variational Hamiltonian assumption (VHA). In this case, the preparation (i.e., the application of a sequence of quantum operations) involves applying a partial time evolution of the original problem to the initial state. However, the trial state representation preparation does not need to have any connection to the physical time evolution. Thus, the problem of a full physical time evolution as described above can be circumvented.

[0133] In general, in this example, the purpose of using variational methods (such as those described above with respect to the apparatus, particularly for fermion-bosonic quantum mechanical descriptions) is to prepare a set of related 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 state represented by the qubit-resonator states, and minimize the energy over the variational parameters of the trial states. However, in other examples, other hardware elements besides resonators can be used to represent the bosonic degrees of freedom, or even additional qubits, without departing from the corresponding principle of preparing trial state representations on different parts of the quantum computer. Furthermore, in other examples, depending on the corresponding problem, other observables besides the energy of the prepared trial state representations can also be selected for optimization.

[0134] Since in this principle the representation of the prepared trial state is measured at only one point in time, the physical properties of the bosonic field representation (e.g., a resonator) in general do not need to correspond exactly to the properties of the simulated bosonic modes, just as the energy splitting of a qubit does not in general correspond to the field energies of a fermionic model.

[0135] Preferably, when determining the tentative state representation, the tentative state determination unit is adapted to utilize a frequency that facilitates a corresponding implementation of the bosonic field for the bosonic field representation (e.g., a physical resonator). Furthermore, preferably, the variational parameter is selected such that the time evolution of the first part and the second part of the tentative state representation is implemented by different times that can be used as the variational parameter. For example, preferably, the tentative state representation unit selects t 跳跃 , t 相互作用 , t 耦合 , τ 等待 (referring to fermion hopping, fermion interaction, fermion-bosonic coupling and waiting time respectively) as variational parameters. This can lead to the following unitary evolution operator in the quantum mechanical description of the above Hamiltonian example:

[0136]

[0137] Preferably, the control signal providing unit is adapted to provide control signals for controlling the quantum computer to prepare a predetermined initial state representation on a quantum representation element of the quantum computer. The unitary evolution operator U can then be converted into a sequence of operations to prepare a representation of a 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:

[0138]

[0139] Ω r is the physical bosonic frequency (e.g., the physical resonator frequency), |ψ0> 费米子 is the fermionic initial state, (e.g., the Hartree-Fock reference state), and |00000...> 玻色子 is the collective bosonic initial state (which may be the ground state). In some embodiments, the trial state determination unit may be adapted to replace the four-index fermion interaction U with a density-density fermion interaction, for example, by applying a low-rank decomposition. ijkl Examples of such low-rank decompositions can be found, for example, in the following article: “Low rank representations for quantum simulation of electronic structure”, M. Motta et al., npj Quantum Inf 7, 83 (2021). Alternatively, in some examples, e.g. depending on the problem, the trial state representation unit can be adapted to apply the Fermi-Hubbard model in order to reduce complexity. In both cases, Replaced by where n jis the number operator for the fermion state j. This modification can also be applied directly to the quantum mechanical description of the problem (e.g., to the Hamiltonian above), or to the trial state representation (e.g., to the equation above).

[0140] In the above equations, a distinction is made between the simulated time using the small Latin letter t and the simulated time (ie the time elapsed in the laboratory) using τ. 相互作用 , τ 耦合 and τ 跳跃 is the time used to implement the corresponding fermion term on a quantum computer, and τ 等待 Can be used as an additional variational parameter. The simulation time t can be used as a variational parameter. To improve accuracy, the number of layers n can be increased. 层 To use a larger number of variational parameters τ(s) and t(s).

[0141] The above example produces or n k n j 、 and The expectation value of is measured as a trial state representation of the observable. Then, using the chosen bosonic frequency ω r Rather than physical frequency Ω r The expectation value of the Hamiltonian (i.e., the energy of the trial state representation) is reconstructed from the measured expectation value as a cost function of the variational optimization. In this particular example of the variational method, the hardware of the quantum computer used must allow the measurement of the excitation energy levels of the resonator

[0142] Generally following the above principles, instead of problems that can be converted into a quantum mechanical description including fermion-bosonic interactions, problems that can be converted into a quantum mechanical description including spin-bosonic interactions can also be handled, for example, by replacing all the above fermion operators with spin operators (e.g., Pauli matrices).

[0143] In the following, a more detailed example of the method for dealing with the problem as described above will be provided. Figure 7 As described above, the method can be executed by corresponding units of the device.

[0144] For example, as described in more detail above, in a first step of the method, for example performed by a problem providing unit, a corresponding problem is provided, which can be converted into a quantum mechanical description comprising a first part and a second part. Typically, this step is performed on a classical computer. For example, the problem description can refer to the Hamiltonian H discussed above. 费米子-玻色子 In a next step, for example performed by a tentative state determination unit, for example as discussed above, the unitary evolution operator U(t跳跃 , t 相互作用 , t 耦合 , τ 等待 ) thereby generating a tentative state representation to determine a tentative state representation of the problem. In addition, in this step, for example, a tentative state determination unit and / or a conversion unit can be used to determine the initial state representation, in particular the fermion initial state |ψ0> 费米子 Furthermore, in this step, quantities present in the representation of the trial state, in particular in the operator U (such as the coupling strength g ) can also be determined on a classical computer, for example by using a Hartree-Fock calculation. ij，r and the integral h ij and U ijkl ). Furthermore, in a next step, the conversion unit may be adapted to convert U(t 跳跃 , t 相互作用 , t 耦合 , τ 等待 ) is encoded with the fermion operators in to determine the sequence of quantum operations that produces the trial state representation. For this step, the iterative control unit can be adapted to select the variational parameters (e.g., different time parameters t and τ 等待 )'s initial value.

[0145] In the next step, the sequence of operations involving the description of the trial state representation operations is converted into control signals, which are sent to the quantum computer by, for example, a control signal providing unit, so that: first, on the quantum computer, according to |ψ0> 费米子 Initialize the qubit registers (ie, quantum elements) and initialize the bosonic pattern in the initial state representation to, for example, |00000...> 玻色子 Secondly, a control signal based on an operation sequence is provided so that: for example, an entangled fermion-boson trial state representation |ψ is created according to the above trial state representation example by applying a sequence representing the unitary operator U. 试探 >, thereby preparing a trial state representation on a quantum computer. In some embodiments, before preparation, the corresponding trial state representation can be determined using an FSIM network algorithm (which uses low-rank decomposition) or a CZ algorithm.

[0146] The corresponding observable value for which the trial state representation is optimized is then measured. For example, for the above exemplary problem, the energy E of the prepared trial state representation is measured on the quantum computer with respect to the Hamiltonian 试探 |H 费米子-玻色子 |ψ 试探 >. To this end, the readout unit is used to measure, for example (or n k nj ), and The iterative control unit can then be adapted to use the model bosonic frequency ω r Rather than physical frequency Ω r , determine H based on the expected value of the measurement 费米子-玻色子 In general, if the observables (e.g., the energy E) have not converged, the iterative control unit can be adapted to adjust all variational parameters, such as t and τ, on a classical computer. 等待 , in order to optimize the observable value (e.g., minimize the energy), and start the repeated part of the iteration by a sequence of quantum operations to determine the new variational parameters, thereby starting the next iterative step. For example, the new variational parameters can be determined using COBYLA, L-BFGS or CG optimization methods. If the observable value has converged according to a predetermined convergence criterion, the final observable value (e.g., the final energy E) is determined, for example, by a result determination unit and used to determine the solution to the problem, for example, as an element for further post-processing on a classical computer and applied to the corresponding specific molecule, solid, material, etc.

[0147] In general, the above invention (e.g., apparatus and method) can be applied to a variety of problems. Preferred applications are described below. For example, the method can be used to simulate physical fermion-bosonic systems. One example involves the simulation of electronic structure systems, which include both molecular systems and condensed matter systems interacting with bosons. Electron-phonon systems can also be solved, for example, vibrational absorption and emission spectra for calculating Franck-Condon factors, IR spectra, etc., as well as electron-vibration coupling in molecules and polaritons in condensed matter systems. Further, problems in the field of electron-photon systems can be addressed, for example, the interaction of molecules with electromagnetic fields leads to electronic transitions related to UV / Vis spectroscopy (e.g., absorption, emission such as fluorescence and phosphorescence) and photoelectron spectroscopy. In addition, the present invention allows for the treatment of: electron-exciton systems; electron-phonon coupling in metals, semiconductors, thermoelectrics, or superconductors to calculate thermal and electrical transport properties; optionally, light-matter interactions (i.e., electron-photon interactions) in quantum sensors; and electron spin coupling to calculate transport properties in magnetic materials (e.g., the Kondo effect).

[0148] In addition, the method and apparatus can be used to simulate physical spin-bosonic systems related to NMR and ESR, such as nuclear spins or electron spins interacting with photons. With respect to physical fermion-bosonic systems, the present application is not limited to systems where fermions are electrons, but can also be used to simulate other physical fermion-bosonic systems, including systems where fermions are other elementary particles (e.g., muons, neutrinos, quarks) or composite particles (e.g., protons and neutrons), and where bosons are gauge bosons (e.g., photons, W and Z bosons, gluons) or quasiparticles (e.g., magnons, plasmas).

[0149] Furthermore, the method can be used to simulate coupled fermion-boson systems obtained by Hubbard-Stratonovich transformations of purely fermion systems. Coupled fermion-boson systems also arise, for example, when calculating electron screening to provide effective frequency-dependent interactions of electrons that are not part of the active space calculation. For such systems, the constrained random phase approximation (cRPA) can preferably be utilized.

[0150] 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.

[0151] For the processes and methods disclosed herein, the operations performed in the processes and methods may be implemented in a different order. Furthermore, the operations outlined are provided as examples only, and some of the operations may be optional, combined into fewer steps and operations, supplemented with more operations, or expanded into more operations without departing from the essence of the disclosed embodiments.

[0152] 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.

[0153] 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.

[0154] The processes such as providing questions, converting questions, generating control signals, etc. performed by one or several units or devices may be performed by any other number of units or devices. These processes may be implemented as program code means of a computer program and / or dedicated hardware.

[0155] The computer program product may be stored / distributed on a suitable medium, such as an optical storage medium or solid-state medium provided together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

[0156] Any unit described herein may be a processing unit as part of a classical computing system. A processing unit may include a general-purpose processor and may also include a field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or any other specialized circuit. Any memory may be physical system memory, which may be volatile, non-volatile, or some combination of the two. The term "memory" may include any computer-readable storage medium, such as a non-volatile mass storage device. If the computing system is distributed, the processing and / or storage capabilities may also be distributed. The computing system may include multiple structures referred to as "executable components." The term "executable component" is well understood in the computing art to mean a structure that can be software, hardware, or a combination thereof. For example, when implemented in software, one of ordinary skill in the art will understand that the structure of the executable component may include software objects, routines, methods, and the like that can be executed on the computing system. This may include executable components in the computing system stack or on a computer-readable storage medium. The structure of the executable component may be present on a computer-readable medium so that, when interpreted by one or more processors of the computing system (e.g., by a processor thread), it causes the computing system to perform a function. Such a structure can be directly computer-readable by a processor, for example, as in the case where the executable component is binary, or it can be constructed to be interpretable and / or compiled, for example, whether in a single level or multiple levels, thereby generating such binary that can be directly interpreted by a processor. In other cases, the structure can be hard-coded or hard-wired logic gates that are implemented exclusively or almost exclusively in hardware, such as in a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or any other dedicated circuit. Therefore, the term "executable component" is a term for a structure that is well known to those of ordinary skill in the computing arts, whether implemented in software, hardware, or a combination. Any embodiment herein is described with reference to actions performed by one or more processing units of a computing system. If such actions are implemented in software, one or more processors direct the operation of the computing system in response to having executed the computer-executable instructions that constitute the executable component. The computing system may also include a communication channel that allows the computing system to communicate with other computing systems, such as over a network. "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 transmitted or provided to a computing system over a network or another communications connection (e.g., hardwired, wireless, or a combination of hardwired and wireless), the computing system properly views the connection as a transmission medium. Transmission media can include networks and / or data links that can be used to carry desired program code means in the form of computer-executable instructions or data structures and can be accessed by general-purpose computing systems or special-purpose computing systems, 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 interacting with a user. The user interface serves as an input or output mechanism for the user, for example, via a display.

[0157] Those skilled in the art will appreciate that at least part of the present invention can be practiced in a network computing environment with various 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, mobile phones, PDAs, pagers, routers, switches, data centers, wearable devices (such as glasses), etc. The present invention can also be practiced in a distributed system environment, where, for example, a local computing system and a remote computing system that are linked by a network by a hardwired data link, a wireless data link, or a combination of hardwired and wireless data links perform tasks together. In a distributed system environment, program modules can be located in both local and remote memory storage devices.

[0158] Those skilled in the art will also understand that at least part of the present invention can be practiced in a cloud computing environment. A cloud computing environment can be distributed, but this is not required. When a cloud computing environment is distributed, it can be distributed across multiple countries within an organization and / or have components across multiple organizations. In this specification and the appended claims, "cloud computing" is defined as a model for implementing on-demand network access to a shared pool of configurable computing resources (such as networks, servers, storage devices, applications, and services). The definition of "cloud computing" is not limited to any of the other numerous advantages that can be obtained from such a model when deployed. The computing system of the accompanying drawings includes various components or functional blocks that can implement the various embodiments disclosed herein as explained. The various components or functional blocks can be implemented on a local computing system, or can be implemented on a distributed computing system that includes elements residing in the cloud or implementing various aspects of cloud computing. The various components or functional blocks can be implemented as software, hardware, or a combination of software and hardware. The computing system shown in the figure can include more or fewer components than those shown in the figure, and some of these components can be combined as needed.

[0159] Any reference signs in the claims should not be construed as limiting the scope.

Claims

1. A device for determining control signals for generating, using a quantum computer, a solution to a problem that can be converted into a quantum mechanical description, wherein: The device (720) comprises: a problem providing unit (721) for providing a problem description indicating the problem to be solved, wherein the problem description indicates a first part and a second part of the problem, wherein the first part includes mutually interacting quantities describing the problem, and the second part includes mutually non-interacting quantities describing the problem, a tentative state determination unit (722) for determining a tentative state representation of the problem description based on a variational method, wherein the tentative state representation includes one or more variational parameters, and wherein the tentative state representation includes a first part and a second part representing the first part and the second part of the problem, respectively, a conversion unit (723) for converting the trial state representation into an operational trial state description for a particular value of the one or more variational parameters, the operational trial state description comprising a sequence of quantum operations to be applied to quantum representation elements of the quantum computer (710) to prepare a representation of the trial state representation on the quantum computer (710), wherein the sequence of operations comprises a) a second operation determined based on a second portion of the trial state representation, and b) a first operation determined based on a first portion of the trial state representation, and A control signal providing unit (724) is configured to provide control signals for controlling application of the determined sequence of quantum operations on the quantum computer (710) to prepare a representation of the trial state representation; and further for controlling a readout of the quantum computer (710) to measure at least one observable value of a 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 control signals relating to the first operations and control signals relating to the second operations are executed by different parts of the quantum computer (710).

2. The device according to claim 1, wherein The apparatus (720) further comprises an iterative control unit (725) for controlling the 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 value or a quantity derivable from the at least one readout observable value converges, wherein the iteration comprises adjusting the one or more variational parameters of the trial state representation and repeating the transformation, providing a control signal for preparing the trial state, and providing a control signal for the readout until the at least one observable value or derivable quantity has converged to at least one final observable value or final derivable quantity, and wherein the apparatus (720) further comprises a result determination unit (726) for determining a solution to the problem based on the at least one final observable value or final derivable quantity.

3. The device according to claim 2, wherein The at least one measured observable is indicative of an energy of the prepared trial state representation, and wherein convergence of the at least one observable is a minimization of the energy.

4. The device according to any one of the preceding claims, wherein The control signal providing unit (724) is adapted to provide control signals for controlling the quantum computer (710) to prepare a predetermined initial state representation on the quantum computer (710) and then apply the determined sequence of operations to prepare the trial state representation.

5. The device according to claim 4, wherein The initial state refers to the ground state of the mean-field representation of the problem or the Hartre-Fock state of the first part of the problem.

6. A device according to any one of the preceding claims, wherein The conversion of the trial state representation into the representative operational trial state representation for a specific variational parameter is based on the Jordan-Wigner transform or the Bravyi-Kitaev transform.

7. A device according to any one of the preceding claims, wherein The problem providing unit (721) is adapted to provide a problem description which is representable as a quantum mechanical problem description including fermion-fermion interactions, wherein the apparatus (720) further comprises a transformation unit adapted to transform the problem description into a problem description representable by a quantum mechanical description including boson-fermion interactions as a first part of the problem and including non-interacting fermions as a second part of the problem.

8. The device according to claim 7, wherein In order to transform the problem description into one that can be expressed as a quantum mechanical problem description including boson-fermion interactions and non-interacting fermions, the Hubbard Stratonovich transformation is utilized.

9. The device according to any one of claims 7 and 8, wherein The problem description comprises at least parts representable by a quantum mechanical description comprising static fermion-fermion interactions as a third part of the problem, and wherein the transformation unit is adapted to approximate these parts of the problem by utilizing a constrained random phase approximation.

10. The device according to any one of the preceding claims, wherein The variational method is referred to as the variational Hamiltonian anatomy or the unitary coupled cluster anatomy.

11. A system for processing a problem, wherein: The problem comprises a first part and a second part, wherein the first part comprises quantities that interact with each other and the second part comprises quantities that do not interact with each other, wherein the system (700) comprises: The device (720) according to any one of the preceding claims, for providing control signals for controlling a quantum computer, and A quantum computer (710) is adapted to process the provided control signal to perform a quantum mechanical calculation.

12. The system according to claim 11, wherein The quantum computer (710) comprises: a second portion of the operation section (711) configured to utilize quantum mechanical states of the quantum elements to form qubits that are manipulable by operations performed on the quantum elements, wherein the operations are related to a second portion of the problem to be processed during quantum computation of the problem, a first partial operation portion (712) configured to couple bosonic fields to the quantum elements, wherein the coupling of the bosonic fields to the quantum elements is manipulable by operations associated with a first portion of the problem to be processed during quantum computation of the problem, a manipulation portion (713) configured to manipulate a) the second partial manipulation portion (711) so as to manipulate the states of the quantum elements based on a control signal indicating an operation related to the second part of the problem to be processed during quantum computation of the problem, and b) the first partial manipulation portion (712) so as to manipulate the coupling of the bosonic fields with the quantum elements based on a control signal indicating an operation related to the first part of the problem to be processed, thereby performing quantum mechanical computation of the problem, and A readout portion (714) is configured to measure a) the quantum mechanical state of each quantum element representing the state of the corresponding quantum bit and b) at least one observable in the bosonic field after manipulating the quantum elements and bosonic couplings to perform the quantum mechanical calculation.

13. A computer-implemented method for determining control signals for generating a solution to a problem convertible to a quantum mechanical description using a quantum computer, wherein: The method (800) comprises: providing (810) a problem description indicative of the problem to be solved, wherein the problem description indicates a first part and a second part of the problem, wherein the first part includes quantities describing the problem that interact with each other and the second part includes quantities describing the problem that do not interact with each other, determining (820) a tentative state representation of the problem description based on a variational approach, wherein the tentative state representation comprises one or more variational parameters, and wherein the tentative state representation comprises a first portion and a second portion representing a first portion and a second portion of the problem, respectively, converting (830) the trial state representation into a representative operational trial state description for a particular value of the one or more variational parameters, the representative operational trial state description comprising a sequence 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, wherein the sequence of operations comprises a) a second operation determined based on a second portion of the trial state representation, and b) a first operation determined based on a first portion of the trial state representation, and providing (840) control signals for controlling application of the determined sequence of quantum operations on the quantum computer to prepare a representation of the trial state representation, wherein the control signals are provided such that control signals relating to the first operations and control signals relating to the second operations are performed by different parts of the quantum computer, and Control signals are provided (850) for controlling a readout of the quantum computer to measure at least one observable value of a quantum mechanical state represented by the prepared trial state representation after applying the determined sequence of quantum operations.

14. A computer program product for solving quantum mechanics problems, wherein: The computer program product comprises program code means for causing an apparatus (720) according to any one of claims 1 to 10 to perform a method (800) according to claim 13.

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

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