Methods for operating a quantum register

Abstract

A method for operating a quantum register (102) may include performing a first read process (201) such that first data (252) representative of a first state of the quantum register (102) is calculated; performing a first drive control (205) for the quantum register (102) in the first state according to a quantum gate (VQC2); performing a second read process (207) such that second data (254) representative of a second state of the quantum register (102) obtained from the first drive control (205); tuning (213) at least one parameter of the quantum gate (VQC2) using the first data (252) and the second data (254) to optimize an objective function (254) dependent on the first data (252) and the second data (254); and performing a second drive control (205) of the quantum register (102) according to the quantum gate (VQC2) obtained from the tuning (213).

Description

[Technical field]

[0001] The present disclosure relates to a method for operating a quantum register. [Background technology]

[0002] The current generation of quantum computers (also called Noisy Intermediate-Scale Quantum, NISQ) has already been applied in the fields of materials research, optimization processes and artificial intelligence. One aspect of materials research is the quantitative development of quantum mechanical systems (herein also called QS for short), e.g. molecules. So far, various methods have been developed to reach the state of QS, some of which are exemplarily described below.

[0003] The so-called Exact Diagonalization (ED) provides an exact mathematical solution of QS by collapsing the complete Hilbert space of all states into eigenstates that can be combined into a thermalized state using matrix diagonalization. However, as QS grows, the resource requirements grow significantly, and even modern supercomputers are not sufficient to obtain a sufficiently exact solution within a reasonable computation time. As an approximation to this, the so-called Density Matrix Renormalization Group (DMRG) reduces the computation time by ignoring higher energy states. Alternative algorithms are based on quantum Monte Carlo methods (QMC) integrated through random variables. Exemplary QMC algorithms include the so-called "Diffusion QMC", "Auxillary-Field-QMC", "Continuous-Time QMC", "Green's Function QMC" or "Hirsch-Fye-QMC". These QMC algorithms have in common that, although the convergence towards the exact solution can certainly be improved at greater computational cost, it is usually only possible within a small parameter domain (e.g., the temperature domain), outside which the so-called "fermion sign problem" prevents convergence.

[0004] These purely classical methods have in common an exponential increase in computational cost as QS increases, which often has to be compensated for by a significant loss of accuracy. This loss of accuracy is mitigated when quantum computers are used based on superposition means. Although the power of quantum computers is indeed constantly increasing, so-called hybrid algorithms, i.e. quantum-classical algorithms, are nevertheless used, which hand over only a part of the calculation to the quantum computer. Quantum-classical algorithms allow to take advantage of the advantages of the two types of computers and, in addition, to reduce the demands on the quantum computer, for example, regarding the number of qubits, the circuit depth and the tolerance to errors during gate operations (the so-called noise or "noise").

[0005] A common representative of hybrid algorithms is the so-called "Variational Quantum Eigensolver" (VQE) and the built-up "Variational Quantum Thermalizer" (VQT). The VQE uses a variational quantum circuit to prepare a so-called starting state in the quantum computer. The quantum computer then measures the energy of said starting state. The classical (i.e. non-quantum mechanical) computer is in charge of optimizing the quantum circuit to converge the starting state towards the basic state of QS (i.e. temperature T=0 K). However, attempts to calculate states of QS above 0 (also called thermalized or excited states) are inaccessible to the VQE.

[0006] The density matrix of the thermalized state (T>0) of QS is given by the Hamiltonian operator

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[0007] The means of calculating such excited states consists in first finding the fundamental state using VQE and then searching for excited states by projecting it from the wave function or by adding additional energy tensioners to the fundamental state. Both require complex quantum circuits that make the calculations difficult and prone to errors. Moreover, a direct measurement of the entropy is not possible with the less complex so-called "thermal field dual state" method, where the system is made large and then collapsed again by a subsequent measurement. To avoid this, it is necessary to calculate the expectation value of ln(ρ) on a quantum computer (for example by using a logarithmic series expansion) and then measure the powers of ρ, which also places high demands on the quantum computer.

[0008] As a generalization of VQE, VQT provides access to the thermal state of the system using an additive machine learning (ML) algorithm trained on a classical probability distribution from which random samples are drawn that are used as input states for VQE. Since quantum circuits do not change entropy, it can be calculated from the classical probability distribution. As with VQE, a variational quantum circuit is optimized and an ML algorithm is trained to minimize the free energy according to relation (2). Such a way of functioning of VQT is already realized with superconducting qubits, but requires a large number of necessary compilations of circuits and a large number of configurations of these circuits. [Means for solving the problem]

[0009] Disclosure of the Invention According to various embodiments, a method is provided for operating a quantum register (QR), comprising: performing a first readout process such that first data is calculated that is representative of (e.g., a function of) a first state (e.g., a superposition state) of the QR (e.g., its probability); performing a first drive control for the QR in the first state or a (e.g., unentangled) state resulting therefrom according to at least one (i.e., one or more) quantum gates (e.g., forming a variational quantum circuit); performing a second readout process (including a readout of the QR) such that second data is calculated that is representative of (e.g., a function of) a second state (e.g., a superposition state) of the QR (e.g., its probability) obtained from the first drive control; tuning at least one (i.e., one or more) parameters of the at least one quantum gate using the first data and the second data to optimize an objective function that depends on the first data and the second data; and performing a second drive control of the QR according to the at least one quantum gate obtained from the tuning. In other words, at least one quantum gate is adjusted by adjusting at least one parameter of the at least one quantum gate, whereby the adjusted at least one quantum gate is used for the second drive control of the QR.

[0010] The method provided herein simplifies the reproducible initialization, simulation and calculation of quantum mechanical states, for example when the quantum mechanical state represents a temperature above 0 K in QS. The method described herein allows the free energy to be calculated efficiently (e.g., according to relation (2)) using quantum algorithms, for example, using a NISQ computer or a so-called "fully error-correcting universal quantum" computer, and further prepares this quantum mechanical state for the measurement of other quantities.

[0011] The methods described herein can be implemented and performed in a resource-friendly and cost-effective manner, for example, because they do not necessarily scale exponentially with the size of QS, and require only a fraction of the resources of a quantum computer (e.g., comparable to VQE). Compared to VQT, the methods described herein incur significantly lower compilation costs, can better map classical statistical distributions, and can be implemented more simply and hardware-efficiently. This is possible, for example, because of the reduced coupling between the CPU and the QPU and the high tolerance to noise of the quantum computer. In more simple terms, the methods described herein open up the possibility of VQT at a cost comparable to VQE.

[0012] Various examples are given below.

[0013] Example 1 presents a method for operating the above-mentioned QR.

[0014] Example 2 is a method according to Example 1, in which the first readout process includes reading out the QR (e.g., its superposition state) or reading out (before or simultaneously with the second readout process) an additional QR (e.g., its superposition state) entangled with the QR (e.g., its first state and / or the state before the first drive control). In the former, resource costs are reduced, for example by requiring fewer qubits and / or less circuit depth. In the latter, intermediate measurements can be omitted.

[0015] Example 3 is a method according to example 1 or 2, further comprising: performing an additional first drive control of QR according to at least one additional quantum gate (which forms, for example, a variational quantum circuit) preferably when QR is in an initial state, where the first state of QR is based on the additional drive control (for example, directly results from the additional drive control), and the adjustment comprises adjusting or setting unchanged at least one parameter of the at least one additional quantum gate using the first data and the second data; and performing an additional second drive control of QR according to the at least one additional quantum gate obtained from the adjustment. That is, in other words, by adjusting at least one parameter of the at least one additional quantum gate, the at least one additional quantum gate is adjusted, whereby the adjusted at least one additional quantum gate is used for the additional second drive control of QR. This makes it easier to simulate more complicated QS (for example, its thermalized state) and / or to prepare classical probability distributions.

[0016] Example 4 is the method according to example 3, wherein the at least one additional quantum gate has fewer parameters than the at least one quantum gate and / or fewer QR qubits are driven (e.g., transitioned from an initial state) according to the at least one additional quantum gate than according to the at least one quantum gate, thereby reducing resource costs (e.g., computation time).

[0017] Example 5 is a method according to any one of Examples 1 to 4, wherein at least one quantum gate and / or at least one additional quantum gate is configured to entangle the QR and / or to transition the QR to a preferably non-entangled or at least partially entangled superposition state (which is read out, for example, in the first readout process and / or the second readout process). This makes it easier to simulate more complex QS (e.g., its thermalization state). The at least partially entangled superposition state can be, for example, a result of entanglement of the QR. The set of entangled superposition states is, for example, a subset of the superposition states.

[0018] Example 6 is the method according to any one of Examples 1 to 5, wherein the tuning comprises tuning one or more parameters for each qubit of the QR and changing the state of the qubit during the drive control according to the parameters, which facilitates obtaining a more accurate result of the calculation.

[0019] Example 7 is the method according to any one of Examples 1 to 6, wherein the first data and / or the second data represent a superposition state of the QR or represent a probability of a ground state that is evident from the superposition state (preferably by a respective readout process), which makes it easier to simulate more complex QS (e.g. its thermalized state).

[0020] Example 8 is the method according to any one of Examples 1 to 7, wherein the objective function represents a physical state quantity and / or the adjustment is based on an output of the objective function that depends on the first data and the second data and / or an output of the objective function that is minimized by the first data and the second data. This makes it easier to simulate more complex QS (e.g., its thermalization state).

[0021] Example 9 is the method according to any one of Examples 1 to 8, wherein the second data is independent of the first data or is dependent on the result of the first readout process (or the first data). This makes it easier to simulate more complex QS or to better take into account their properties and / or to simplify or configure the tuning process more efficiently. For example, the second data may be dependent on the first data, for example if the second data has one or more descriptions that are a function of the first data (or a description thereof). For example, if the first readout process results in a qubit being in state |1), the second readout process will yield a different result than if the first readout process results in a qubit being in state |0).

[0022] Example 10 is the method according to any one of Examples 1 to 9, further comprising: calculating a description of a physical quantity (e.g., QS) based on the result of the second drive control and / or the additional second drive control, the description preferably depending on or at least different from the output of the objective function obtained from the optimization, thereby facilitating the evaluation of the physical quantity (observable) at the calculated thermal state.

[0023] Example 11 is a (eg, non-quantum mechanical) controller configured to perform a method according to any one of examples 1 to 10.

[0024] Example 12 is a computer program configured to cause a (e.g. non-quantum mechanical) processor executing the computer program to perform a method according to any one of Examples 1 to 10.

[0025] Example 13 is a computer readable medium having stored thereon instructions for causing an instruction executing (e.g., non-quantum mechanical) processor to perform the method according to any one of Examples 1 to 10. Examples 11 to 13 facilitate performing the method.

[0026] In the drawings, like reference characters generally refer to the same parts throughout the various views. The drawings are not necessarily drawn to scale, emphasis instead being placed upon generally illustrating basic principles of the invention. In the following description, various aspects are described with reference to the following drawings:

[0027] FIG. 1 shows in a schematic diagram the structure and operation of a quantum processor according to various embodiments, FIGS. 2 and 3 and FIGS. 6-8 and 10 show in various schematic diagrams respective methods according to various embodiments, and FIGS. 4A and 4B and FIGS. 5 and 9 show in various schematic diagrams respective operational sequences according to various embodiments. [Brief description of the drawings]

[0028] [Figure 1] 1 is a schematic diagram illustrating the structure and operation of a quantum processor in accordance with various embodiments. [Diagram 2] FIG. 2 is a schematic diagram illustrating a method according to one embodiment. [Diagram 3] FIG. 2 is a schematic diagram illustrating a method according to one embodiment. [Figure 4A] FIG. 2 is a schematic diagram illustrating an operation sequence according to one embodiment. [Figure 4B] FIG. 2 is a schematic diagram illustrating an operation sequence according to one embodiment. [Diagram 5]FIG. 2 is a schematic diagram illustrating an operation sequence according to one embodiment. [Figure 6] FIG. 2 is a schematic diagram illustrating a method according to one embodiment. [Figure 7] FIG. 2 is a schematic diagram illustrating a method according to one embodiment. [Figure 8] FIG. 2 is a schematic diagram illustrating a method according to one embodiment. [Figure 9] FIG. 2 is a schematic diagram illustrating an operation sequence according to one embodiment. [Figure 10] FIG. 2 is a schematic diagram illustrating a method according to one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0029] The following detailed description refers to the accompanying drawings, which show, for illustration purposes, specific details and aspects of the present disclosure that may be used to implement the present invention. Other aspects may be used and structural, logical and electrical changes may be made without departing from the scope of the present invention. Various aspects of the present disclosure are not necessarily mutually exclusive, since some aspects of the present disclosure may be combined with one or more other aspects of the present disclosure to form new aspects.

[0030] Various examples are described in detail below.

[0031] FIG. 1 is a schematic diagram illustrating the structure and operation of a quantum processor ("quantum process unit" or QPU for short) 100 according to various embodiments. The QPU includes a QR 102 and a driver 104. The concept of a "quantum register" (QR) is a register that stores multiple (e.g., n) quantum bits (herein illustratively referred to as q1 through q n1 illustrates an apparatus that may implement a QR 102 (referred to as a QR 102). Exemplary components of the QR 102 include an ion trap, a plurality of (e.g., superconducting) circuit resonators, a plurality of quantum dots, an optical system, a laser, an electromagnetic coil, and the like. The driving device 104 is configured to drive (e.g., actuate) the QR 102, for example, according to a sequence 106 (also referred to as an operation sequence). An exemplary process of the operation sequence 106 includes starting QR 101 (i.e., moving QR to an initial state Z0), driving control QR 103, and / or reading QR 102 110. In the initial state Z0 of QR 102, each quantum bit may be unentangled and / or in a ground state (exemplarily |0)), but this need not necessarily be the case for all quantum bits.

[0032] The specific implementation of the actuator 104 or the operation sequence 106 depends on the type and architecture of the qubit. The actuator 104 may have one or more transducers configured to interact with the QR 102 or its environment, e.g., to change and / or detect at least its state Z. Exemplary implementations of actuator transducers include actuators (e.g., adjustment elements), sensors, transceivers, etc. Exemplary actuator transducers are configured to transmit and / or detect one or more of optical radiation, magnetic fields, electric fields, electric charges, particle radiation to and / or by the QR 102. The QPU is further a component of a quantum computer having a housing environment for at least the QPU and control electronics.

[0033] The term "qubit" refers to a two-state quantum system that is mathematically represented by two basis vectors in a two-dimensional Hilbert space (here illustratively expanded by |0) and |1). The implementation of a qubit may be of different types and architectures. Examples include energy levels in a trapped ion, polarization states of a photon, spins in quantum dots or silicon, and energy levels of a superconducting circuit resonator.

[0034] Overall, the drive control 103 of the QR 102 is adjusted to excite a change in state of the QR 102 (also called a state transition). The drive control 103 of the QR 102 is performed according to one or more quantum gates 108 (see also FIG. 5). The concept of a "quantum gate" (also called a quantum logic gate or gate) represents the quantum mechanical analogue to a logic gate of an electric circuit. It should be noted that the quantum gate 108 corresponds to a process of influence on the QR 102 that changes the state Z of the QR 102, for example the state Z of one or more qubits of the QR 102. By using the quantum gate 108, unitary functions can be realized in a similar way to logic gates, specifically their Boolean functions. Mathematically, a quantum gate is a gate that converts a qubit from a state |x) to a state |x|

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[0035] The concept of "quantum algorithm" (also called quantum circuit) generally refers to a process (e.g. quantum gate) of interaction with QR102 or a set of processes within QR102 that triggers or at least excites a change in state Z of QR102 (e.g. at least one qubit thereof). For better understanding, quantum circuits are depicted as circuit diagrams, similar to electronic circuits, with one axis (here, from left to right) representing the passage of time. As with electrical circuits, the sum of multiple quantum circuits can also be considered as a quantum circuit. From this perspective, the entire sequence of operations 106 can be understood as a quantum circuit, but the components of the quantum circuit can also be understood as processes, e.g. drive control 103 or readout 110. From the data processing point of view, each quantum circuit transfers a state of QR102 (also called input state of the quantum circuit) to another state of QR102 (also called output state of the quantum circuit). Here, the output state of the drive control 103 process (also called drive control process 103) can be, for example, |x i )|x j ) (1≦i,j≦n), but not necessarily with entangled qubits. If the output state of the quantum circuit is a superposition state (e.g., with entangled qubits), the quantum circuit is also referred to herein as a starting circuit (or a preparation circuit). In general, the superposition state may, for an individual qubit, have a superposition of the states of the individual qubits, and / or, for multiple qubits, have the entanglement of multiple qubits and / or a superposition of their states. Thus, the starting circuit may be configured to transition the qubits into a superposition state, which does not necessarily result in entanglement of the qubits, but is still entirely possible.

[0036] The starting circuit is preferably configured to vary the square of the magnitude of the amplitude and the phase of the qubit. The quantum circuit optionally comprises or consists of one or more quantum gates (e.g. multi-qubit quantum gates) parameterized with at least one parameter (also called variation parameter) (also called variation circuit or VQC for short in the case of the starting circuit). The starting circuit may optionally comprise one or more non-parameterized quantum gates and / or one or more multi-qubit quantum gates. The parameterization of the quantum circuit is described here by a vector (also called parameter vector in this case) for notational simplicity, but may, but does not necessarily have more than one parameter as a component. The output state of a parameterized quantum circuit is thus a function of the parameter vector, the vector components being the parameters of the quantum circuit.

[0037] The process of reading 110 of the QR 102 (also referred to as the readout process 110) involves detecting, by sensor technology (i.e., using a sensor), the state of the QR 102, which may be, for example, a superposition state and / or a result of the drive control process 103. During the readout 110, the state of the QR 102 is detected as a measurement-based ground state of the readout process (here, exemplarily Z A) into the state of the sensor 102. To improve the accuracy of the expectation, the readout process 110 (also called quantum mechanical measurement process or measurement for short) can be repeated several times, for example for each parameter vector and / or each term of the Hamiltonian. The input states of the readout process 110 can be the output states of the drive control process 103. The sensor can be part of a measurement chain with a corresponding infrastructure (including, for example, a processor, a storage medium and / or a bus system, etc.). The measurement chain can be configured to drive and control the sensor, process the detected state as an input quantity and, based on this, output data representative of the input quantity. The measurement chain is realized or can be realized, for example, by the drive 104. The sensor can have one or more measurement bases, one of which is the measurement base for performing the readout process 110. In simple terms, the measurement base is a property of the sensor on which the readout process 110 is performed. Mathematically speaking, the measurement base is the expansion of the Hilbert space of states onto which the QR state is projected during the readout. A QPU may implement one or more measurement bases, depending on the technical implementation. Optionally, a QPU may implement multiple measurement bases, thereby allowing the choice of measurement base to be parameterized instead of and / or in addition to parameterized quantum gates.

[0038] FIG. 2 shows a schematic diagram of a method according to various embodiments 200 that can be performed, for example, by a controller 202. The concept of a "controller" can be understood as any type of entity (e.g., processor) that can process data or signals. The data or signals can be processed according to at least one (i.e., one or more) special functions executed therein by, for example, the controller or processor. The controller, for example, its processor, can include or consist of analog circuits, digital circuits, logic circuits, microprocessors, microcontrollers, central processing units (CPUs), graphic processing units (GPUs), digital signal processors (DSPs), programmable gate array (FPGA) integrated circuits, or any combination thereof. Any other manner of realizing the respective functions described in detail herein can also be understood as a processor or logic circuit. One or more of the individual method steps described herein can be performed (e.g., realized) by one or more special functions executed by the processor. The processor of the controller can be, for example, a classical (i.e., non-quantum mechanical, for example, transistor-based) processor.

[0039] A process sequence 602 of the method (also referred to as optimization process sequence 602) is shown. The process sequence 602 comprises an operation sequence 106 that can be implemented by a QPU (e.g., according to embodiment 100), and comprises (e.g., exactly one) adjustment process 213 that can be implemented, for example, by a controller 202. The QPU operates on multiple qubits (here, exemplarily designated q1 through q n(Let K be the number of iterations of the QPU). It can be appreciated that not all of the components of the tuning process 213 necessarily have to be executed by a classical processor, but rather can be executed at least in part by the QPU itself, depending on the performance of the QPU. The method can optionally include repeating the optimization process sequence 602 multiple times (e.g., K times) (see also FIG. 6).

[0040] The operation sequence 106 begins with a first execution 201(m S or a first read process 201), thereby calculating 204 first data 252 representing a first state 204a (for example, Z1=Z(t1)) of the QR 102 (at a first time t1), performing drive control 205 (also referred to as start preparation 205) of the QR 102 in the first state 204a, and performing a second execution 207 (m E or second readout process 207) to calculate 209 second data 254 representative of a second state 204b (here exemplarily Z2=Z(t2)) of QR102 (for example at a second time t2>t1) obtained from the drive control 205. Depending on the concrete implementation (see also Fig. 4A and Fig. 4B), the first state 204a is a ground state (i.e. a state without superposition) for example if the state is an output state of the first readout process 201 or at least is based on it, or a superposition state for example if the state is an output state of an additional drive control 211 of QR102 (also referred to as thermalization 211) or at least is based on it. If the operation sequence 106 comprises a thermalization 211 of the QR 102, preferably in the initial state and / or before the first time point t1, this facilitates initializing the quantum mechanical state at a temperature above 0 K, since in this case the capabilities of the QPU are utilized. The readout process 201 and the second readout process 207 can be performed, for example, according to the same measurement basis of the quantum gate 108.

[0041] The initiation preparation 205 may include one or more quantum gates 108 (e.g., per quantum bit) and / or at least one parameter (e.g., per quantum bit).

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[0042] For each optimized process sequence 602, a parameter vector of that optimized process sequence 602 (also called a tuning process)

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[0043] The tuning process 213 can be performed, for example, such that an objective function dependent on the first data and the second data is optimized, e.g., such that the output is minimized. The objective function (e.g., the output) can represent, for example, a QS, e.g., a state quantity, which will be described in more detail below.

[0044] FIG. 3 shows a schematic diagram of a method according to various embodiments 300 that can be implemented, for example, based on a variational method (e.g., Rayleigh-Ritz method) using a control device 202, which is exemplarily configured here as a CPU. The embodiment 300 can be configured similarly to the embodiment 200, where the output 302a of the objective function 302 can be expressed, for example, as a function of the state quantity (e.g., free energy F) of the thermalized QS, preferably the entropy S and energy E of the thermalized QS, and more preferably according to the relation (2). In this case, the first data 252 represents the entropy calculated based on the QPU measurements, and the second data 254 represents the energy of the thermalized QS, calculated based on the QPU measurements. The exemplary description here of the free energy (e.g., as an output of the objective function) can be applied to any other state quantity of the (e.g., thermalized) QS as well.

[0045] The optimization of the objective function 302 can be performed by a so-called optimization algorithm 304, which determines, based on the output 302a of the objective function 302, the parameter vector of the action sequence 106.

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[0046] The optimization process sequence 602 is

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[0047] 4A and 4B show schematic diagrams of operation sequences 106 according to various embodiments 400a, 400b, which can also be realized, for example, in the embodiments 100 to 300, with the common feature that the operation sequence 106 (also called "Full Quantum Variational Thermalizer" or FQVT for short) comprises two process pairs, each of which comprises a VQC (VQC1 or VQC2) and a subsequent readout process 110. The VQC of each process pair is configured to provide, as an output state (state of the qubit), a superposition of multiple quantum states (also called superposition states), each having a different amplitude. The readout process 110 of each process pair can be configured to operate on the superposition and move it to one basis state.

[0048] VQC1 and VQC2 can be executed sequentially. VQC1 is the first parameter vector

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[0049] According to embodiment 400a, the first read process (m S ) includes detecting (measuring) the output state of VQC1, that is, reading QR102 according to VQC1 after drive control is performed. The output state of VQC1 is measured m S The FQVT 106 can be run multiple times for each optimization process sequence 602, where the measurements m S Statistics are collected on the output of FQVT106. After FQVT106 is repeated at high frequency, the measurement m S From the measurement m in the new round S The probability p of obtaining ground state i in i The probability p i Based on this, the entropy of a quantum mechanical system can be expressed, for example, by the following relation:

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[0050] Furthermore, the operation sequence 106 according to the embodiment 400a uses VQC2 to perform the first read process m S to superposition as the second state 204b.

[0051] If the QPU is unable to perform the readout process 110 (also referred to as intermediate measurement) between two VQCs, or if the intermediate measurement is not performed for other reasons, the operation sequence 106 according to embodiment 400b can be used. According to embodiment 400b, the available qubits have multiple groups, in which a first group of qubits (also referred to as logical master registers) and a second group of qubits (also referred to as logical auxiliary registers or accessory qubits) are configured to be mutually entangled. The master registers (q1 to q n ) and auxiliary registers (here, a1 to a n For ease of understanding, the auxiliary registers 102 and 103 are treated herein as (logically) separate QRs 102, but it should be understood that they may, but do not necessarily, be part of the same (physically) QR 102. The auxiliary register has at least as many qubits as the main register, e.g., a multiple of n qubits.

[0052] According to embodiment 400b, only the main register is driven and controlled according to VQC1 and VQC2, and m E The operation sequence 106 according to embodiment 400b further includes entangling 410 (also referred to as entanglement process 410) the output state of VQC1 (which may be, for example, a superposition state) with an auxiliary register. The entanglement process 410 may include, for example, entangling each qubit of the master register with (for example, exactly) one qubit of the auxiliary register using at least one CNOT gate. The output of the entanglement process 410 includes multiple (for example, n) pairs of mutually entangled qubits, each pair including a qubit from the master register and a qubit from the auxiliary register.

[0053] Furthermore, the operation sequence 106 according to the embodiment 400b includes transitioning (only) the state of the (for example) master register resulting from the entanglement process 410 (which is, for example, a stacked state) to stacked as the second state 204b using VQC2. In this case, the first read process m S includes detecting (measuring) the state 214b of the auxiliary register resulting from the entanglement process 410. The state 214b of the auxiliary register is determined by the measurement m S , we can use the probability p of the quantum bit at the end of the sequence of operations 106 to transition to the ground state with probability p (given by the amplitude of the ground state here). In this case, by measuring (e.g., jointly) all the quantum bits at the end of the sequence of operations 106, we can obtain the energy (q i ) and entropy (a i In one example, the first read process m (of the auxiliary register) S (in time), for example, the second read process m E Immediately before or after the second read process m E At the same time, or for example, a second read process m E This is done immediately after.

[0054] 5 shows a schematic diagram of an operation sequence 106 according to various embodiments 500, illustrating an example implementation of embodiment 400a for two qubits. t (θ j ) is, for example, θ which indicates the rotation angle j represents the rotation around the t-axis (t=x, y or z) depending on Φ i or

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[0055] In one embodiment, for two qubits, the Hamiltonian operator is:

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[0056] 6 is a schematic diagram of a method according to various embodiments 600 to illustrate additional exemplary implementations of embodiments 100 to 500. The method may optionally include repeating the optimization process sequence 602 multiple times (e.g., K times) until, for example, a number of rounds k (also referred to as a round counter) reaches a target number K or until the variation of the output of the objective function falls below a threshold. If the criteria are met, the parameter vectors updated in the last run of the optimization process sequence 602 are

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[0057] The or each optimization process sequence 602 may generate a parameter vector based on the results of the tuning process 213.

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[0058] Optionally, the or each optimization process sequence 602 may include performing the operation sequence 106 multiple times, for example, until a criterion is met, for example, until the number of rounds r reaches a target number R. In this case, the adjustment process 213 may be based on first and second data from the multiple operation sequences 106. The method optionally begins at the start of the optimization process sequence 602 by selecting 601 a parameter vector

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[0059] In a first exemplary implementation (specifically showing a segmentation optimization), the method (e.g. for optimizing the free energy) comprises a number of stages, in each of which one or more optimization process sequences 602 are performed. See FIG. 8, which specifically shows the first exemplary implementation in a schematic diagram 800 similar to embodiment 600. In a first stage 801 of the stages (specifically showing a VQC1 optimization with a simplified Hamiltonian), the operation sequence 106 consists of:

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[0060] In a second exemplary implementation (specifically an approximate FQVT), the method includes shrinking VQC1 and not changing all qubits variationally. For this, see FIG. 9, which shows the first exemplary implementation in a schematic diagram 900 similar to embodiment 400a. In other words, VQC1 is configured to change only a part of QR102 and / or to change fewer qubits than VQC2. As a result, only a small number of states exist after entropy measurement. Thus, the approximate FQVT here only considers the lowest excited state in energy, and therefore requires much fewer parameters, which also reduces the energy requirement and error vulnerability of the method. Especially for large systems, such modifications significantly reduce the required resources (e.g., computation time) without significant accuracy loss.

[0061] 7 shows a schematic diagram of a method according to various embodiments 700, showing the output 701 of an objective function (here illustratively the free energy) that depends on a round counter 703. Curve 706 shows the method described herein compared to theoretical values ​​(curve 702), ideal transitions with precisely calculated probabilities for each state (curve 704), and a Fake Vigo Simulator (curve 708) that uses an error model derived from IBM's real quantum chip "Vigo". The solid lines show the average of each series of trials, and the surface area shows the error range defined by the standard deviation.

[0062] In a first embodiment, the method (e.g., each optimization process sequence) comprises performing the first read process and / or the second read process at least 100 times (e.g., at least 1000 times, e.g., at least 10000 times, e.g., at least 30000 times). In the first or second embodiment, the output 701 of the objective function is calculated using the "Limited Memory BFGS Algorithm" ("L_BFGS_B") of Qiskit as optimization algorithm, where a Hamiltonian operator according to relation (3) and an operation sequence 106 according to embodiment 500 with β=1 are used. In a second or third embodiment, the method according to embodiment 600 is performed at least 20 times, where a parameter vector

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[0063] In a fourth embodiment, the method described herein (e.g. its FQVT) is used to solve the so-called quantum impurity problem (also called "quantum impurity problem"). Thus, in the framework of the so-called Dynamical Mean Field Theory (DMFT), the properties of materials with strongly correlated electrons can be calculated. This includes, for example, materials with elements containing d- or f-electrons and / or materials with potentials applied, for example, in superconductivity, electrolysis, batteries, (quantum) sensor devices or fuel cells. In the fifth embodiment or the second embodiment, the optimization algorithm takes as input a gradient

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[0064] 10 shows a schematic diagram of a method according to various embodiments 1000 that can be implemented, for example, based on a variational scheme (e.g., Rayleigh-Ritz method) using, for example, the control device 202, here exemplarily configured as a CPU. The method can be configured according to one or more of the embodiments 100 to 900, for example, at least according to the embodiment 600 (also referred to as FQVT optimization 600). QR 102 is an output vector output by FQVT optimization 600.

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[0065] Although specific embodiments have been illustrated and described herein, those skilled in the art will recognize that the specific embodiments illustrated and described may be modified into various alternative and / or equivalent implementations without departing from the scope of protection of the present invention. This application is intended to cover any adaptations or variations of the specific embodiments described herein. Therefore, the present invention is limited only by the claims and their equivalents.

Claims

1. A method for operating a quantum register (102), comprising: performing a first read process (201) such that a first datum (252) representative of a first state of said quantum register (102) is calculated; At least one quantum gate (VQC ２ performing a first drive control (205) on the quantum register (102) in the first state according to performing a second read process (207) such that second data (254) representative of a second state of the quantum register (102) obtained from the first drive control (205) is calculated; said at least one quantum gate (VQC) using said first data (252) and said second data (254) to optimize an objective function that depends on said first data (252) and said second data (254). ２ ) adjusting (213) at least one parameter of The at least one quantum gate (VQC) obtained from the adjustment (213). ２ ) performing a second drive control (205) of the quantum register (102) according to the The method includes:

2. The first read process (201) comprises: reading the quantum register (102); or reading out an additional quantum register entangled by said quantum register (102); The method of claim 1 , comprising:

3. At least one additional quantum gate (VQC １ ), wherein the first state of the quantum register (102) is based on the additional drive control (211), and the adjustment (213) includes adjusting the at least one additional quantum gate (VQC) using the first data (252) and the second data (254). １ ) adjusting or setting unchanged at least one parameter of The at least one additional quantum gate (VQC １ ) performing an additional second drive control (211) of the quantum register (102) according to The method of claim 1 or 2, further comprising:

4. The at least one additional quantum gate (VQC １ ) according to said at least one quantum gate (VQC ２ 4. The method of claim 3, wherein fewer qubits of the quantum register (102) are driven according to

5. The at least one quantum gate (VQC ２ ) and / or said at least one additional quantum gate (VQC １ 5. The method of claim 1, wherein the quantum register (102) is configured to transition to an unentangled superposition state or an at least partially entangled superposition state.

6. The method of claim 1 , wherein the objective function represents a physical state quantity to be minimized.

7. 7. The method according to claim 1, wherein the adjustment (213) is based on an output (701) of the objective function that depends on the first data (252) and the second data (254) and / or on an output (701) of the objective function that is minimized by the first data (252) and the second data (254).

8. A control device (202) configured to implement the method according to any one of claims 1 to 7.

9. A computer program arranged to cause a processor, when executed by said computer program, to carry out the method according to any one of claims 1 to 7.

10. A computer readable medium having stored thereon instructions configured to cause a processor executing the instructions to perform a method according to any one of claims 1 to 7.

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