Quantum computers that perform quantum operations

Abstract

The invention relates to a quantum computer (710) that performs an operation based on a control signal that determines a solution to a problem comprising a first and a second part. A fermionic operation unit (711) is configured to utilize a state of the quantum element that can be manipulated by an operation, the operation relating to the second part. A bosonic operation unit (712) is configured to couple a bosonic field to the quantum element, the coupling being manipulable by an operation relating to the first part. A manipulation unit (713) manipulates the fermionic operation unit based on an operation relating to the second part and manipulates the bosonic operation unit based on an operation relating to the first part. A readout unit (714) measures observables of the state of each quantum element that represent the state of each qubit and the bosonic field, the measurement being indicative of a solution to the problem.

Description

[Technical field]

[0001] FIELD OF THEINVENTION The present invention relates to a quantum computer for performing quantum operations and to an apparatus for determining a solution to a problem using a quantum computer. Further, the present invention relates to a system, a method, and a computer program product for solving a problem using a quantum computer, and to the use of a quantum computer. [Background technology]

[0002] 2. Background of the Invention Quantum computers are generally a completely new kind of computational system that exploits the unique behavior of quantum mechanical systems to perform computations on problems that, under appropriate conditions, would be completely impossible to perform in a reasonable time on a normal computer. Moreover, it has already been shown that quantum computers are particularly suited to solving problems that can be related to the quantum mechanical world, i.e. problems that can be transformed into a quantum mechanical description. Such problems relate, for example, to electronic structure problems, molecular problems, condensed matter problems, etc. However, it is known that problems outside the description of physical quantum mechanical systems can also be transformed into a quantum mechanical description, for example encoding and decoding problems, complex analytical problems, optimization problems, etc., can be transformed into a quantum mechanical description that can be processed by a quantum computer. Examples of such problem transformations can generally be found, for example, in the paper "Quantum algorithms: an overview." by Montanaro, A., npj Quantum Inf 2, 15023 (2016). However, quantum computers already existing today often suffer from being inherently susceptible to errors due to relaxation and decoherence, as well as imperfect control of the quantum mechanical system that forms the heart of the quantum computer and readout errors. These difficulties with the accuracy of quantum mechanical calculations are directly related to the number of qubits, i.e. quantum mechanical elements that contain at least two states, used, and the time of the quantum mechanical calculation, as well as the amount of qubit operations performed in the quantum mechanical system. Thus, to date, problems that can be solved with quantum mechanical computers are often limited by the burden of the necessary quantum mechanical calculations. Therefore, it would be extremely advantageous to provide a solution that allows quantum computers to calculate more advanced problems with greater reliability. Summary of the Invention [Means for solving the problem]

[0003] Summary of the Invention The object of the present invention is to provide a quantum computer, an apparatus, a method and a computer program product that can improve the reliability and accuracy of solving problems. Moreover, the present invention allows more complex problems to be solved. Furthermore, the present invention allows a wider variety of problems to be solved by a quantum computer. In particular, problems derived from perturbation theory applied to certain problems, such as problems derived using the restricted random phase approximation (cRPA), that include frequency-dependent dynamic interactions of the quantities in question.

[0004] In a first aspect of the present invention, there is provided a quantum computer that performs quantum operations based on control signals that determine a solution to a problem comprising a first and a second portion in a quantum computer computation, the first portion including quantities that describe the problem interacting with each other and the second portion including quantities that describe the problem without interacting with each other, the quantum computer comprising: i) a fermionic operation portion configured to form qubits that are manipulable by operations performed on the quantum elements utilising quantum mechanical states of the quantum elements, the operations relating to a second portion of the problem to be solved during the quantum computer computation of the problem; and ii) a bosonic operation portion configured to couple a bosonic field to the quantum elements, wherein the coupling of the bosonic field to the quantum elements affects the first portion of the problem to be solved during the quantum computer computation of the problem. a) a bosonic computing unit operable by operations on a first portion of the problem to be solved; and iii) a manipulation unit configured to a) operate the fermionic computing unit such that states of the quantum elements are manipulated based on control signals indicative of operations on a second portion of the problem to be solved during a quantum computer computation of the problem, and b) operate the bosonic computing unit such that couplings of the bosonic fields to the quantum elements are manipulated based on control signals indicative of operations on a first portion of the problem to be solved such that a quantum mechanical computation of the problem is performed; and iv) a readout unit configured to measure at least one observable of a) the quantum mechanical state of each quantum element representing a respective qubit state and b) the bosonic field after manipulating the quantum elements and the bosonic couplings to perform the quantum mechanical computation, wherein a result of the measurement is indicative of a solution to the problem.

[0005] Since quantum computers are configured such that different parts of a problem can be solved by different parts of the quantum computer, the presence of different dedicated parts of the quantum computer results in a more reliable solution, in particular since each interacting part of the problem does not need to be simulated by the same part of the problem as the non-interacting quantities, e.g. since it is not necessary to utilize quantum devices just to perform the calculations of the interacting parts, the calculations use less resources in hardware, i.e. less entanglement operations that require advanced control of the quantum mechanical system.

[0006] Furthermore, the readout unit is configured to measure not only one observable of the quantum mechanical state of each quantum element representing each qubit state, but also the state of the bosonic fields, in particular the representation of the bosonic fields in the quantum computer coupled to each quantum element, thus providing additional information about the interacting quantities of the problem. This allows more degrees of freedom for solving problems on the quantum computer. Furthermore, since bosonic fields are generally easier to implement and offer simpler control concepts in hardware implementation, quantum mechanical calculations are less prone to errors and therefore more reliable. Thus, more advanced problems can be solved with greater accuracy.

[0007] Generally, quantum computer can be realized in any known manner of quantum computer, so the following embodiment describes a preferred manner of realization. For example, quantum computer can be based on superconducting elements, quantum dots, neutral atoms in optical lattices, nitrogen-vacancy centers in diamond, Bose-Einstein condensates, trapped ions, etc. There are multiple different ways of realization, so different parts of quantum computer can be realized in multiple different ways. For example, in superconducting quantum computer, boson field can be represented by electromagnetic resonator, while in trapped ion quantum computer, boson field can be represented as vibration mode of trapped ion. Preferably, quantum computer refers to quantum computer based on quantum gate.

[0008] Quantum computers are generally adapted to perform quantum operations based on control signals that determine the solution to a problem. A quantum operation may refer to an operation that is performed directly or indirectly on elements of a quantum computer that realize a quantum mechanical description of a problem, i.e. that can be described in terms of quantum mechanical laws instead of classical physics. However, while elements of a quantum computer can be used to realize a quantum mechanical description of a problem, i.e. that can be described according to quantum mechanical laws, the elements themselves do not necessarily correspond to quantum mechanical systems, e.g. atoms or ions. For example, in some embodiments, electromagnetic resonators are used to represent bosonic fields in a quantum computer that generally obey the laws of classical physics, but these resonators can also be described as quantum mechanical quantities in the context of a quantum computer. Advantageously, quantum operations include all operations that can directly or indirectly affect quantum elements, i.e. the qubit states of a quantum computer. For example, an operation performed on a representation of a bosonic field will also affect the quantum elements through the coupling of the bosonic field and the quantum elements. Thus, an operation performed on a representation of a bosonic field may also refer to a quantum operation. Quantum operations therefore include direct operations on quantum elements, and thus on qubits, boson fields, and on the coupling of boson fields and quantum elements.

[0009] The control signals on which the operations performed by the quantum computer are based may for example be provided by a user via a user interface. The respective user interface may be a general classical computer adapted to be provided with the respective problem and to generate the respective control signals. An example of a device that can be realized as a classical computer and allowing to generate the respective control signals is described in relation to further embodiments of the invention. However, the control signals may also already be stored in a storage device and provided to the quantum computer only for further execution.

[0010] The problem to be solved by the quantum computer corresponds to a problem comprising a first part and a second part, the first part comprising quantities describing the problem as they interact with each other and the second part comprising quantities describing the problem without interacting with each other. In an embodiment, the first part may only comprise quantities describing the problem as they interact with each other and / or the second part may only comprise quantities describing the problem without interacting with each other. Preferably, the problem can be provided in the form of a quantum mechanical description, in which the first part is represented by boson fields interacting with fermions and thus describing the quantities of the problem as they interact with each other and the second part is preferably described by fermions that do not interact with each other and thus describing the quantities of the problem without interacting with each other. Preferably, the interaction of the quantities describing the problem in the first part refers to a dynamic interaction, i.e. a frequency or time dependent interaction of each interacting quantity, which may be a delayed or a transgressive interaction. Furthermore, the problem may comprise a third part, also comprising quantities describing problems that interact with each other, in particular interacting with each other statically, i.e. with no time or frequency dependence on the interaction between each interacting quantity. The third part of the problem is preferably also processed by a fermion processor of the quantum computer. Thus, in some embodiments, the third part of the problem can be considered to be part of the second part of the problem, which is also processed by a fermion processor of the quantum computer. If the problem is provided in a quantum mechanical description, the third part of the problem may, for example, correspond to statically interacting fermions, e.g., density-density interactions of fermions.

[0011] The fermionic operator is configured to utilize the quantum mechanical state of the quantum element to form a qubit that can be manipulated by an operation performed on the quantum element. In general, the fermionic operator may correspond to any hardware of a quantum computer that allows operations to be performed on the quantum element. For example, the fermionic operator may include elements that can be used to perform operations on the quantum element as well as the quantum element itself. However, the fermionic operator may refer only to hardware parts of a quantum computer that are adapted to perform operations on the quantum element. In this context, the fermionic operator is adapted to be able to perform operations on the quantum element related to a second part of the problem to be solved during the quantum computer computation of the problem. Thus, the fermionic operator can perform operations on quantum elements related to non-interacting quantities of the problem. For example, if the problem is described in a quantum mechanical description, the fermionic operator is preferably adapted to allow operations to be performed on quantum elements related to non-interacting fermions of the quantum mechanical description of the problem.

[0012] In the case where the problem includes a third part corresponding to static interactions of the quantities describing the problem, while the first part of the problem corresponds to dynamic interactions of the quantities describing the problem, the fermionic operator may also be configured to perform operations on quantum devices relating to the third part of the problem.

[0013] The bosonic computing unit is configured to couple the bosonic field to the quantum element. In general, the bosonic field corresponds to an entity that represents a bosonic mode in the quantum mechanical description of the quantum computer system. In some implementations of the quantum computer, the coupling of the bosonic field and the quantum element may correspond to a hardware-induced coupling of the hardware element representing the bosonic field with the quantum element, such as the bosonic element, i.e., the hardware representation of the bosonic field may affect the quantum element. However, in other implementations of the quantum computer, the bosonic field may be represented in a controllable specific state of the quantum element, e.g., a vibrational mode, so that no additional hardware element that directly represents the bosonic field is required. Advantageously, since the bosonic field is non-interacting in the quantum mechanical description, the representation of the bosonic field may also be configured to be non-interacting. For example, the hardware bosonic elements may be configured to be non-interacting, i.e., not to include any connections or couplings with each other.

[0014] The bosonic operation unit may generally correspond to any hardware element that allows the coupling of the bosonic field to the quantum element, e.g. that brings about the coupling of the bosonic field to the quantum element, and that allows the execution of operations on the quantum element and / or optionally on the bosonic element. In this context, it is again noted that the bosonic field itself can be realized by a hardware element, but also as a specific state of one or more elements of the quantum computer, e.g. the quantum element itself. The bosonic operation unit may therefore include a bosonic element adapted to represent the bosonic field during the quantum computer calculation in question, as well as the hardware necessary to couple the bosonic element to the quantum element, as well as the hardware elements that allow the coupling and preferably the manipulation of the bosonic element. However, in other embodiments, the bosonic operation unit may only correspond to the hardware adapted to allow the coupling of the bosonic field to the quantum element, and generally the hardware parts that allow the manipulation of the coupling. For example, if the quantum computer refers to an ion trapping system quantum computer, the bosonic field can be represented by the vibrational modes of the ions that form the quantum element, and the coupling and / or the manipulation of the coupling can be performed by a control laser that can irradiate the trapped ions with laser light having a specific wavelength.

[0015] The coupling of the bosonic fields to the quantum elements can be manipulated by operations on a first part of the problem to be solved during the quantum computer computation of the problem. Thus, in particular the operations concern quantities describing the problem in interacting fashion, in particular quantities describing the problem in dynamic interacting fashion. The interacting quantities of the problem are therefore represented in a quantum mechanical computation system as bosonic fields interacting with the quantum elements. If the problem is provided in a quantum mechanical description corresponding to a fermion-boson system as described above, the interacting quantities can be mapped to the boson-fermion interactions. This kind of representation of the interacting quantities allows the use of hardware elements that are much easier to handle and manipulate than the quantum elements themselves to represent at least some of the quantities of the problem. Thus, the qubit operations that would otherwise have to represent the interaction of the quantities can be replaced by quantum operations performed on the couplings and / or bosonic fields, thus reducing the qubit operations that correspond to performing operations directly on the quantum elements. Since the number of qubit operations performed on the quantum elements is related to the accuracy of the solution of the problem, the use of coupled bosonic fields to solve the problem with interacting quantities allows the accuracy of each result to be improved.

[0016] The manipulation unit is configured to manipulate a) the state of the quantum device and b) the coupling of the bosonic field to the quantum device. In general, the manipulation is based on a control signal indicative of an operation intended to be performed on the quantum device or the coupling of the bosonic field. Preferably, the quantum device is manipulated based on a control signal indicative of an operation on the second part of the problem, and the coupling of the bosonic field is manipulated based on a control signal indicative of an operation on the first part of the problem. The manipulation unit may generally correspond to any hardware configured to manipulate the state of each of the quantum devices or the coupling of the bosonic field based on the control signal. Thus, the manipulation unit can be considered to correspond to a) the software and / or hardware elements utilized to provide the control signal, and b) the interface of the fermionic and bosonic computing units of the quantum computer that realizes the quantum computer calculation. For example, the manipulation unit may correspond to a controller of the fermionic and / or bosonic computing units. If the quantum computer corresponds to an ion trapping device in which the operation on the ions is performed by a laser, the manipulation unit can be realized as a controller of the laser.

[0017] The readout unit is configured to measure at least one observable of the quantum mechanical state of each quantum element representing each qubit state after the quantum mechanical calculation has been performed, and further to measure the bosonic field, i.e. the state of the representation of the bosonic field in the quantum mechanical calculation, e.g. the state of the bosonic element or a specific state of the quantum element representing the bosonic field. In general, the one or more observables measured by the readout unit depend on the respective realization of the quantum computer. For example, if the quantum computer corresponds to an ion trapping device, the observables measured for the quantum elements may correspond to the electronic states of each quantum element, and the observables measured for the bosonic field may correspond to each vibrational mode of the ion in the ion trap. However, also depending on the problem, the energy of each system can be measured as an observable. In general, the measurement result of each observable indicates a solution to the problem. In particular, depending on the transformation of the problem into a quantum mechanical description, the result of the measurement can be used during further calculations or can be converted back from the quantum mechanical solution to a respective "real world" solution of the problem.

[0018] In one embodiment, the quantum computer further includes a control unit configured to provide control signals to control the manipulation unit to a) operate the fermionic operator such that the state of the quantum elements is manipulated based on an operation related to a second part of the problem to be solved during the quantum computer computation of the problem, and b) operate the bosonic operator such that the coupling of the bosonic field to the quantum elements is manipulated based on an operation related to a first part of the problem to be solved so that a quantum mechanical computation of the problem is performed. In general, the control unit can be realized as dedicated hardware and / or software adapted to provide the control signals defined above to the manipulation unit, and the manipulation unit can be considered as functioning as an interface between the control unit providing the dedicated control signals and the fermionic and bosonic operators of the quantum computer. However, the control unit and the manipulation unit can also be realized as the same hardware and / or software combining the functions of the control unit and the manipulation unit. For example, the control unit can be configured to provide control signals to the manipulation unit based on an operation determined for a particular problem to be solved by the quantum computer, and the manipulation unit can then manipulate the fermionic and bosonic operators to perform the operations. Furthermore, since the control unit provides dedicated control signals determined specifically for the second part of the problem and manipulating the state of the quantum elements of the fermionic computing part, and / or further provides dedicated control signals determined for the first part of the problem and manipulating the coupling of the bosonic field and optionally the bosonic field itself, the hardware parts controlled by each control signal can be considered as being part of the fermionic computing part and / or the bosonic computing part accordingly. Thus, by controlling each hardware element of the quantum computer as defined above, it is possible to define which parts of the quantum computer belong to the fermionic computing part and which parts of the quantum computer belong to the bosonic computing part. It is noted that in this context some parts of the quantum computer can also be considered as belonging to both the fermionic computing part and the bosonic computing part.

[0019] In one embodiment, the bosonic coupling of the bosonic field to the quantum element is adapted to be adapted to represent a specific coupling of the first part of the quantity in question during the quantum computer calculation, and the manipulation unit is further adapted to adapt the coupling. In this context, the manipulation of the coupling of the bosonic field to the quantum element is considered to correspond to the general possibility of determining which bosonic field should be coupled to which quantum element by implementing and controlling such coupling, e.g. by using quantum operations, and the possibility of performing operations on the coupling of the bosonic field and optionally the bosonic field itself. The adaptation of the coupling of the bosonic field to the quantum element provides the possibility of adapting the effect of the bosonic field specifically to at least one quantum element coupled to the field, by performing the respective operation or by adapting the hardware settings, e.g. by using a switch before or during the quantum mechanical calculation. The manner in which the effect of the bosonic field on the quantum element is determined is generally based on the respective realization of the quantum computer. For example, in the case of a trapped ion quantum computer in which the bosonic field is represented by the vibrational modes of the ion, the influence on the quantum element represented by the electronic state of the ion can be controlled by controlling the environment of the ion, e.g. by using a laser to transfer energy from the vibrational modes to the electronic state. However, in other implementations of quantum computers, the effect of the boson field on the quantum elements coupled to it can be controlled in other ways.

[0020] In one embodiment, the bosonic computing unit is configured to couple at least one bosonic field to each quantum element forming one quantum bit. In a preferred embodiment, the bosonic computing unit is configured to couple two or more bosonic fields to each quantum element forming one quantum bit, preferably four bosonic fields to each quantum element. It is further preferred that the computing unit is configured to couple a bosonic field to only one quantum element forming one quantum bit. In this way, each quantum element may 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 precisely controlled so that unintended interactions can be avoided. Such control can improve the accuracy of the quantum mechanical calculation results, since unintended interactions lead to inaccurate or erroneous quantum mechanical calculations.

[0021] In the following, preferred alternative embodiments of the quantum computer and each defined part of the quantum computer defined above are described. In a first preferred alternative, the quantum computer refers to a superconducting quantum computer in which the quantum elements are realized as superconducting circuits and the coupling of the bosonic field to the quantum elements is realized by providing an electromagnetic resonator, preferably also based on superconducting technology, coupled to the superconducting circuit via an electromagnetic field. Preferably, in this embodiment, the bosonic operation part includes a resonator as a bosonic element, the electromagnetic field of the resonator representing the bosonic field during the quantum mechanical calculation. In particular, the electromagnetic resonator coupled to the superconducting circuit corresponds to an additional electromagnetic resonator dedicated to representing the bosonic field. In this context, it is to be noted that the electromagnetic resonator used in the superconducting quantum computer to measure the state of the superconducting quantum element, i.e. to read out the quantum bit, is considered to be, for example, part of the readout unit and cannot be used to represent the bosonic field in general. Each readout operation performed on the readout resonator destroys the state of the bosonic field represented by the resonator and the coupling of the bosonic field to the quantum element being read out, so that the result of the readout becomes unreliable. Thus, the electromagnetic resonator which induces a coupling to the superconducting circuit for coupling the quantum device to the bosonic field does not correspond to the electromagnetic resonator used for readout of the superconducting circuit and is therefore an additional electromagnetic resonator. In this embodiment, the bosonic coupling section may include or utilize a microwave source for manipulating the electromagnetic field generated by the resonator and thus for expressing the bosonic field. Furthermore, a microwave source may be used for manipulating the coupling of the electromagnetic field generated by the resonator with the superconducting circuit forming the quantum device.

[0022] In a second alternative preferred embodiment, the quantum computer refers to a trapped ion quantum computer, the quantum element is realized as an ion trapped in an ion trapping device, and the coupling of the bosonic field to the quantum element is realized as the coupling of a vibrational mode of the trapped ion to an electronic state of the trapped ion forming a qubit. In this embodiment, the bosonic computing unit can include or utilize a laser that manipulates the coupling of the electronic state or mode of the ion with the vibrational mode. For example, a laser light having a frequency and amplitude at or near resonance with each wavelength or mode can be used to turn on or off the coupling or to manipulate the strength of the coupling. In particular, the coupling of the electronic mode with the vibrational mode refers to the transfer of energy between these modes. Thus, in the absence of coupling, substantially no energy is transferred between the modes, but in the presence of coupling, the amount of energy transferred determines the strength of the coupling. Preferably, the laser is tunable, in particular the laser can be tuned to the resonance frequency of the quantum mechanical problem description, i.e. the resonance frequency of the trapped ion quantum element. Resonance as utilized in this context preferably refers to the carrier transition resonance, the red sideband resonance, and the blue sideband resonance. The carrier transition resonances correspond to transition frequencies of the trapped ion between electronic states used in quantum computing calculations without initiating energy transfer to or from the vibrational modes of the ion. The red sideband transition resonances correspond to frequencies that allow energy transfer from an electronic state of the ion to a vibrational mode of the ion within the ion trap, or vice versa. The blue sideband transition resonances correspond to frequencies that allow simultaneous excitation of a lower energy electronic state of the ion to a higher energy electronic state and increased excitation of a vibrational mode, or simultaneous transition of a higher energy electronic state of the ion to a lower energy electronic state and decreased excitation of a vibrational mode, thereby allowing both to be manipulated simultaneously.

[0023] In a third alternative preferred embodiment, the quantum computer may refer to any type of quantum computer, where the bosonic coupling is realized by performing additional coupling operations on the quantum elements forming the bosonic field and the qubits representing the coupling of the bosonic field to the quantum elements. In this embodiment, the quantum elements used to represent the bosonic field are preferably coupled to each other so that two-qubit operations can be applied, and at least one of the quantum elements representing each bosonic field is coupled to a quantum element representing a fermion interacting with each bosonic field so as to represent the interacting fermion, i.e., the first part. By using such a coupling configuration, it is possible to reduce the control and operation requirements for the quantum computer hardware, for example, compared to a fully interacting fermion calculation without a bosonic field. Furthermore, it is possible to reduce the depth of the circuitry performing the quantum mechanical calculation of the problem in this configuration, i.e., to reduce the number of quantum operations to be performed for the simulation of the bosonic field, compared to the simulation of the problem with other coupling configurations.

[0024] In a further aspect of the present invention, there is provided an apparatus for providing a control signal for controlling a quantum computer for determining a solution to a problem comprising a first and a second part in a quantum computer calculation preferably using the quantum computer described above, the first part comprising quantities describing the problem interacting with each other and the second part comprising quantities describing the problem without interacting with each other, the apparatus comprising: i) a problem providing unit for providing a problem description indicating a problem to be solved comprising the first and second parts; ii) a problem providing unit for converting the problem description into a) a second plurality of operations to be applied to a fermionic computation portion of the quantum computer, the second plurality of operations being determined based on the second part of the problem, and b) a first plurality of operations to be applied to a bosonic computation portion of the quantum computer, the first plurality of operations being determined based on the first part of the problem. a conversion unit for converting the quantum computer's quantum state representation into a representative operation description indicative of a sequence of operations including a first plurality of operations, the sequence including a first plurality of operations and a second plurality of operations; iii) a control unit for generating control signals for controlling an operation unit of the quantum computer to a) operate the fermionic operation unit such that states of the quantum elements are manipulated based on the second plurality of operations, and b) operate the bosonic operation unit such that couplings of bosonic fields to the quantum elements are manipulated based on the first plurality of operations such that a quantum mechanical calculation of a problem is performed, the control unit being further adapted to provide control signals for controlling a readout unit of the quantum computer to read out one or more observables indicative of a solution to the problem after performance of the quantum mechanical calculation; and optionally iv) a result determination unit for determining a solution to the problem based on the one or more read out observables.

[0025] In general, the apparatus can be realized in the form of software or hardware or a combination of both, where the hardware can correspond to any known dedicated or general-purpose classical computer hardware. For example, the apparatus can be realized as a known computing device such as a PC. However, the apparatus can also be realized as a cloud environment, a computer network, etc., where at least parts of the apparatus can also be realized as a network solution, and thus distributed across multiple computing devices. The apparatus is preferably adapted to use a quantum computer in relation to any of the above-mentioned embodiments to perform quantum computer calculations to determine the solution to the problem. However, the quantum computer is not part of the apparatus itself.

[0026] The problem providing unit is adapted to provide a problem description indicating the problem to be solved comprising a first and a second part. In particular, the problem providing unit may correspond to a storage unit in which the problem description is already stored. However, the problem providing unit may also comprise an input unit, by means of which, for example, a user can indicate the problem description to the problem providing unit. The problem description may correspond to any form of problem description that allows to determine the quantities describing the problem and the form of interaction between these quantities. Preferably, the problem description corresponds to a mathematical description of the problem. However, the problem description may also correspond to any other unambiguous notation form of the problem. In a preferred embodiment, the problem description is a quantum mechanical description of the problem. A quantum mechanical description allows to express a problem in terms of quantities that obey quantum mechanical laws, i.e. to express a problem in the quantum mechanical world.

[0027] The conversion unit is adapted to convert the problem description into a representative operation description. In particular, the conversion unit is adapted to determine the representative operation description from the problem description, so as to include a set of operations to be performed by the quantum computer to perform the quantum computer computation. In particular, the set of operations includes a) a second plurality of operations to be applied to the quantum elements of the fermionic operation part of the quantum computer, and b) a first plurality of operations to be applied to the representation of the coupling of the bosonic field to the quantum elements and optionally the bosonic field itself, provided by the bosonic operation part of the quantum computer. In this way, the problem is divided by dividing the set of operations into different parts of the quantum computer. According to the concept of the quantum computer already described above, the first plurality of operations is determined in particular based on a first part of the problem, and the second plurality of operations is determined based on a second part of the problem. Thus, the fermionic operation part of the quantum computer is used to perform operations on non-interacting quantities of the problem, and the bosonic operation part is used to perform operations on the interacting parts of the problem. If the problem further includes a third part corresponding to quantities that describe the problem while statically interacting, the conversion unit can further be adapted to convert the problem description into a representative operation description including a sequence of operations including a further third operation determined based on the third part of the problem and to be applied to the quantum elements of the fermionic operation portion as well.

[0028] If 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 by mapping the problem description to a Hamiltonian of a quantum mechanical system that defines similar relationships between and influences on the quantities as a problem, to map the problem description to a description of a quantum mechanical system that can generally be simulated by each selected quantum computer. Thus, for example, an optimization problem corresponding to the field of optimizing production parameters such as temperature, pressure, flow rate, etc. for producing a product can be converted to a quantum mechanical description that represents the problem in the quantum mechanical world of a quantum computer. In such a case, for example, an Ising model can be utilized for the conversion. However, if the problem already refers to a quantum mechanical problem, for example an electronic structure problem, this particular step of converting the problem to a quantum mechanical description can be omitted. In general, the conversion unit may be adapted to convert the problem description based on predefined rules or predefined models for a particular problem category, or can be adapted to convert the problem description interactively based on user input. In case of interactive processing, 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 select the respective set of rules or models to be applied to transform the provided problem. However, other interactions may also be performed by the user interface to transform the problem. Furthermore, to transform the provided problem, the transformation unit may also be adapted to access a storage device in which transformations for certain problems, e.g. problems already solved before, with different parameters, etc., are already saved.

[0029] The control unit is configured to generate control signals for controlling the operation of the quantum computer according to the determined sequence of operations. In general, the control unit of the device can be omitted if the quantum computer itself already provides a control unit adapted to control the operation such that the state of the quantum element is operated based on the second plurality of operations and the coupling of the bosonic field is operated based on the first plurality of operations. In this case, the conversion unit only provides the determined sequence of operations to the control unit, which may already be part of the quantum computer, for example in the form of dedicated hardware. However, the control unit can also be adapted to cooperate with the control unit of the quantum computer. For example, the control unit of the device can be adapted to provide control signals in a generally known form, whereas the control unit of the quantum computer can be adapted to convert a common control signal into a dedicated control signal specific to the hardware of the respective quantum computer. The control unit can thus be considered to correspond to an interface between the quantum computer, in particular the hardware of the quantum computer, and the software for solving the respective problem running on a generally known classical computer. Furthermore, the control unit is adapted to control a readout unit of the quantum computer such that one or more observables are measured, i.e. read out, after the execution of the quantum mechanical calculation. In particular, the control unit is adapted to receive the readout content of the readout part and provide the readout content to a result determination unit which may for example be part of the classical computing environment, such that also for the readout content the control unit together with the readout part can act as an interface between the classical electronic computing environment and the quantum computer.

[0030] The result determination unit is adapted to determine a solution to the problem based on the one or more retrieved observables. For example, the result determination unit can be adapted to convert the one or more retrieved observables indicative of a solution to the representative quantum mechanical description of the problem into respective solutions in the problem description, for example using the same conversion manner used to convert the problem description into the representative quantum mechanical description. Additionally or alternatively, the result determination unit can be adapted to perform further calculations or operations based on the one or more retrieved observables to determine the solution to the problem. For example, an averaging process, an error correction process, a further optimization process, etc. can be applied based on the one or more retrieved observables to determine the solution to the problem. In general, the solution to the problem can then be presented to a user via an output, for example a display, or further utilized to directly control the production of a product, for example with the respective optimized production parameters.

[0031] In one embodiment, the problem providing unit is adapted to provide a problem description indicating a problem including a part with quantities that describe the problem while interacting, and the system further includes a conversion unit adapted to convert the interacting parts of the problem description into a problem description including a first and a second part. Depending on the respective problem description, the conversion unit can use mathematical methods and / or approximations or logic functions that make it possible to determine a problem description that allows for example to split the interactions into a first and a second part. For example, the interacting quantities of the problem can be converted into new quantities, some of which interact and others of which do not. Additionally or alternatively, an approximation scheme can be applied to the problem description, approximating at least some of the interacting quantities as non-interacting quantities. In general, the conversion of a purely interacting problem into a problem that can be described in the form of a first and a second part allows an optimal use of the aforementioned hardware of the quantum computer, such that fewer operations have to be performed on the quantum elements of the quantum computer itself. This leads to a simplification of the technical aspects as well as an increase in accuracy, compared to trying to solve the problem directly by simulating the interacting quantities without the conversion.

[0032] In a preferred embodiment, the problem description is expressible by a quantum mechanical description including fermion-fermion interactions, and the conversion unit is adapted to convert the problem description into a problem description expressible by a quantum mechanical description including boson-fermion interactions as a first part of the problem and non-interacting fermions as a second part of the problem. Furthermore, a representation of non-interacting boson fields can also be considered as part of the first part of the problem. In general, the conversion is preferably adapted to convert the fermion-fermion interactions of the quantum mechanical description of the problem into a fermion-boson interaction that defines a link between the fermion-fermion interactions, the resonance frequency of the boson field, and the coupling strength of the fermion-boson field. Optionally, the converted quantum mechanical description may further include statically interacting fermions as a third part. For example, the problem description can be provided directly as a quantum mechanical description of a fermion-fermion interaction problem, or the problem description can be generally expressed by a quantum mechanical description of a fermion-fermion interaction problem. It is preferred that the conversion unit is adapted to convert the problem description into a quantum mechanical description before the conversion unit converts the problem, so that the conversion unit is adapted to utilize the respective quantum mechanical laws and algorithms in the conversion of the problem. However, the conversion unit may also be adapted to convert the problem description into any other form or notation that clearly describes the problem, in which case each conversion utilized may be based on rules inferred from the quantum mechanical conversion into the quantum mechanical description of the problem. In a preferred embodiment, the conversion unit is adapted to convert the problem description into a corresponding quantum mechanical description including fermion-fermion interactions by utilizing the Hubbard-Stratonovich transformation. However, other known conversion algorithms may also be utilized.

[0033] In one embodiment, the problem description comprises at least a number of parts that can be represented by a quantum mechanical description including static fermion-fermion interactions as a third part, and the conversion unit is adapted to approximate these parts of the problem by applying the restricted random phase approximation (cRPA) to the quantum mechanical description of the problem. This allows to reduce the number of fermion states to be simulated during the quantum mechanical calculation of the problem, and therefore the number of operations and the number of quantum elements used in the calculation. Thus, more complex and larger problems, i.e. problems represented by a larger number of fermion states, can be calculated on a quantum computer. In general, cRPA allows to distinguish between fermions that play an active role in solving the problem and fermions that are considered to be a general background for the fermions that play an active role. For example, when simulating a reaction between different molecules, it can be considered that only the electrons present in the outer orbitals, i.e. valence orbitals, play an active role in solving the problem, whereas the electrons present in the inner orbitals of the atoms merely provide a background for the electrons present in the outer orbitals. Another example is transition metal oxide materials, where only narrow d states close to the Fermi energy play an active role in the calculation, while other electronic states are considered as an effective screening background by cRPA. By applying the constrained random phase approximation, background fermions rather than individuals in this situation can be described as charge clouds interacting with the active fermions, providing a screening effect for the active fermions in particular.

[0034] In one embodiment, the problem description refers to a quantum mechanical description, and the transformation unit is adapted to transform the quantum mechanical description of the problem into a rotating reference frame, in particular by applying a rotating wave approximation, before the transformation into the representative computation description. Advantageously, the transformation unit is adapted to further apply a rotating wave approximation to the quantum mechanical description in the rotating reference frame. By utilizing a rotating reference frame and a rotating wave approximation to the quantum mechanical description, different time scales resulting from different parts of the hardware acting on these different time scales can be simplified. For example, a fermionic computation unit can act on a different time scale than a bosonic computation unit, depending on the actual realization of the quantum computer. The rotating reference frame and the rotating wave approximation allow these different time scales to be more easily synchronized during the quantum mechanical computation of the problem.

[0035] In one embodiment, the problem description refers to a quantum mechanical description, and the transformation unit is adapted to apply a low-rank decomposition to the quantum mechanical description of the problem before transformation to the representative quantum description. Applying a low-rank decomposition to the quantum mechanical description can reduce the number of required representations of the bosonic fields, making the problem easier to control and enabling more efficient quantum mechanical computations.

[0036] In one embodiment, the problem description includes at least a number of parts expressible by a quantum mechanical description including interacting clusters with static local fermionic interactions embedded in static nonlocal long-range interactions reaching outside the clusters as a third part of the problem, and the transformation unit is adapted to approximate the nonlocal long-range parts of the problem by utilizing the Hubbard-Stratonovich transformation. In general, the nonlocal long-range interactions can be determined based on a predefined range parameter that distinguishes nonlocal interactions from local interactions. However, each part of the problem can also be pre-determined, for example by a user defining which interactions correspond to nonlocal interactions and which interactions correspond to local interactions. Furthermore, it can be defined that all interactions outside the interacting clusters are referred to as long-range interactions, such that the definition of the cluster also directly defines which interactions are long-range interactions. More preferably, the parts of the problem resulting from the Hubbard-Stratonovich transformation, in particular the resulting propagator terms, are calculated using a quantum computer, and each calculation result is then used in a Dynamical Mean Field Theory (DMFT) self-consistent loop, i.e. an iterative process for calculating a solution to the complete problem.

[0037] In one embodiment, the conversion unit is adapted to convert the problem description into a representative operation description that includes operations to widen the Boson peak by including in the sequence of operations an operation that utilizes an additional external electromagnetic field configured to manipulate the coupling of the Boson field to the ancilla qubits and / or quantum elements. In general, the interaction of the Boson field with the fermions is frequency dependent, and the frequency dependence includes a frequency range where the interaction is strong and a frequency range where the interaction is weak. The frequency range where the interaction is strong forms a peak in the frequency dependence diagram, and is referred to herein as the Boson peak. Each peak has a certain width, i.e. a quality factor, determined by the respective formulation of the quantum mechanical description of the problem, and the representation in the quantum computer depends, for example, on the configuration and type of the quantum computer. However, the width of the Boson peak, and therefore the quality factor, can be manipulated, in particular widened, for example by utilizing an additional external electromagnetic field configured to manipulate the coupling of the Boson field to the ancilla qubits and / or quantum elements. Extending the Boson peak has the advantage that it is technically easier to configure a quantum computer so that each frequency dependency can be realized by the quantum computer, and for example, if the frequency range of interaction, i.e., the Boson peak, is wide, the technical requirements for the resonator can be reduced. In this way, by realizing the extension of the Boson peak, the technical requirements for the hardware of a quantum computer for the calculation of a specific problem can be reduced, and therefore more different problems can be calculated by a specific quantum computer.

[0038] In a further aspect of the present invention, there is provided a system for determining a solution to a problem by quantum computer computation, the system comprising: i) a quantum computer as described above; and ii) an apparatus as described above, the apparatus further comprising a result determination unit configured to determine a solution to the problem based on one or more retrieved observables.

[0039] In a further aspect of the invention, there is provided a method for providing control signals for controlling a quantum computer to determine a solution to a problem comprising a first and a second portion by quantum computer computation, the first portion comprising quantities describing the problem interacting with each other and the second portion comprising quantities describing the problem without interacting with each other, the method comprising the steps of i) providing a problem description indicating the problem to be solved comprising the first and second portions, ii) converting the problem description into a) a second plurality of operations to be applied to a fermionic computation portion of the quantum computer, the second plurality of operations being determined based on the second portion of the problem, and b) a first plurality of operations to be applied to a bosonic computation portion of the quantum computer, the first plurality of operations being determined based on the first portion of the problem. a first plurality of operations determined based on the first plurality of operations; iii) generating control signals for controlling an operating portion of the quantum computer to operate a) the fermionic operating portion such that the states of the quantum devices are manipulated based on the second plurality of operations, and b) the bosonic operating portion such that the couplings of the bosonic fields to the quantum devices are manipulated based on the first plurality of operations such that a quantum mechanical calculation of a problem is performed; iv) providing control signals for controlling a readout portion of the quantum computer to read out one or more observables indicative of a solution to the problem after performance of the quantum mechanical calculation; and optionally v) determining a solution to the problem based on the one or more read out observables.

[0040] In a further aspect of the present invention there is provided a computer program product for providing control signals for controlling a quantum computer to determine a solution to a problem, the computer program product including program code means for causing an apparatus as described above to perform the method as described above.

[0041] In a further aspect of the invention, there is provided the use of the quantum computer, the device, the system, the method and the computer program product as described above for solving problems related to electronic structure problems. Electronic structure problems may be particularly intended for molecular problems and condensed system problems. Preferably, molecular problems include problems related to at least one of organometallic compounds containing transition metals, including lanthanides and actinides, chelators interacting with metals, catalysts, biomolecules with active centers, polymeric systems and transition metal compounds embedded in solution or in the environment. Preferably, condensed system problems include problems corresponding to at least one of transition metal oxides and rare earth elements, such as perovskites used in solid oxide fuel cells, oxide-based battery cathodes, hard magnets for electric engines, catalysts for fuel cells, transition metal heterostructures for sensors, magnetic semiconductor sandwich structures for spintronics and high temperature superconductors.

[0042] It will be understood that the above mentioned devices, the above mentioned systems and the above mentioned computer program products have similar and / or identical preferred embodiments, in particular as defined in the dependent claims.

[0043] It will be understood that a preferred embodiment of the invention can also be any combination of the dependent claims or the above-mentioned embodiments with the respective independent claim.

[0044] 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]

[0045] [Figure 1] 1 illustrates a qubit state representation used in a quantum computing device. [Diagram 2] 1 shows a schematic example of a quantum computing device that uses quantum bits as a computing unit. [Diagram 3] 1 shows a schematic example of a method for generating control signals to perform an operation on a quantum computing device and processing measurement signals from the quantum computing device. [Figure 4]1 shows a schematic example of a hybrid system including classical and quantum computing devices. [Diagram 5] 1 shows a schematic example of a quantum computing device based on a superconductor. [Figure 6] 1 shows a schematic example of a trapped ion based quantum computing device. [Figure 7] 1 illustrates, in a schematic and exemplary manner, one embodiment of a system for determining a solution to a problem. [Figure 8] 1 shows, by way of example only, a flow diagram of a method for determining a solution to a problem. [Figure 9] 1 shows, in a schematic and illustrative manner, an example of a sequence of operations that can be applied to perform a quantum mechanical calculation. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0046] Detailed Description of the Drawings In the following, we will first briefly introduce the general basic principles of quantum computers and their computational performance. Furthermore, the general principles are also described in “Quantum Computation and Quantum Information: th Anniversary Edition”, MA Nielsen and ILChuang (2010).

[0047] A classical computing device uses a transistor-based processor. Each transistor has two controllable states, 1 or 0, which represent digital binary or bits. To execute operations on a classical computing device, human-readable program code is converted into machine-readable instructions through a compiler. The machine-readable instructions are control signals for each transistor, such as voltage settings. Representations of machine-readable instructions include binary or hexadecimal representations. Based on these machine-readable instructions, operations are executed by the processor of the classical computing device.

[0048] Quantum computing is a relatively new method of computing that uses quantum effects such as superposition and entanglement to perform certain calculations more efficiently than classical digital computers. In contrast to digital computers, which as discussed above represent information in the form of bits (e.g., "1" or "0"), quantum computing devices, or quantum computers, use qbits, or quantum bits, to represent information. Quantum computing devices are based on quantum elements that obey the physical laws of quantum mechanics, such as superconductors, ions, atoms, quantum dots, photons, particle spins, bosons, etc. These quantum elements can be manipulated in a controlled manner to perform operations.

[0049] Qubits and their operations can be described in terms of their mathematical properties, and each such qubit may be implemented in any of a variety of different ways into a physical quantum element, examples of which include superconducting materials, trapped ions, photons, optical cavities, individual electrons trapped in quantum dots, point defects in solids (e.g., phosphorus donors in silicon or nitrogen-vacancy centers in diamond), molecules (e.g., alanine, vanadium complexes), or any medium that exhibits qubit behavior, including quantum states and transitions between them that can be induced or detected in a controllable manner.

[0050] In general, for any given physical quantum element that implements a qubit, any of a variety of properties of that physical unit may be selected to implement the qubit. For example, if an electron is selected to implement a qubit, then the x, y or z components of the electron spin degree of freedom may be selected as the electron's property to represent the qubit state. For any particular degree of freedom, the physical quantum element may be controllably placed into a superposition or entanglement state, and measurements may then be made at the selected degree of freedom to read out the qubit value.

[0051] In contrast to the transistors of a classical computing device, each quantum element of a quantum computing device can be in not only a basis state |1〉 or |0〉, but also a superposition of basis states, e.g., the state |X〉 below. The state of each quantum element is represented by a quantum bit, or q-bit state, as shown in a simplified two-dimensional diagram in Figure 1. To represent such states, Dirac notation is commonly used in quantum mechanics. In Dirac notation, states in an n-dimensional complex vector space, such as Hilbert space, are represented by bracket notation, e.g., |X〉. In conventional terminology, a superposition of the states "0" and "1" in a quantum computing device can be represented by the following equation: α|0〉+β|1〉. The states "0" and "1", or bits, of a classical computing device are respectively analogous to the basis states |1〉 and |0〉, or qubits, of a quantum computing device. The value |α| 2 represents the probability that the qubit is measured in the |0〉 state, whereas |β| 2 represents the probability that a qubit is measured in the |1〉 state. When more than one qubit is present, 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, and furthermore, in the entangled state, each qubit cannot be identified as an individual qubit. In general, a register of N qubits in a quantum computer can be in a superposition of multiple basis states at once, whereas a register of N classical bits can only be in one basis state at a time. Thus, in contrast to classical computing devices, a quantum computer can have two N The ability to simultaneously manipulate and process basis states allows for essentially exponential parallel processing.

[0052] A computational method for solving a given problem can be converted into qubit operations to perform the operations on the quantum computing device, which may be converted into control signals that manipulate the qubits. The representation of the machine-readable instructions may include a general quantum mechanical representation of the operations in Hilbert space. Depending on the specific realization of the quantum computer, different representations of the qubit states may be selected. Setting any state in the quantum computing device can be represented by operations that act on the qubit states. The operations can be converted into control signals that control parts of the quantum computer, which signals depend on the type of quantum computing device used. In this way, operations can be performed on a quantum equivalent of a classical processor as part of the quantum computing device, based on the operations that act on the qubit states.

[0053] Operations acting on qubit states are typically single or multi-qubit operations. A single qubit operation can change the state of one qubit into a particular superposition, e.g. corresponding to the rotation of the vector |X〉 as shown in Figure 1. For example, in a superconducting quantum computer this can be achieved by a microwave pulse, or in a trapped ion quantum computer by irradiating the ions with a laser beam. A multi-qubit operation can create entanglement between two or more qubits. For example, in a superconducting quantum computer this can be achieved by connecting the qubits through an intermediate electrical coupling circuit, or in a trapped ion quantum computer by controlling the collective oscillations of the trapped ions.

[0054] In general, to prepare an operation to solve a given problem, each quantum mechanical representation of the problem is converted into a qubit operation, which is executed to prepare the given solution. After preparing the given solution, i.e., after applying the operation to the qubits of the quantum computer, projective measurements of the individual qubits are performed to return either a 0 or a 1 for each qubit. This measurement is achieved in a quantum computing device by applying a hardware-specific readout protocol of a sequence of readout operations including control pulses and monitoring the response to the control pulses. For example, a superconducting qubit may be coupled to a hardware resonator. The measured shift in the resonator frequency depends on the coupled qubit state, and therefore the qubit state can be determined. For example, in the case of a trapped ion, an optical readout can be used, e.g. if the ion emits light, the qubit state is 1, if it does not emit light, the qubit state is 0, or vice versa. In this way, qubits can be used to implement logic circuits and gates in a similar manner to classical computing devices.

[0055] A schematic example of a quantum computer is shown in Fig. 2. The quantum computer calculation device 100 shown in Fig. 2 includes a quantum register 104 configured to perform a quantum computer calculation, an operation unit 106 configured to operate the quantum register, in particular the quantum elements forming the qubits, and a readout unit 108 configured to collect a measurement signal from the quantum register 104 to read out the qubits after a quantum mechanical calculation. The operation unit 106 provides, in particular, an operation signal to operate the quantum register, and the operation signal is generated based on a received control signal determined based on each operation to be performed on the qubits. In an embodiment, a feedback loop can be provided between the operation unit 106 and the measurement unit 108.

[0056] In contrast to classical computation, in which a single measurement cycle yields the state of a transistor, quantum computation involves performing multiple measurement cycles to obtain probability densities or probabilities of qubit states.

[0057] The quantum register 104 may be based on different quantum elements that represent quantum bits. In some embodiments, the quantum bits may be implemented as quantum elements by photons. Such an optical quantum computing device may include a laser that generates photons that are sent into a waveguide. A beam splitter may be provided to manipulate the photon state based on a manipulation signal, such as a mechanical rotation applied to a mirror. The measurement unit 108 may be a photon detector in such an embodiment, and the measurement signal may be a photon.

[0058] In other embodiments, the qubits can be implemented by electronic states of ions trapped in a magnetic field. The manipulation unit 106 can in such a case utilize a laser, and the manipulation signal can provide a control laser pulse. Furthermore, in this case the readout unit 108 can be a photon detector combined with a readout laser pulse, and the measurement signal 102 can be a photon. Other qubit implementations can be based on superconductors as quantum elements, semiconductor materials with helium as quantum elements, etc.

[0059] 3 is a schematic illustrating an exemplary method for generating control signals for performing operations on a quantum computing device and for processing measurement signals from a quantum computing device. In most embodiments of quantum computing devices known today, the control signals for the quantum computing device are provided by a classical computing device, and the measurement signals provided by the quantum computing device are further processed by the classical computing device. However, other embodiments are possible as quantum computing devices mature.

[0060] In order to generate control signals to perform operations on the quantum computing device, a problem to be solved with the aid of the quantum computing device is provided in step S10, preferably in a mathematical description. Such a problem may, for example, include determining material properties based on a mathematical description of the electronic structure of a material. Other problems may include optimization problems and associated objective functions. Based on the problem to be solved, an operational description of the problem or subproblem may be generated in step S12, the operational description including operations to be applied to the qubits of the quantum computer to solve the problem with quantum mechanical calculations. Furthermore, the operational description may include reference states that allow generating a representation of an initial qubit state on the quantum computer, and then further operations are applied on the quantum computer by manipulating the qubit states. Based on the operational description, control signals for controlling the quantum computer can be generated in step S14, for example by providing control signals to an operation unit, which can then operate the qubits based on the control signals. In step S16, the operation unit then applies the operation operations to individual or multiple qubits of the quantum computer, which perform quantum mechanical calculations based on the operation operations. After the operations, a measurement signal can 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 states after applying the manipulation operation to the initial qubit states. The measurement signals are then converted to measurands in a classical computer in step S20 and, in the case of subproblems, fed back to the problem to be solved. Finally, the results of the computation of the problem, including quantum mechanical computations, may be provided to the classical computing device in step S22.

[0061] FIG. 4 shows a schematic example of a hybrid system including a classical computing device and a quantum computing device. As described with respect to the method shown in FIG. 3, a quantum computing device is often used in conjunction with a classical computing device. As shown in FIG. 4, the problem preparation system can be realized as a classical computing device 110, for example, performing steps S10, S12, S20, S22 of the method shown in FIG. 3. A control unit can then be provided as an interface between the classical computing device 110 and the quantum computer 100, and the control unit can also be a classical computing device, for example, performing step S14. The control unit can then be communicatively coupled to an operation unit 106, which can control a manipulator of the quantum computing device. The operation unit 106 can also be realized as classical control hardware that controls certain hardware elements of the classical computing device, for example the quantum computer, that perform the operation of the qubits. However, the operation unit 106 is generally considered to be part of the quantum computer, since it directly affects the quantum register. The quantum computing device 100 is adapted to perform the quantum operation S16, in particular by the operation of the qubits of the quantum register. The measurement unit 108, which is also generally considered to be part of the quantum computing device, can then perform step S18 by utilizing classical hardware. The measurement unit 108 may then be communicatively coupled to a configuration system 110 for further processing of the measurement signal.

[0062] FIG. 5 shows a schematic example of a quantum computing device based on superconductors. A superconducting quantum computing device is one of the solid-state quantum computing technologies. Here, the quantum register 104 may include superconducting circuits 520, 522, 524 based on Josephson junctions. The qubits may then correspond to charge, flux, transmon, or phase qubits, for example, depending on the amount of superconducting circuits selected to represent the qubits. FIG. 5 is a simplified diagram of a superconducting quantum computer utilizing charge qubits. For charge qubits, the different states of the qubits are represented by an integer number of Cooper pairs in the superconducting islands. Quantum operations can then be performed by manipulating the qubits via microwave pulses. Resonators 512, 514, 516 can be used to manipulate the qubit states by applying microwaves or read out the qubit states by measuring the respective microwaves, and typically different resonators are used to manipulate the qubit states and read out the qubits. Additionally, resonator 518 can be used to apply microwaves that entangle the qubits. However, entanglement can also be achieved by inductive or capacitive coupling of a superconducting circuit rather than by a resonator 518, or by providing another qubit, here a superconducting circuit, between the qubits to be entangled.

[0063] Such systems are maintained at extremely low temperatures, for example, tens of mK, at the computational level. Extreme cooling of the system helps to keep the superconducting material below its critical temperature and avoid unwanted state transitions. To maintain such low temperatures, quantum information processing systems may be operated in cryostats, such as dilution refrigerators. In some implementations, control signals are generated in a hotter environment and transmitted to the quantum computer using covered impedance-controlled GHz-compatible transmission lines, such as coaxial cables. In some implementations, superconducting qubit state measurements are realized using a distributed detection scheme. To read out or detect the state of any qubit, a probing signal, for example a traveling microwave, can be excited along a readout transmission line coupled to the qubit via each readout resonator. The frequency of the probing signal may be in the vicinity of the resonant frequency of the readout resonator. Depending on the internal quantum mechanical state of the qubit, the reflectivity of the readout resonator coupled to the qubit changes, so that the intensity or phase of the probing signal transmitted along the readout transmission line may change. This allows for qubit state detection, where during readout of the qubit state, the qubit state collapses, i.e., is projected into one of the basis states, with each probability. Each probability can be determined by performing multiple quantum mechanical calculations and readouts. Further details of superconducting quantum devices are described in, for example, European Patent Application Publication Nos. 3830867A1, 3449427A1, US Patent Application Publication No. 2020272925A1, Chinese Patent Application Publication No. 212061223U, and US Patent Application Publication No. 2019019099A1.

[0064] A schematic example of a quantum computing device based on ions in an ion trap is shown in Figure 6. Similar to neutral atom traps, ion traps using, for example, positively charged calcium ions can also be used to implement quantum computing devices. Here, ions 626 are trapped in an oscillating electromagnetic field 624 in a high or ultra-high vacuum. The ions 626 are laser cooled and held in the oscillating electric field 624. Laser light 628 of different frequencies may be used for qubit operations such as superposition or entanglement.

[0065] In general, gate model type computations can be performed on quantum computer hardware architectures based on the above quantum computer implementation methods. Gate model type computations are based on quantum gates. In contrast to classical gates, there are an infinite number of one-qubit quantum gates that can transform the state vector of a qubit. Changing the state of a qubit state vector is typically referred to as a one-qubit rotation, also referred to herein as a state change or one-qubit quantum gate operation. A rotation, state change, or one-qubit quantum gate operation can be mathematically expressed as a unitary 2×2 matrix with complex elements. A rotation corresponds to a rotation of a qubit state in a Hilbert space, which can be conceptualized as a rotation of a vector on the Bloch sphere, commonly known as a geometric representation of the space of pure states of qubits. A multi-qubit gate changes the quantum state of a collection of qubits. For example, a two-qubit gate rotates two qubit states as a rotation in the four-dimensional Hilbert space of two qubits, and as commonly known, a Hilbert space is an abstract vector space with a structure of an inner product with measurable length and angle. Furthermore, Hilbert spaces are complete, meaning that there are limits in the space that allow the use of calculus techniques.

[0066] Hereinafter, the term operation description refers to a representation of a problem that includes a sequence of quantum operations to be applied during a quantum mechanical computation of the problem. The term "quantum operations" may include all types of quantum gates mentioned above in the context of the present invention. Furthermore, the term may also include operations performed on elements of a quantum computer that represent couplings of quantum elements and bosonic fields forming qubits, and optionally also elements that represent the bosonic fields themselves. These operations refer to any kind of change in the state of the couplings or bosonic fields that represent the elements, for example switching a coupling on / off, or changing the frequency of the field. Furthermore, in some applications quantum operations may also include measurement operations. This allows the implementation of algorithms using measurement feedback. For example, in such algorithms the quantum computer may execute a quantum gate defined by a sequence of quantum operations and then measure only a subset, i.e. not all, of the other computational elements, such as qubits or bosonic field states in the quantum computer, and then decide which further quantum operations to perform next based on the results of one or more measurements. In particular, measurement feedback is useful for performing quantum error correction, but is not limited to its use in performing quantum error correction.

[0067] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Below, embodiments of the present invention are described, emphasizing differences from the commonly known quantum computing devices described above.

[0068] 7 shows a schematic and exemplary embodiment of a system 700 for determining a solution to a problem, e.g. an electronic structure problem, in a quantum computer calculation. The system is specifically adapted for solving a problem comprising a first and a second part, the first part comprising quantities that describe the problem interacting with each other and the second part comprising quantities that describe the problem without interacting with each other. Preferably, the problem can be represented by a quantum mechanical description comprising as a first part a fermion-boson interaction and optionally bosonic fields that interact with the fermions but not with each other, and as a second part non-interacting fermions. Furthermore, the problem may comprise a third part corresponding only to statically interacting quantities, the third part being preferably represented by a quantum mechanical description as a static fermion-fermion interaction.

[0069] The system includes a quantum computer 710 and a device 720. Additionally, a control unit 730 is shown as an interface between the device 720 and the quantum computer 710, and the control unit 730 may be distributed as either part of the device 720 or part of the quantum computer 710, or both.

[0070] Quantum computer 710 includes a fermionic operator 711 configured to utilize the quantum mechanical states of quantum elements to form qubits. For example, the fermionic operator may utilize, and optionally include, a quantum register, such as described with respect to Figure 2. In general, the quantum elements that form the qubits are manipulable by quantum gate operations performed on the quantum elements.

[0071] Furthermore, the quantum computer 710 includes a bosonic operator 712 in addition to the fermionic operator 711 and different from the commonly known quantum computer as described in FIG. 2. The bosonic operator 712 is configured to couple a bosonic field to the quantum device, and the coupling of the bosonic field to the quantum device and optionally the bosonic field itself can also be manipulated by quantum operations performed on the bosonic field and / or the coupling of the bosonic field itself. Thus, as indicated by the two-headed arrow, the fermionic operator 711 and the bosonic operator 712 interact with each other through the coupling of the bosonic field to the quantum device utilized by the fermionic operator 711, such that the bosonic field can affect the state of the quantum device. Furthermore, in a preferred embodiment, the interaction also includes a step in which the state of the quantum device can affect the bosonic field. In general, the bosonic operator 712 can be realized in a number of different ways depending on the construction principle on which the quantum computer 710 is based. For example, if quantum computer 710 refers to a superconducting quantum computer in which the quantum elements are realized as superconducting circuits as already mentioned above, then bosonic computing unit 712 can utilize and optionally include additional resonators, i.e. resonators not used for reading or computing the quantum elements, as bosonic elements representing the bosonic fields, which are coupled to the quantum elements for coupling the bosonic fields to the quantum elements. Thus, in such an exemplary embodiment, the bosonic fields are represented by the electromagnetic fields generated by the resonators, and the coupling is represented by the interaction of the respective electromagnetic fields with the superconducting circuits forming the quantum elements. A more detailed description of this embodiment and further exemplary embodiments of the realization of the bosonic computing unit will be discussed in relation to more detailed embodiments of the present invention.

[0072] In general, the fermionic operator 711 is adapted to allow the operation by operations on the second part of the problem of the quantum elements, which includes quantities that describe the problem without interacting with each other. In contrast, the bosonic operator 712 is configured exclusively for the operation by operations on the first part of the problem, which corresponds to quantities that describe the problem while interacting with each other. Thus, structuring the quantum computer 710 to include the fermionic operator 711 and additionally the bosonic operator 712, in contrast to the quantum computer described in FIG. 2, allows the representation or simulation of the interacting quantities of the problem to be moved to the interaction of different parts of the quantum computer 710, for example the interaction of additional resonators with independently controllable superconducting circuits. Furthermore, due to the separation of the two parts of the problem, the representation of the bosonic operator 712 by a system constructed to control it in a technically different way than the quantum elements allows the number of quantum gate operations that need to be explicitly performed on the qubits to solve a given problem to be reduced. Thus, not only does it allow a better control to improve the accuracy of the calculation, but it also reduces the qubit resources required, allowing more complex problems to be calculated with a given qubit resource.

[0073] Furthermore, the quantum computer 710 includes a manipulation unit 713 configured to manipulate a) the fermionic operator 711 and b) the bosonic operator 712. In particular, the manipulation unit 713 is configured to manipulate the fermionic operator 711 such that the state of the quantum element is manipulated based on a control signal that is in particular indicative of an operation on the second part of the problem as described above. Furthermore, the manipulation unit 713 is configured to manipulate the bosonic operator 712 such that the coupling of the bosonic field and optionally the bosonic field itself is also manipulated based on a control signal that is indicative of an operation on the first part of the problem as described above. For example, the manipulation unit 713 can be considered to be part of the fermionic operator 712 and can be considered to be a controller of a laser that allows the operation of quantum elements, i.e. qubits, in a quantum computer realized as an ion trapping device. Alternatively, the manipulation unit 713 can correspond to a controller of a microwave source that is utilized to manipulate qubits and / or bosonic fields in a quantum computer realized as a superconducting quantum computer. In this way, the operation section 713 is provided with control signals from the control unit 730 which indicate, for example, the operations to be performed by the fermion operation section 711 and the boson operation section 712, and uses these control signals to appropriately control each part of the quantum computer.

[0074] Furthermore, the quantum computer 710 includes a readout unit 714 configured to read out the quantum elements used by the fermionic operator 711 and the bosonic field used by the bosonic operator 712. In general, the readout of the quantum elements and the bosonic field corresponds to measuring at least one observable of the quantum mechanical state of each quantum element used by the fermionic operator 711 and to measuring the state of the representation of the bosonic field used by the bosonic operator 712. The measurement of the bosonic field may refer to, for example, the measurement of an observable or a signal provided by a bosonic element representing the bosonic field. For example, if the quantum computer is a superconducting computer in which the bosonic field is represented as a resonator, the readout unit can be adapted to measure the electromagnetic field provided by the resonator or a change in said electromagnetic field. Alternatively, if the quantum computer refers to a trapped ion quantum computer in which the bosonic field is represented by the vibrational modes of the trapped ion, the measurement unit can be adapted to measure the frequency of the vibrational modes of the trapped ion. The measurement results of the readout unit 714 indicate a solution to the calculated problem.

[0075] In general, the functions of the quantum computer 710 can be controlled by the control unit 730. The control unit 730 is adapted to provide control signals to the operator 713 indicative of the desired operations to be performed by the fermionic operator 711 and the bosonic operator 712, which then executes each operation, for example by controlling a laser source or a microwave source of the fermionic operator 711 or the bosonic operator 712, respectively. Furthermore, the control unit 730 can also be adapted to control the readout unit 714 to read out each result of the quantum mechanical calculation after the operation is performed. In particular, the readout unit 714 can then be adapted to provide a signal indicative of the measurement result to the control unit 730. Thus, the control unit 730 can generally be considered as part of the quantum computer 710. Furthermore, the control unit 730 can also be realized as software and / or hardware together with the operator 713, for example as part of a laser or microwave source controller. However, control unit 730 may also be separate from operation 713 and provided in the form of separate software and / or hardware that controls quantum computer 710. Furthermore, control unit 730 may also be fully or partially implemented as part of device 720. For example, the software providing the functionality of control unit 730 may be split between device 720 and quantum computer 710, with each software portion providing multiple computational functions that together provide the functionality of control unit 730. However, each dedicated hardware or software combination may also be divided accordingly. Control unit 730 may therefore generally be considered to form an interface between device 720 and quantum computer 710.

[0076] In particular, the control unit 730 is configured to provide a control signal for controlling the manipulator 713 such that the manipulator 713 operates the fermionic operator 711 such that the state of the quantum device is manipulated based on an operation related to the second part of the problem. Furthermore, the control unit 730 is configured to provide a control signal for controlling the manipulator 713 such that the manipulator 713 operates the bosonic operator 712 such that the coupling of the bosonic field to the quantum device is manipulated based on an operation related to the first part of the problem. In this way, the control unit 730 is dedicatedly adapted to control the manipulator 713 according to the principle of providing an operation related to different parts of the problem. In general, the control unit 730 can be adapted to provide control signals already stored in a storage device, for example, for controlling the manipulators. However, the control unit 730 can also be adapted to generate the respective control signals, for example by cooperating with the device 720. This preferred embodiment will be described below.

[0077] The device 720 is particularly adapted to determine a solution to a problem as described above. However, while in the following embodiments the device is adapted directly to solve the problem, in other embodiments the device 720 may only be adapted to provide a control signal that controls the determination of the solution in the quantum computer. In this case the readout signal may be provided to another functional part, leaving out the result determination unit.

[0078] The apparatus 720 comprises a problem providing unit 721 adapted to provide a problem description indicating a problem to be solved comprising a first and a second part. Preferably, the problem description corresponds to a quantum mechanical description of the problem, e.g. a quantum mechanical description of an electronic structure problem. However, the problem description may correspond to any other problem representation that unambiguously describes the problem to be solved, in which case the conversion unit 722 is adapted to convert the provided problem description into a quantum mechanical description that can be solved by the quantum computer 710. The problem description may for example be stored in a storage device and then provided by the problem providing unit 721 or may be received by the problem providing unit 721 via an input, e.g. where a user provides input of the problem description. Thus, in a preferred embodiment, the problem providing unit 721 corresponds to a user interface that allows a user to define a problem to be solved such that the problem description can be provided to the conversion unit 722.

[0079] The conversion unit 722 is then adapted to convert the problem description into a representative operation description, and optionally, if the problem description is not provided as a quantum mechanical description, the conversion unit 722 may also first convert the problem description into a quantum mechanical description of the problem. The representative operation description of the problem indicates a sequence of operations to be performed on the quantum computer 710. For example, known algorithms and methods can be used to convert the quantum mechanical problem description into respective operations on the quantum computer, as described in an exemplary implementation of the quantum computer 710 in a more detailed embodiment. In particular, the conversion unit 722 is adapted to convert the problem description into a sequence of operations including a) a second plurality of operations and b) a first plurality of operations. The second plurality of operations are to be applied to each fermionic operator 711 of the quantum computer 710 and are determined based on a second portion of the problem. The first plurality of operations are to be applied to each bosonic operator 712 of the quantum computer 710 and are determined based on a first portion of the problem. For example, the sequence of quantum operations may include respective predefined quantum gates that manipulate qubits of quantum computer 710, or may correspond to operations that manipulate optional elements of bosonic operator 712, e.g., if the bosonic fields are represented by respective additional components. The representative operation description indicating the sequence of operations is then provided by conversion unit 722 to control unit 730.

[0080] The control unit 730 then acts as an interface between the apparatus 720 and the quantum computer 710, as already mentioned above, and is adapted to provide or optionally generate control signals for controlling the operator 713 to perform a predetermined sequence of operations. For example, the control unit 730 can be adapted to generate the control signals based on a respective conversion table that converts the predetermined operations provided by the conversion unit 722 into respective control signals leading to control the operator 713 to respectively perform said operations. Such conversion tables are therefore typically provided specifically for each hardware and / or software utilized by the operator 713.

[0081] Furthermore, the control unit 730 provides control signals for controlling the readout unit 714 as described above, and receives from the readout unit 714 one or more read out observables as a result of the quantum mechanical calculation. In particular, the readout unit 714 is controlled to measure one or more observables of the quantum device as qubit states. Furthermore, the readout unit 714 is controlled to read out one or more observables of the bosonic field by measuring one or more observables representing the bosonic field, such as the oscillation frequency of a trapped ion or the electromagnetic field strength of a resonator. These read out observables, i.e., measurement results, are provided by the control unit 730 to a result determination unit 723 adapted to determine a solution to the problem based on the one or more read out observables. In particular, the result determination unit can be adapted to perform further calculations or algorithms on the results in order to determine a solution to the problem based on the read out observables. For example, the result determination unit 723 can be adapted to convert one or more read out observables into a respective representation of the problem description in order to provide a solution to the problem. Furthermore, the result determination unit 723 can also be adapted to apply more complex algorithms to one or more retrieved observables, for example for error correction or when one or more retrieved observables indicate only a part of the solution to the problem. The result determination unit 723 can then be adapted to provide the result as a solution to the problem to a user, for example via an output such as a display. However, the result determination unit 723 can also be adapted to provide the result as a solution to the problem as an input to a further computing system, for example a production control system for controlling an optimized production of a product. The result determination unit 723 can generally be part of the device 720, but can also be part of a stand-alone device or a separate computing device.

[0082] In Fig. 8, a flow diagram of a method for determining a solution to a problem is shown, in a schematic and exemplary manner. In particular, the method 800 corresponds to a problem comprising a first and a second part, the first part comprising quantities describing the problem interacting with each other and the second part comprising quantities describing the problem without interacting with each other. In particular, the method 800 is adapted to perform the method using a quantum computer as described above. The method 800 comprises a first step 810 of providing a problem description indicating the problem to be solved comprising a first and a second part. In general, the same principles can be applied to said step 810 as described, for example, with respect to the problem provision unit 721. Furthermore, the method 800 comprises a step 820 of converting the problem description into a representative operation description, again as described in more detail already, for example with respect to the conversion unit 722. Furthermore, the method 800 comprises a step 830 of providing control signals for controlling the operation of the quantum computer. In particular, the control signal is adapted to control the operator to operate the fermionic operator such that the state of the quantum device is manipulated based on the second plurality of operations and further to operate the bosonic operator such that the coupling of the bosonic field to the quantum device is manipulated based on the first plurality of operations. This allows a quantum mechanical calculation of the problem to be performed. In a next step 840, a control signal is provided to control a readout unit of the quantum computer such that after the quantum mechanical calculation is performed, the observables readout one or more observables are indicative of a solution to the problem. In a final step 850, the method 800 includes determining a solution to the problem based on the one or more readout observables.

[0083] In the following, examples of preferred embodiments of the present invention will be described in more detail, with the examples presented mainly corresponding to problems provided in a quantum mechanical description of fermion-fermion or fermion-boson interactions. However, as already mentioned above, other problems can also be solved by the present invention, especially if they can be converted to the respective quantum mechanical description. In general, quantum computers in principle allow for extremely efficient and accurate simulation of, for example, many-electron systems, but gate-based quantum computers that are close to practical use are often limited by the number of quantum gates that can operate the qubits, prepare the solution of the problem, and finally read out the state of the qubit register, which is a challenge especially for complex fermion-fermion interactions. Furthermore, even with error-corrected quantum computers, complex fermion-fermion interactions require a large number of quantum gates, which can lead to long calculation times. In general, to simulate fermion-fermion interactions described by four-exponential vertices, such as problems with the electronic structure of molecules and solids, a computation time of O(N 4 ) quantum gate operations are required, where N is a measure of the size of the problem.

[0084] As described above, the present invention reduces the number of quantum gates to O(N 2), any fermion-fermion interaction can be implemented in a quantum computing architecture, for example a quantum computer based on superconductivity and ion trapping devices. In the case where a problem is provided that can be represented by a quantum mechanical description, for example including dynamical fermion-fermion interactions, which also allows for retarded or over-progressive interactions, it is preferred that the above mentioned device further includes a transformation unit adapted to transform the problem description into a problem description including boson-fermion interactions as a first part and into a problem description including non-interacting fermions as a second part. Thus, by means of said transformation unit, for example interacting fermions can be mapped into a non-interacting system of fermions coupled to an isolated boson field. As already mentioned above, the quantum computer hardware is then modified specifically to solve the resulting problem. In the following, the algorithms, approaches and modifications of existing hardware elements for solving the problem are described in more detail with preferred examples.

[0085] In the following, suitable variants of generally known quantum computers that can be advantageously used to solve each problem are described. In general, quantum elements forming qubits already present in the hardware architecture are preferably used for digital or analog simulation of parts of the problem that can be represented by non-interacting fermionic modes as a second part of the problem, for example by fermionic operators. The variants therefore mainly correspond to the implementation of isolated bosonic modes and their coupling to fermionic modes by introducing bosonic operators.

[0086] In a first preferred embodiment, the quantum computer refers to a superconducting quantum computer. In this case, the bosonic modes, i.e., bosonic fields, can be represented by preferably providing additional hardware resonators, e.g., LC circuits, as bosonic elements, since, for example, the readout resonator cannot be used to both read out and represent the bosonic modes. Thus, it is preferred that O(N) additional resonators are arranged on a chip that includes the superconducting circuit forming the quantum bit. In particular, it is preferred that 2-4 resonators are provided per quantum bit, i.e., quantum element, and arranged to be coupleable to each quantum bit. For example, if the conversion unit is adapted to apply a restricted random phase approximation to the quantum mechanical description of the problem, one resulting frequency-dependent interaction part can be converted into a quantum operation to be applied to 2-4 hardware resonators. In another example, if the quantum mechanical description of the problem includes a four-exponential interaction term, such as exists in a molecular Hamiltonian, then O(N 2 ) additional resonators are preferably provided. Since it is difficult to place this amount of resonators on a chip, the transform unit is preferably adapted to apply a low-rank decomposition to the quantum mechanical description of the problem to reduce the O(N) or O(NlogN) resonator requirements.

[0087] In some hardware realizations, it may be difficult to provide a resonator containing the desired frequency for a particular problem, since the resonator frequency is often fixed within a certain threshold due to the fixed length of the resonator and the superconducting gap. In particular, the resonator must provide high frequencies when the quantum mechanical description of the problem includes static fermionic interactions. In this case, it is preferred that the transformation unit of the device is adapted to transform the quantum mechanical problem description into the rotating reference frame of the resonator, for example using the rotating wave approximation. Since this approach may still lead to a complex effective time evolution of the hardware elements, in a further preferred embodiment, the bosonic computing unit can be adapted to utilize an oscillating driving field for coupling and / or manipulating the bosonic fields.

[0088] Preferably, the coupling between the quantum element and the resonator is configured to be digitally switchable and adjustable. In particular, a bosonic computing unit can allow for manipulation of the coupling strength. However, in general, the coupling may be physically constrained, e.g. for transmon qubits the lateral coupling may be stronger than the longitudinal coupling, while for flux qubits the lateral and longitudinal coupling strengths may be equal. Furthermore, the coupling energy may be physically limited to about 10% of the qubit-level splitting energy of the transmon. Preferably, a coupling energy of about 1% is used for the coupling.

[0089] When using a resonator to represent the bosonic field, two different time scales need to be synchronized during the quantum mechanical calculation. In particular, the simulated, e.g. Trotterized, time evolution of the qubit and the real, i.e. physical time evolution of the resonator need to be synchronized. Advantageously, to meet this condition, the conversion unit is adapted to convert the quantum mechanical description of the problem into quantum operations, such that the simulated time is less than or equal to the real time, and by using a wait operation corresponding to the wait time. During the wait operation, no further operations are performed and the bosonic field can interact with the quantum element.

[0090] An advantage of such a superconducting quantum computer is that quantum operations, in general, and quantum gates, can be applied in parallel. This also allows the transformation unit to take parallelism into account when generating the sequence of quantum operations, for example by determining a sequence of quantum operations that can be applied simultaneously. A further advantage is that the resonators can apply a broadening of the Boson peak to increase the broadening, for example via a measurable external magnetic field or via coupling of the Boson magnetic field to an ancilla qubit. Furthermore, it is advantageous to measure the Boson field directly, for example by measuring a characteristic of the field generated by each resonator.

[0091] In a further preferred embodiment, the quantum computer utilized refers to trapped ion quantum hardware. In particular, the vibrational modes of the trapped ions can be used in this case to represent the bosonic modes, i.e., the bosonic fields. In this embodiment, it is not necessary to provide hardware bosonic elements to represent the bosonic fields. Instead, the bosonic computing unit can be configured to manipulate the already existing vibrational modes of the trapped ions to interact, i.e., couple, with the electronic states of the trapped ions forming the qubits. Since the bosonic fields in this case are represented by vibrational modes, the number of bosonic fields is naturally limited by the number of ions, to about 3N bosonic fields.

[0092] In general, it is preferred that the bosonic operation unit allows the manipulation of the frequency of the bosonic field to provide energy to each vibrational mode of the trapped ions in order to transfer energy from the vibrational modes to the electronic modes or from the electronic modes to the vibrational modes. In the case of a trapped ion quantum computer, the manipulation of the frequency of the bosonic field can be realized by manipulating the distance between the trapped ions, for example by manipulating the electromagnetic field that traps the ions in the ion trapping device, by manipulating the frequency of the laser used to manipulate the quantum element, or by utilizing a rotating frame. This allows the coupling and / or the bosonic field itself to be manipulated very simply. Furthermore, it is also preferred that in this case the transformation unit is adapted to transform the quantum mechanical problem description into a rotating reference frame, which can be chosen more flexibly due to the possibility of utilizing a laser for the manipulation of the vibrational modes. Furthermore, it is preferred that the transformation unit is adapted to provide an operational description of the problem including a quantum operation of tuning a laser to resonate with the frequency of the fermionic and / or bosonic modes such that complex time evolution effects are suppressed. In general, in contrast to the above-mentioned superconducting quantum computer realizations, in trapped ion realizations the time scales of the time evolution of the qubit and the time evolution of the boson field are identical since both are realized by the same quantum mechanical system.

[0093] In contrast to superconducting hardware, the coupling of bosonic fields to quantum devices can be seen as occurring naturally via the possibility of transferring energy from vibrational modes to the electronic states of the trapped ions and / or from the electronic states of the trapped ions to the vibrational modes, and the bosonic computing unit is therefore preferably configured to enable such coupling by controlling the coupling via laser pulses.

[0094] In a trapped ion quantum computer, quantum gates can generally only be applied serially. Therefore, in this embodiment, the transformation unit is preferably adapted to take this into account by providing an operation description such that each sequence of quantum operations corresponds only to quantum operations that are applied serially. However, if solutions are found that allow for the parallel application of quantum operations in a trapped ion quantum computer, the transformation unit can also take these new solutions into account.

[0095] Again, the transformation unit can be adapted to utilize quantum operations that result in broadening of the Boson peak, for example corresponding to coupling of an external field to the Boson field, or corresponding to increased broadening by utilizing measurable ancilla qubits.

[0096] Advantageously, the transformation unit is in this case particularly adapted to apply the restricted random phase approximation to the quantum mechanical description of the problem while deriving the effective electron-electron interactions, the hardware described above being particularly useful for such interactions provided by the problem.

[0097] In a further preferred embodiment, the bosonic degrees of freedom can also be implemented in quantum devices using specially determined qubit gates, rather than being implemented as superconducting resonator lines or using vibrational modes of trapped ion hardware. In this case, the bosonic operation unit is adapted to utilize the overhead of the number of quantum elements forming the qubits representing the bosonic field and the coupling of the bosonic field with the quantum elements representing other quantities of interest. It is therefore preferred in this embodiment that the operation unit provides specific quantum operations for encoding the coupling and the bosonic field with the overhead qubits. In this case, it is preferred that the operation unit defines a cut-off threshold for the number of qubits available to represent the bosonic field, thereby limiting the number of excitations in the bosonic modes that can be simulated. The threshold can be defined by utilizing a phenomenological approach.

[0098] In this embodiment, bosonic coupling is also performed using quantum elements forming qubits, but since the bosonic fields themselves do not interact and the time evolution can be applied in parallel to all bosonic fields as with fermionic quantum elements, the set of quantum operations for a given problem also does not necessarily contain substantially more quantum operations as with any of the above implementation schemes. Furthermore, the overhead quantum elements preferably have a lower probability of interaction than quantum elements dedicated to the representation of non-interacting fermions. This has the advantage that this embodiment allows for better control at low excitation levels of the bosonic modes.

[0099] Additionally, other quantum computer architectures can also be modified to provide bosonic operators that represent bosonic fields and allow coupling between bosonic fields and quantum devices, for example ultra-cold / Rydberg atomic quantum hardware architectures can also be utilized and modified according to the principles described above.

[0100] In the following, we will describe in more detail how the problems already mentioned above are solved using each specific quantum computer variant. The following functions can be performed, for example, by functional parts of the device to provide respective control signals for the quantum operations that solve the problem on the quantum computer:

[0101] The following description focuses on an implementation scheme that utilizes a superconducting quantum computer with an additional digitally switchable resonator representing the bosonic field. Such a resonator offers more flexibility and is easier to implement in quantum computer hardware. However, the general solution described below is at least partially applicable to other cases, particularly other quantum computer hardware.

[0102] It is generally preferred that the conversion unit is adapted to utilize a Trotterization algorithm to perform the time evolution of the Hamiltonian representing the quantum mechanical description of the problem. This leads in some realizations of quantum computers to the appearance of additional time scales other than the simulated time scales in the frame of each problem to be solved and in the approach of dividing the problem into a first and a second part. In particular, the real-world time course governing the evolution of some representations of bosonic fields such as the resonators mentioned above deviates from the simulated time course of the qubits. In such implementations, it is preferred that the conversion unit is adapted to convert the problem into an operational description such that the total real time course during a Trotter step is equal to the simulated time of the Trotter step. Furthermore, the bosonic computing unit preferably enables coupling of the bosonic fields to the quantum devices that is strong enough to represent an effective simulated interaction between the bosonic fields and the quantum devices, where in the case of a superconducting quantum computer the effective interaction between the qubits and the resonator is given by a physical coupling scaled by the real-world simulation time, and the strength of the simulated effective interaction is the coupling of the bosonic fields to the fermions determined by a Hamiltonian describing the problem scaled by the simulated time.

[0103] It is further preferred that the transformation unit is adapted to transform the quantum mechanical description of the problem into a rotating reference frame. This allows, in particular, when using resonators as bosonic elements, to tune the problem to the respective resonator frequency. However, this transformation is also advantageous in other quantum computer hardware realizations. By using this approach, the representation of the bosonic modes in the hardware elements can be more easily controlled, but the time evolution of the quantum mechanical description of the problem becomes more complex. It is therefore further preferred that the transformation unit applies a rotating wave approximation to the quantum mechanical description in the rotating reference frame, which results in the dropping of the most complex terms, i.e. the terms with the highest rotational frequency. It is further preferred that the manipulation unit is adapted to enable a frequency-dependent manipulation of the quantum elements, the bosonic fields, and / or the coupling of the bosonic fields and the quantum elements. In particular, when applying the rotating wave approximation, the frequency-dependent manipulation allows, for example, to set the frequency of manipulation of the quantum elements to a frequency that results in a substantial cancellation of the time evolution of each term in the quantum mechanical description represented by the quantum elements so manipulated. In this way, the quantum mechanical calculations can be further simplified since the influence of some terms of the quantum mechanical description can be strengthened while other terms can be neglected. In particular, the transformation unit can then be adapted to include quantum operations corresponding to this frequency-dependent operation to fit into a sequence of quantum operations that represents the problem.

[0104] In particular, by using a rotating frame, it is possible to simulate frequency-dependent density-density interactions in a quantum mechanical description of the problem. When using a rotating frame, it is further preferred that the transformation unit is adapted to provide each topological quantum operation into a set of quantum operations that represent the problem and allow the implementation of the phase factors in a quantum mechanical calculation. In general, these topological quantum operations may depend on the hardware used. For example, in a trapped ion quantum computer, the topological quantum operations may correspond directly to the manipulation of the laser light used to manipulate the bonds, while in other hardware realizations, the topological quantum operations may correspond to modified standard quantum gates applied to the qubits.

[0105] In general, it is preferred that the conversion unit is adapted to utilize phase operations to convert the first part of the problem corresponding to the fermion-boson interaction in the quantum mechanical description into an operation description. In particular, the phase operations may correspond to specially modified standard quantum gates available in the hardware realization of the respective quantum computer device. In general, the pure fermion-fermion interaction can be represented by standard one-qubit and two-qubit gates, but the inclusion of bosonic modes leads to quantum operations that preferably also implement a phase that depends on the state of the bosonic field, for example represented by the electromagnetic field in the resonator. In particular, the phase operations may refer to additional quantum gate operations and subsequent latency while the qubits, i.e. quantum elements, and the representation of the bosonic field interact in the real world.

[0106] An example of phase operations for a modification of the well-known FSWAP algorithm used to implement an efficient time evolution of quantum mechanical systems is described below. For boson-fermion interactions, the FSWAP gate needs to additionally account for the phase shift due to the bosonic modes. As already mentioned above, this is achieved by introducing a waiting time into the sequence of FSWAP gates, i.e. a time during which the representations of the bosonic fields and each quantum element can interact. The unitary matrix representation of the FSWAP gate is given by

[0107]

number

[0108] Here, b is the boson annihilation operator, b †is the bosonic generation operator, g represents the coupling strength of the fermion or quantum element with the bosonic mode, and t is the waiting time. An example of a corresponding gate sequence is shown in Figure 9. The top two rows of boxes represent gate operations performed on each of the two qubits, and the boxes in the third row represent operations performed on the bosonic field or the coupling of the bosonic field to the qubit. Within these boxes are shown each mathematical operator to which the operations correspond in the quantum mechanical description of the problem. In this example, we use an FSWAP gate with a phase shift due to the bosonic mode, as well as a controlled Z (CZ), a SWAP gate, a single qubit gate, and a U phys The bosonic gates, which take into account the phase shift, can be considered as phase operations in this case and correspond to the latency during which the interaction of the qubit with the bosonic field occurs. In general, the above decomposition, i.e., the sequence of quantum operations, can be provided as appropriate for each hardware implementation of the quantum computer.

[0109] The measurement, i.e. readout, of the Hamiltonian and other observables of the quantum mechanical system preferably also includes the measurement of the bosonic field, e.g. the measurement of one or more observables of the electromagnetic field generated by the resonator. It is therefore preferred that the readout is adapted accordingly. Since the qubit operator and the bosonic operator are in communication, the readout can be adapted to measure the observables of the quantum device and the observables of the bosonic field simultaneously or sequentially. Standard Hamiltonian averaging of the measurements can be used in the following processing of the measurement results.

[0110] In a preferred application of the quantum computer and methods described above, the problem can be transformed into a quantum mechanical description corresponding to electrons moving in electrical potentials generated by atomic nuclei and interacting via direct Coulomb repulsion or another, potentially effective screened quasiparticle interaction. The following electron system is a special case of the more general fermion system. Advantageously, the fermion system can be described in the quantum mechanical description by the following fermion-fermion Hamiltonian:

[0111]

number

[0112] Here, c i † The operator is a creation operator of fermions in state i, which adds fermions to the state, and c i is the annihilation operator that removes a fermion from state i, and h ij describes non-interacting fermions moving from, for example, atomic nuclei or an electromagnetic field to an external potential, which may be time-dependent, for example an oscillating electromagnetic field, or static, and U ijkl describes time-independent fermionic interactions, e.g. the Coulomb repulsion of electrons.

[0113] Furthermore, many problems of interest can be transformed into fermionic systems governed by density-density interactions. A famous example of such a system is the Fermi-Hubbard model. The density-density interactions have the form

[0114]

number

[0115] Here, n i is the particle number operator for fermion state i. To apply the general principle of the invention of splitting a problem into a first, second and optionally a third part, it is preferred that the device further comprises a transformation unit, if the problem contains terms representing interacting fermion systems, such as the above-mentioned fermion systems. The transformation unit then transforms the problem into a problem of a form including the first and second parts. In particular, if the problem contains a fermion-fermion interacting system and is representable, it is preferred that the transformation unit is adapted to transform the fermion-fermion interactions into boson-fermion interactions. Advantageously, the transformation unit is adapted in this case to utilize the Hubbard-Stratonovich transformation, which is a method known from solid-state field theory. Its application to fermion quantum fields allows the decoupling of the fermion-fermion interactions at the expense of a newly introduced boson quantum field coupled to the fermion fields.

[0116] Applying the Hubbard–Stratonovich transformation leads to the fermion-boson system described below. In general, bosons are non-interacting, i.e. one boson does not interact with another. The Hubbard–Stratonovich transformation, for the Hamiltonian above, gives the general fermion-boson Hamiltonian:

[0117]

number

[0118] The fermion operators are the same as those mentioned above for purely fermionic systems. The operator b s is the boson annihilation operator that removes one boson from mode s, and b s † is the creation operator that adds bosonic excitations to mode s. g ij,s describes the coupling strength between bosonic mode s and fermionic states i and j, e.g., from the Hubbard-Stratonovich transformation of an interacting fermionic system. ω sis the characteristic frequency of a bosonic mode, e.g., the resonator frequency of a superconducting device or the phonon frequency of an ion-trapping device. Thus, through the transformation, a problem containing interacting quantities is transformed into a system containing a first part corresponding to bosonic fields interacting with other interacting quantities, e.g., fermions, and a second part corresponding to non-interacting quantities, e.g., non-interacting fermions. In general, the application of the Hubbard-Stratonovich transformation involves applying the Hubbard-Stratonovich transformation to a quantum field representation of the interacting fermionic operation part of the problem. Based on the application results, the fermion-boson interacting system representing the interacting fermionic operation part of the problem can be defined in the form of a Hamiltonian that allows the use of known transformations to represent and compute Hamiltonians on a quantum computer. In general, if the representation of the fermion-boson system in the Hamiltonian is correctly defined, the quantum field representation of the fermion-boson system and the quantum field representation of the Hubbard-Stratonovich transformed interacting fermionic operation part of the problem are identical. However, in some cases, further dynamical frequency-dependent boson propagators appear in the field representation of the fermion-boson representation of the Hamiltonian. In general, in some cases, these additional boson propagators are generally assumed to be small and therefore can be neglected. However, in preferred embodiments, the boson computing parts of the quantum computer, e.g., resonators, are controlled or adapted so that the boson propagators can be considered small and therefore can be neglected. Furthermore, a parameter g describing the coupling strength between the boson mode s and the fermion states i,j is introduced. ij,s and ω, which describes the eigenfrequencies of the bosonic modes in the Hamiltonian representation. s It is preferable to adjust the values ​​so that the boson operator can accurately represent the computation problem.

[0119] In order for the fermion-boson Hamiltonian shown above to be a good representation of the original fermion-fermion problem, the dynamical frequency-dependent boson propagator in the corresponding quantum field representation is ignored. However, in a further preferred embodiment, this frequency dependence of the boson-fermion coupling, i.e. the boson propagator, can also be advantageously used for problems that can be transformed into fermionic systems with effective dynamical, i.e. frequency-dependent interactions. Typically, such effective dynamical frequency-dependent fermionic interactions arise in problems where only a subsystem embedded in a larger system is calculated. For example, such problems may correspond to a quantum mechanical subsystem or embedded system, such as a subsystem constructed by cRPA calculations, where for example only d-states are considered in the active part of the calculation, and all other electronic states are integrated out to provide only an effective frequency-dependent screening of the interactions between the active electrons. Another example could be an optically active molecule embedded in a larger molecule or protein, or a defect in a metal where the conduction electrons provide an effective screening.

[0120] In the following, two preferred possibilities in this embodiment are described. For example, the problem description can be used to define an active space for the electronic system, which corresponds to the space or molecular orbitals considered to be relevant for the particular problem. In particular, in this case, the interacting fermion system can be split into two parts. Based on this split problem description, the transformation unit can be adapted to calculate the influence of electrons outside the active space on electrons in the active space using an embedding or screening method. For example, the transformation unit can be adapted to apply a restricted random phase approximation calculation to the Hamiltonian to describe the non-active electrons as an effective screening of the Coulomb interaction of the active electrons. This results in frequency-dependent interactions in the many-body perturbation description of the active space, e.g. Green's functions or actions, for which there is no direct transformation to the Hamiltonian. However, such a representation is usually suitable for performing calculations on a quantum computer. Therefore, in this case, the transformation unit is further adapted to apply a Hubbard-Stratonovich transformation to the part of the problem description describing the active region under the influence of screening by the remaining electrons. Therefore, again, this is done by introducing an additional bosonic field, thus leading to a fermion-boson Hamiltonian corresponding to a quantum mechanical description including a first and a second part and optionally a third part as in the first exemplary embodiment. The action of this fermion-boson Hamiltonian now has interactions that are significantly frequency dependent. In particular, from this example we obtain

[0121]

number

[0122] In general, the quantities in this equation correspond to those already mentioned in the equations above. There is no Hamiltonian formulation for the dynamical interaction from the screening electrons. However, the fermion-boson system with the Hamiltonian given above has the same action description as the frequency-dependent interacting fermion system and can therefore be used to represent the system in a quantum computer. The advantage of this embodiment is that the dynamical properties of the screened Coulomb interaction and the boson field in the active region can be mapped onto each other. This allows a wider variation of hardware for realizing the problem in a quantum computer, for example using resonators with a narrower frequency range.

[0123] In a further example, the transformation unit is adapted to apply extended dynamical mean field theory (DMFT) calculations to systems with nonlocal interactions in the problem description, for example a general fermion-fermion Hamiltonian as defined above. In DMFT, clusters interacting with local fermion interactions are embedded in the remaining nonlocal fermion interactions. To handle nonlocal long-range interactions that reach outside the clusters, the transformation unit applies the Hubbard-Stratonovich transformation to terms corresponding to nonlocal interactions between fermions. The resulting Hamiltonian of an effective boson-fermion system for nonlocal interactions is used to calculate the corresponding propagators of said interactions on a quantum computer. These propagators can then be used, for example, as input to a DMFT self-consistent loop, i.e. a loop that iteratively calculates the solution of the complete problem.

[0124] In general, for all problem statements, it is preferred that the conversion unit is adapted to convert the problem statement into a representative operation statement that includes an operation that causes the broadening of the Boson peak by including in a series of operations a plurality of operations that utilize an additional external electromagnetic field configured to manipulate the coupling of the Boson field to the ancilla qubit and / or quantum element. The broadening of the linewidth of the Boson peak spectral line can be artificially increased, in particular with the aid of an ancilla qubit whose coupling to the Boson field is adjustable. It is therefore preferred that the Boson operation unit is adapted to enable such an adjustable coupling. In general, for quantum computers, which refers to superconducting quantum computers that include resonators to represent the Boson field, the broadening of the Boson peak is related to the inverse of the quality factor of the resonators that represent each Boson field. Furthermore, for superconducting quantum computers, the broadening is proportional to the decay time of the excitation of the resonators that represent each Boson field. For quantum computers that realize the Boson field as an additional quantum element, the broadening is related to the error rate of the quantum element. In the case of a quantum computer implemented as a trapped ion quantum computer, broadening is related to the decay time of the trapped ion's electronic states and to fluctuations in the energy or natural frequency of the trapped ion's vibrational modes caused by, for example, an electromagnetic field that traps the ion.

[0125] To increase the broadening of the Boson peak, the following protocol is preferably used, for example by converting the problem description into respective operations that make the quantum computer follow the respective protocol. First, an operation is preferably applied to the quantum computer to initialize the ancilla qubit to its ground state. In a next step, an operation is applied that produces a SWAP operation between the boson field and the ancilla qubit, which transfers the excitation from the boson field to the ancilla qubit. In a final step, an operation is applied that measures the ancilla qubit and returns it to its ground state if it was measured in an excited state. The protocol can be repeated if necessary.

[0126] This computational protocol effectively reduces the number of excitations of the bosonic field. Due to the measurements the protocol is not unitary. This non-unitary reduction of excitations corresponds to the typical damping of a bosonic field represented for example by a resonator and leads to an increase in the linewidth of the bosonic field, i.e. a broadening of the bosonic peak. The strength of the broadening can be controlled by the frequency at which the protocol is applied, i.e. the number of repetitions per time unit.

[0127] As mentioned above, according to the invention, the quantum computer, the device and the method are preferably applied to a problem involving a fermion system interacting with each other in a quantum mechanical description. The device is then preferably adapted to convert the fermion system into a coupled fermion-boson system. The device is then further adapted to convert the problem into a sequence of operations leading to the mapping of all remaining fermion modes, i.e. non-interacting and statically interacting fermions onto quantum elements, and all bosonic modes onto their respective representations, for example by providing respective control signals to a fermion operation part and a bosonic operation part of the quantum computer. Furthermore, the determined sequence of operations preferably allows a unitary development of the quantum mechanical calculations on the quantum computer. The device is then preferably adapted to initiate measurements of the state of the qubits and the bosonic field, for example by providing respective control signals to a readout part of the quantum computer, and to process the measurement results to obtain a final result of the original interacting fermion system. In general, the transformation used to transform the fermion-fermion interaction to the fermion-boson interaction defines a relationship between the fermion-fermion interaction, the resonance frequency of the boson field, and the coupling strength of the qubit-boson field. This relationship allows fitting the desired interaction with the frequency, width, and coupling strength of the boson field represented by each utilized hardware. This fitting can be controlled by allowing manipulation of the coupling strength between the boson field and the qubit, manipulation of the resonance frequency of the boson field, computation of the number of boson fields, the width of the boson field, i.e., the quality factor. This manipulation can be based on each quantum operation defined by the transformation unit according to each quantum mechanical problem description. In general, a cost function for optimizing the fitting is defined by the area under the peak of the dynamical interaction, the position of the peak, the energy window, or the hardware constraints, optionally weighted.

[0128] In all embodiments of the present invention, it is further preferred that the problem can be expressed in a quantum mechanical description involving a fermionic system corresponding to the electronic system.

[0129] Furthermore, in all embodiments of the present invention, it is preferred that the transformation unit is adapted to utilize the Hubbard-Stratonovich transformation to transform a part of a problem that can be expressed in a quantum mechanical description as interacting fermions into a problem that can be expressed in a quantum mechanical description as interacting fermions and bosons. In general, the Hubbard-Stratonovich transformation provides a link between the fermion-fermion interaction, the resonance frequency of the boson field, and the fermion-boson coupling strength. This link allows fitting of the desired interaction with the boson frequencies, widths, and coupling strengths.

[0130] In particular, it is further preferred that in all embodiments of the invention the transformation unit is adapted to apply a low-rank decomposition to the quantum mechanical description of the problem in order to reduce the number of bosonic fields required to solve the problem and, if necessary, to reduce the quantum mechanical description to density-density type interactions.

[0131] It is further preferred that in all embodiments of the present invention, the transformation unit is adapted to transform the quantum mechanical description of the problem into a rotating reference frame. This allows for an effective control of the effective resonator eigenfrequency seen by the fermionic system. This approach is particularly advantageous when the original interaction corresponds to a density-density interaction. In the general case, it is preferred that the transformation unit includes in the operation description quantum operations corresponding to additional resonance control pulses in boson modes to suppress the possibility of undesired resonances occurring. Furthermore, the transformation unit can be further adapted to apply a rotating wave approximation to simplify the effective time evolution during the quantum mechanical calculation.

[0132] In all embodiments of the present invention it is further preferred that the bosonic computing unit is configured to utilize an external oscillating field to control the broadening of the bosonic field.

[0133] In all embodiments of the present invention it is further preferred that the bosonic computing unit is configured to couple the ancilla qubits to the bosonic field in order to control the broadening of the bosonic field. Furthermore, the readout unit can be adapted to further measure the ancilla qubits in order to further increase the broadening of the bosonic field based on the provided control signal.

[0134] In all embodiments of the present invention, it is further preferred that the part of the problem representable by a quantum mechanical description corresponding to electron screening is calculated such that an effective frequency-dependent screening interaction of electrons that is not part of the active space calculation is provided, for example by utilizing the restricted random phase approximation.

[0135] In some embodiments of the present invention, it is further preferred that the transformation unit is adapted to utilize Dynamical Mean Field Theory (DMFT) during the transformation of the quantum mechanical problem description and to apply the Hubbard-Stratonovich transformation to the resulting non-local fermion interactions and to the interactions of fermions that are not part of the active cluster, respectively. In another embodiment, cRPA is utilized during the transformation of the quantum mechanical problem, and the Hubbard-Stratonovich transformation is applied to the active space of the problem. The resonance frequencies and coupling strengths of the bosonic fields are determined by the transformation unit, for example with a Dynamical Mean Field Theory algorithm using a self-consistent loop.

[0136] In general, the principles of the invention already mentioned above can be applied in particular to problems that can be represented as general multi-fermion systems in a quantum mechanical description. For example, the proposed principles can be combined with virtually any quantum simulation algorithm for electronic structure problems on a quantum computer, such as ground state algorithms, excited state algorithms, time evolution algorithms, Green's function algorithms, etc. Furthermore, for example, the above-mentioned algorithms can be combined with standard electronic structure approaches, such as the use of discrimination resolution (RI) approximations, spatial and spin symmetries (e.g. point group symmetries), active space selection procedures based on e.g. orbital entanglement information, single orbital entropy, localization, population analysis, etc. Furthermore, these principles can also be combined with embedding techniques, such as different Hamiltonian operators, e.g. Hamiltonian operators in the Born-Oppenheimer approximation, Hamiltonian operators including additional potentials, relativistic Hamiltonians, Hamiltonian operators including solvation models describing the effects of the solvent / environment, multi-scale approaches, e.g. ONIOM, QM / MM, etc.

[0137] In general, the invention, for example as described above, can be advantageously used to simulate electronic structure problems that are divided into an active space and an environmental / non-active space that are large enough to have continuous or quasi-continuous states. A more specific example is molecular problems. In particular, the above-mentioned principles of the invention can be applied to problems involving organometallic compounds containing transition metals, including lanthanides and actinides, i.e. strongly correlated homonuclear or oligonuclear centers in weakly correlated environments. For example, problems involving chelating agents that interact with transition metals, for example relevant to cleaning agents or selective extraction of metals in mining, etc., can be computed. Furthermore, problems involving catalysts essential for the production of fine chemicals, active ingredients and polymers that are homogeneously catalyzed, for example by initiating or promoting the underlying chemical reactions under mild conditions, can also be solved. Problems involving large biomolecules with active centers, for example enzymes such as peptidases and esterases, (bio)macropolymer systems, and transition metal compounds embedded in solution or in the general environment can also be advantageously solved with the above-mentioned principles. Furthermore, the method is not limited to transition metal chemistry but may be advantageously applied to strongly correlated systems in general, e.g., in the context of bond breaking and formation in organic molecules during transition state chemical reactions, and to the description of certain common backbone systems such as ozone and polyenes.

[0138] The method is not limited to strongly correlated systems but can be applied to all electronic structure problems. For all the above examples, the principles described above allow the calculation of electronic energies that can be used to predict chemical reactivity, e.g., thermodynamics and kinetics of chemical reactions, spectroscopic properties, e.g., photovoltage, etc. In addition, physicochemical properties other than energy, e.g., electrostatic multipole moments, hyperfine couplings, electric fields and gradients for Mössbauer spectroscopy, diamagnetic shielding for Nuclear Magnetic Resonance (NMR) spectroscopy, etc., can also be calculated by electronic structure simulation.

[0139] Moreover, the above principles can also be applied to the class of condensed matter problems. In the field of condensed matter or solid state physics related materials simulation, these principles are particularly suitable for solving problems related to transition metal oxides and rare earth element containing materials, including but not limited to perovskites used in, for example, solid oxide fuel cells, oxide-based battery cathodes, hard magnets for electric engines, catalysts for fuel cells, transition metal heterostructures for sensors, magnetic semiconductor sandwich structures for spintronics, and high temperature superconductors. In all these cases, starting from density functional theory calculations, all-electron calculations or first principles or ab-initio calculations of the material of interest, a second quantized model of the relevant strongly correlated electronic states can be constructed, for example, by maximally localized Wannier functions, density functional perturbation theory or restricted random phase approximation calculations, which can be solved very efficiently using the above mentioned quantum computers, devices and methods. Furthermore, any electronic or fermionic second quantized matter model that includes frequency-dependent effective electron-electron or fermion-fermion interactions mediated by bosonic modes, such as plasmons, magnons, phonons, etc., can be solved very efficiently using the principles described above with minimal quantum computing resources.

[0140] 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.

[0141] For the processes and methods disclosed herein, the operations performed in the processes and methods may be performed in different orders. Furthermore, the outlined operations are presented only as examples, and some of the operations may be optional and may be combined into fewer steps and operations, supplemented with further operations, or expanded with additional operations without departing from the essence of the disclosed embodiments.

[0142] 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.

[0143] A single functional 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.

[0144] The steps performed by one or more functional units or devices, such as providing a problem, transforming the problem, generating the control signals, etc., may be performed by any number of other functional units or devices. These steps may be implemented as program code means of a computer program and / or as dedicated hardware.

[0145] The computer program product may be stored / distributed on any suitable medium, such as an optical storage medium or a solid-state medium, may be supplied together with or as part of other hardware, but may also be distributed in other forms, for example via the Internet or other wired or wireless telecommunications systems.

[0146] Any of the functional units described herein may be a processing unit that is part of a classical computing system. The processing unit may include a general-purpose processor, a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or any other dedicated circuit. Any memory may be physical system memory, which may be volatile, non-volatile, or a combination of both. The term "memory" may include any computer-readable storage medium, such as non-volatile mass storage devices. If the computing system is distributed, the processing and / or storage capacity may also be distributed. The computing system may include multiple structures as "executable elements." The term "executable elements" is a structure well understood in the computing arts as a structure that may be software, hardware, or a combination of both. For example, if implemented in software, one skilled in the art will understand that the structure of the executable elements may include software objects, routines, methods, etc. that can be executed on the computing system. This may include both executable elements in the heap of the computing system, or executable elements on a computer-readable storage medium. The structures of executable elements may reside on a computer-readable medium that, when interpreted by one or more processors of a computing system, e.g., by processor threads, cause the computing system to execute a function. Such structures may be directly computer readable by a processor, e.g., where the executable elements are binary, or may be structured and / or compiled to be interpretable, e.g., in a single or multiple steps to generate binary directly interpretable by a processor. In other examples, these structures may be hard-coded or hardwired logic gates implemented exclusively or nearly exclusively in hardware, e.g., in a field programmable gate array (FPGA), application specific integrated circuit (ASIC), or any other dedicated circuit. Thus, the term "executable element" refers to structures that are well understood by those skilled in the computing arts, whether implemented in software, hardware, or a combination thereof.Any embodiment herein is described with reference to operations performed by one or more processors of a computing system. When such operations are implemented in software, one or more processors direct the operation of the computing system in response to executing computer-executable instructions that include executable elements. A computing system may also include a communication channel that allows the computing system to communicate with other computing systems, for example, via a network. A "network" is defined as one or more data links that allow the transmission of electronic data between computing systems and / or modules and / or other electronic devices. If information is transferred or provided to a computing system via a network or other communication connection, for example, either wired, wireless, or a combination of wired and wireless, the computing system properly considers the connection as a transmission medium. A transmission medium may include a network and / or data link that can be used to transmit the desired program code means in the form of computer-executable instructions or data structures and that can be accessed by a general-purpose or special-purpose computing system or combination thereof. Although not all computing systems require a user interface, in some embodiments, the computing system includes a user interface system that is used to interface with a user. The user interface serves as an input / output mechanism with the user, for example, via a display.

[0147] Those skilled in the art will appreciate that at least a portion of the present invention may be implemented in a networked computing environment having many types of computing system configurations, such as personal computers, desktop computers, laptop computers, message processors, handheld devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, cell phones, PDAs, pagers, routers, switches, data centers, wearable devices such as glasses, etc. The present invention may also be implemented in a distributed system environment where both local and remote computing systems perform tasks that are linked through a network, for example, by either wired data links, wireless data links, or a combination of wired and wireless data links. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

[0148] Those skilled in the art will also appreciate that at least a portion of the present invention may be implemented in a cloud computing environment. The cloud computing environment may be distributed, but this is not required. If distributed, the cloud computing environment may have elements distributed internationally within an organization and / or owned across multiple organizations. In this specification and the claims that follow, "cloud computing" is defined as a model that allows on-demand network access to a shared pool of configurable computing resources, such as networks, servers, storage, applications, and services. The definition of "cloud computing" is not limited to any of the many other advantages that are obtained when such a model is deployed. The illustrated computing system includes various elements or functional blocks that can implement various embodiments disclosed herein, as described above. The various elements or functional blocks may be implemented in a local computing system or in a distributed computing system that includes elements that reside in the cloud or that implement aspects of cloud computing. The various elements or functional blocks may be implemented as software, hardware, or a combination of software and hardware. The illustrated computing system may include more or fewer elements than those shown in the figures, and may combine some elements depending on the circumstances.

[0149] Any reference signs in the claims shall not be construed as limiting the scope. The present invention relates to a quantum computer that performs operations based on control signals that determine a solution to a problem that includes a first and a second portion. A fermionic operator is configured to utilize states of quantum elements that are manipulable by an operation, the operation relating to the second portion. A bosonic operator is configured to couple a bosonic field to the quantum elements, the coupling being manipulable by an operation relating to the first portion. A manipulator operates a) the fermionic operator based on an operation relating to the second portion, and b) the bosonic operator based on an operation relating to the first portion. A readout unit measures a) the state of each quantum element that represents the state of each quantum bit, and b) an observable of the bosonic field, the measurements being indicative of a solution to the problem.

Claims

1. 1. A quantum computer (710) for performing quantum operations based on control signals that determine a solution to a problem in a quantum computer computation, the problem including a first and a second portion, the first portion including quantities that describe the problem interacting with each other, the second portion including quantities that describe the problem without interacting with each other, the quantum computer comprising: a fermionic operator (711) configured to utilize the quantum mechanical state of a quantum device to form a qubit that is manipulable by operations performed on the quantum device, the operations relating to the second part of the problem to be solved during a quantum computer computation of the problem; a bosonic operation unit (712) configured to couple a bosonic field to the quantum device, the coupling of the bosonic field to the quantum device being operable by an operation related to the first portion of the problem to be solved during a quantum computer computation of the problem; an operation unit (713) configured to: a) operate the fermionic operation unit (711) such that the state of the quantum device is operated based on a control signal indicative of an operation related to the second part of the problem to be solved during a quantum computer calculation of the problem; and b) operate the bosonic operation unit (712) such that the coupling of the bosonic field to the quantum device is operated based on a control signal indicative of an operation related to the first part of the problem to be solved such that a quantum mechanical calculation of the problem is performed; a readout unit (714) configured to measure at least one observable of a) the quantum mechanical state of each quantum element representing a respective qubit state and b) the bosonic field after manipulating the quantum elements and the bosonic couplings to perform the quantum mechanical calculation, the result of said measurement being indicative of a solution to the problem. A quantum computer (710).

2. 2. The quantum computer (710) of claim 1, further comprising a control unit (730) configured to provide control signals to control the manipulation unit (713) to a) operate the fermionic operator (711) such that states of the quantum elements are manipulated based on operations on the second portion of the problem to be solved during quantum computer computation of the problem, and b) operate the bosonic operator (712) such that couplings of the bosonic field to the quantum elements are manipulated based on operations on the first portion of the problem to be solved so that a quantum mechanical computation of the problem is performed.

3. 3. The quantum computer (710) of claim 1, wherein the bosonic couplings of the bosonic field to the quantum elements are adapted to be adaptable to represent a particular coupling of the first portion during the quantum computer computation of the quantum mechanical problem, and the manipulation unit (713) is further adapted to adapt the couplings.

4. 10. The quantum computer (710) of any one of the preceding claims, wherein the bosonic operation unit (712) is configured to couple at least one bosonic field to each quantum element forming a qubit.

5. 10. The quantum computer (710) of any one of the preceding claims, comprising: a) a superconducting quantum computer, in which the quantum elements are realized as superconducting circuits and the coupling of the bosonic field to the quantum elements is realized by providing an electromagnetic resonator coupled to the superconducting circuit; or b) a trapped ion quantum computer, in which the quantum element is realized as an ion trapped in an ion trapping device, and the coupling of the boson field to the quantum element is realized as the coupling of vibrational modes of the trapped ion to electronic states of the trapped ion forming the qubit; or c) any type of quantum computer in which the bosonic coupling is realized by performing additional coupling operations on the quantum elements forming quantum bits. A quantum computer (710).

6. 11. An apparatus (720) for providing control signals to control a quantum computer (710) for determining a solution to a problem in a quantum computer computation comprising a first and a second part, the apparatus (720) being adapted to perform a computation using a quantum computer (710) according to any one of the preceding claims, the first part comprising quantities that describe the problem interacting with each other and the second part comprising quantities that describe the problem without interacting with each other, the apparatus (720) comprising: a problem provision unit (721) for providing a problem description indicating said problem including said first and second parts to be solved; a conversion unit (722) for converting the problem description into a representative operation description showing a set of operations including a) a second plurality of operations to be applied to a fermionic operation portion (711) of the quantum computer (710) and b) a first plurality of operations to be applied to a bosonic operation portion (712) of the quantum computer (710), the first plurality of operations being determined based on the first portion of the problem, and the second plurality of operations being determined based on the second portion of the problem; a control unit (730) for generating control signals for controlling an operation unit (713) of said quantum computer (710) to a) operate said fermionic operation unit (711) such that the state of said quantum elements is manipulated based on said second plurality of operations, and b) operate said bosonic operation unit (712) such that the coupling of said bosonic field to said quantum elements is manipulated based on said first plurality of operations so that the quantum mechanical calculation of the problem is performed. wherein the control unit (730) is further adapted to provide a control signal to control a readout portion (714) of the quantum computer (710) to read out one or more observables after performance of the quantum mechanical calculations that are indicative of a solution to the problem.

7. 7. The apparatus (720) of claim 6, wherein the problem providing unit (721) is adapted to provide a problem description indicating a problem including a portion having a quantity that describes the problem interactively, and the apparatus (720) further includes a conversion unit (720) adapted to convert the interactive portion of the problem description into a problem description including a first and a second portion.

8. 8. The apparatus (720) of claim 7, wherein the problem statement is representable by a quantum mechanical description including fermion-fermion interactions, and the conversion unit is adapted to convert the problem statement into a problem statement 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.

9. 9. The apparatus (720) of claim 7 or 8, wherein the problem description includes at least a plurality of portions representable by a quantum mechanical description including static fermion-fermion interactions as a third portion of the problem, and the conversion unit is adapted to approximate the plurality of portions of the problem by utilizing a restricted random phase approximation.

10. The apparatus (720) according to any one of claims 6 to 9, wherein the problem description refers to a quantum mechanical description, and the transformation unit (722) is adapted to transform the quantum mechanical description of the problem into a rotated frame, in particular by applying a rotated wave approximation, prior to transformation into the representative operation description.

11. The apparatus (720) of any one of claims 7 and 8, wherein the problem description includes as a third part of the problem at least a plurality of parts representable by a quantum mechanical description including interacting clusters with static local fermionic interactions embedded in static nonlocal long-range interactions reaching outside the clusters, and the transformation unit is adapted to approximate the nonlocal long-range parts of the problem by utilizing a Hubbard-Stratonovich transformation.

12. 1. A system (700) for determining a solution to a problem in quantum computing, the system comprising: A quantum computer (710) according to any one of claims 1 to 5; The apparatus (720) of any one of claims 6 to 11, further comprising a result determination unit (723) for determining a solution to the problem based on one or more retrieved observables. A system (700) comprising:

13. A method of providing control signals to control a quantum computer (710) to determine a solution to a problem in a quantum computer computation, the problem comprising a first portion and a second portion, the method comprising using a quantum computer (710) according to any one of claims 1 to 5, the first portion comprising quantities that describe the problem interacting with each other, and the second portion comprising quantities that describe the problem without interacting with each other, the method comprising: providing a problem description indicating the problem to be solved including a first and a second part; converting the problem description into a representative operation description that indicates a set of operations including: a) a second plurality of operations to be applied to a fermionic operation portion (711) of the quantum computer (710); and b) a first plurality of operations to be applied to a bosonic operation portion (712) of the quantum computer (710), the first plurality of operations being determined based on the first portion of the problem, and the second plurality of operations being determined based on the second portion of the problem; Controlling an operation unit (713) of the quantum computer (710) to generate control signals for a) operating the fermionic operation unit (711) such that the state of the quantum element is operated based on the second plurality of operations, and b) operating the bosonic operation unit (712) such that the coupling of a bosonic field to the quantum element is operated based on the first plurality of operations so that the quantum mechanical calculation of the problem is performed; providing control signals to control a readout portion of said quantum computer (710) to read out one or more observables after performing said quantum mechanical calculations that are indicative of a solution to said problem; A method comprising:

14. A problem-solving computer program product, said computer program product comprising program code means for causing an apparatus (720) according to any one of claims 6 to 11 to perform the method according to claim 13.

15. Use of a quantum computer (710) according to any one of claims 1 to 5, a system (700) according to claim 12, a method according to claim 13 and a computer program product according to claim 14 for solving a problem corresponding to an electronic structure problem.

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