How to operate 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] This disclosure relates to a method for operating a quantum register. [Background technology]

[0002] Current-generation quantum computers (also known as NISQ: Noisy Intermediate-Scale Quantum) are already being 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 (hereinafter abbreviated as QS), such as molecules. Various methods have been developed to reach the QS state, some of which are described exemplified below.

[0003] So-called exact diagonalization (ED) provides an exact mathematical solution to QS by using matrix diagonalization to collapse the complete Hilbert space of all states into eigenstates that can be combined into a thermal state. However, as QS increases, the required resources increase dramatically, and even modern supercomputers are not sufficient to obtain a solution with sufficient rigor within a reasonable computation time. As an approximation of this, the so-called density matrix renormalization group (DMRG) reduces computation time by ignoring higher energy states. Alternative algorithms are based on quantum Monte Carlo (QMC) methods integrated through random variables. Exemplary QMC algorithms include so-called "diffusion QMC," "auxillary-field QMC," "continuous-time QMC," "Green's function QMC," or "Hirsch-Fye QMC." These QMC algorithms can certainly improve convergence toward an exact solution with increased computational cost, but they generally only improve within a small parameter domain (e.g., the temperature domain), and outside of that, the so-called "fermion coding problem" prevents convergence.

[0004] These purely classical methods share the common characteristic of exponentially increasing computational costs as the QS increases, which is often compensated for by a significant loss of precision. This loss of precision is mitigated when quantum computers are used, based on superposition mechanisms. Although the capabilities of quantum computers are certainly constantly increasing, so-called hybrid algorithms, i.e., quantum-classical algorithms, are still used, which hand over only a portion of the computation to the quantum computer. Quantum-classical algorithms leverage the advantages of both types of computers and further reduce the demands on quantum computers regarding, for example, the number of qubits, circuit depth, and tolerance to errors during gate operations (so-called noise or "noise").

[0005] Common examples of hybrid algorithms include the so-called "Variational Quantum Eigensolver" (VQE) and the "Variational Quantum Thermalizer" (VQT) built upon it. The VQE utilizes a variational quantum circuit to prepare the so-called starting state in a quantum computer. The quantum computer then measures the energy of this starting state. A classical (i.e., non-quantum mechanical) computer is responsible for optimizing the quantum circuit to converge the starting state toward the fundamental state of QS (i.e., temperature T=0K). However, attempts to compute QS states above 0 (also called thermal states 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 involve first finding the fundamental state using VQE, and then searching for excited states by projecting that fundamental state from the wave function, or by adding an additional energy tensioner to that fundamental state. Both methods require complex quantum circuits that make calculations difficult and are prone to errors. Furthermore, in the less complex so-called "hot-field double-state" method, where the system is enlarged and then collapsed again by subsequent measurements, direct measurement of entropy is impossible. To avoid this, it is necessary to calculate the expectation value of ln(ρ) in the quantum computer (for example, using a logarithmic series expansion), and then measure the power of ρ, which also places a high demand on the quantum computer.

[0008] As a generalization of VQE, VQT provides access to the thermal state of a system using an additional machine learning (ML) algorithm trained on a classical probability distribution. From this probability distribution, random samples are drawn that are used as input states for VQE. Since quantum circuits do not change entropy, entropy can be calculated from the classical probability distribution. Similar to VQE, the variational quantum circuit is optimized and the ML algorithm is trained to minimize the free energy according to relation (2). Such functional methods of VQT have already been realized by superconducting qubits, but a large number of necessary compilations of the circuits and a large number of configurations of these circuits are required.

Means for Solving the Problems

[0009] Disclosure of the Invention According to various embodiments, a method for operating a quantum register (QR) includes performing a first readout process such that first data representing a first state (e.g., superposition state) of the QR (e.g., its probability) is calculated; performing first drive control on the QR in the first state or a state resulting therefrom (e.g., an entangled-free state) 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 reading the QR) such that second data representing a second state (e.g., superposition state) of the QR (e.g., its probability) obtained from the first drive control is calculated; adjusting at least one (i.e., one or more) parameter of at least one quantum gate using the first data and the second data to optimize an objective function dependent on the first data and the second data; and performing second drive control of the QR according to at least one quantum gate obtained from the adjustment. That is, in other words, by adjusting at least one parameter of at least one quantum gate, at least one quantum gate is adjusted, whereby the adjusted at least one quantum gate is used for the second drive control of the QR.

[0010] By the above method provided in this specification, for example, when the quantum mechanical state represents a temperature above 0K of QS, the reproducible initialization, simulation, and calculation of the quantum mechanical state are simplified. The above method described in this specification uses a quantum algorithm to efficiently calculate the free energy (e.g., according to Equation (2)), for example, using a NISQ computer or a so-called "fully error-corrected universal quantum" computer, and further enables the preparation of this quantum mechanical state for the measurement of other quantities.

[0011] The method described in this specification is, for example, resource-friendly and cost-efficiently realizable and executable. This is because the method does not necessarily scale exponentially with the size of QS and requires only a small amount of resources of a quantum computer (e.g., equivalent to VQE). Compared with VQT, the method described in this specification causes only a significantly lower compilation cost, can map the classical statistical distribution well, and can be realized more simply and hardware-efficiently. This is made possible because, for example, the coupling degree between the CPU and the QPU becomes small and a high tolerance to the noise of the quantum computer is achieved. More plainly speaking, the method described in this specification opens up the possibility of VQT at a cost equivalent to VQE.

[0012] The following shows various examples.

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

[0014] Embodiment 2 is a method according to Embodiment 1, wherein the first readout process includes reading a QR (e.g., its superposition state), or reading an additional QR (e.g., its superposition state) entangled with a QR (e.g., its first state and / or state before the first drive control) (before or simultaneously with the second readout process). 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, wherein the above method is further modified to preferably perform an additional first drive control of QR according to at least one additional quantum gate (which, for example, forms a variational quantum circuit) when QR is in an initial state, where the first state of QR is based on the additional drive control (for example, directly arising from the additional drive control), and the tuning includes tuning or setting invariant at least one parameter of at least one additional quantum gate using first and second data, and performing an additional second drive control of QR according to at least one additional quantum gate obtained from the tuning. In other words, at least one additional quantum gate is tuned by tuning at least one parameter of at least one additional quantum gate, thereby the tuned at least one additional quantum gate is used for an additional second drive control of QR. This facilitates the simulation of more complex QS (e.g., its thermalized state) and / or facilitates the preparation of classical probability distributions.

[0016] Example 4 is a method according to Example 3, wherein at least one additional quantum gate has fewer parameters than at least one quantum gate, and / or, fewer qubits with a QR than that of at least one quantum gate are driven and controlled (e.g., transitioned from an initial state) according to at least one additional quantum gate. This reduces 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 transition to preferably an entangled superposition state or at least partially entangled superposition state (these are read, for example, in a first readout process and / or a second readout process). This facilitates the simulation of more complex QS (e.g., its thermalized state). The at least partially entangled superposition state may, for example, be the result of entanglement of the QR. The set of entangled superposition states is, for example, a subset of superposition states.

[0018] Example 6 is a method according to any one of Examples 1 to 5, wherein the tuning involves tuning one or more parameters for each qubit of the QR, and the state of the qubit is changed during drive control according to those parameters. This makes it easier to obtain more accurate results from the calculations.

[0019] Example 7 is a method according to any one of Examples 1 to 6, wherein the first data and / or the second data represent the superposition state of the QR, or (preferably by their respective readout processes) the probability of the ground state evident from the superposition state. This facilitates the simulation of more complex QS (e.g., its thermal state).

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

[0021] Example 9 is a method according to any one of Examples 1 to 8, wherein the second data is independent of the first data or depends on the result of the first readout process (or the first data). This facilitates the simulation of more complex QS or better consideration of its characteristics, and / or simplification or more efficient configuration of the tuning process. For example, the second data may depend on the first data if, for example, the second data has one or more descriptions that are functions of the first data (or its description). For example, if the result of the first readout process is that the qubit is in state |1), the second readout process will yield a different result than if the result of the first readout process was that the qubit is in state |0).

[0022] Example 10 is a method according to any one of Examples 1 to 9, wherein the above method further comprises calculating a description of a physical quantity (e.g., QS) based on the results of a second drive control and / or an additional second drive control, wherein the description preferably depends on, or at least differs from, the output of the objective function obtained from optimization. This facilitates the evaluation of the physical quantity (observable quantity) in the calculated thermal state.

[0023] Example 11 is a control device (e.g., non-quantum mechanical) configured to perform the method according to any one of Examples 1 to 10.

[0024] Example 12 is a computer program configured to cause a processor (e.g., a non-quantum mechanical one) that executes the computer program to perform any one of the methods described in Examples 1 to 10.

[0025] Example 13 is a computer-readable medium that stores instructions for a processor (e.g., a non-quantum mechanical one) to execute the method according to any one of Examples 1 to 10. Examples 11 to 13 facilitate the execution of the method.

[0026] In the drawings, similar reference numerals generally refer to the same parts throughout the various drawings. The drawings are not necessarily drawn to scale, but rather the emphasis is on illustrating the basic form of the present invention in general. In the following description, various embodiments will be described with reference to the following drawings.

[0027] Figure 1 shows schematic diagrams of the structure and operation methods of quantum processors according to various embodiments, Figures 2 and 3, and Figures 6 to 8 and 10 show schematic diagrams of the respective methods according to various embodiments, and Figures 4A and 4B, and Figures 5 and 9 show schematic diagrams of the respective operation sequences according to various embodiments. [Brief explanation of the drawing]

[0028] [Figure 1] This is a schematic diagram showing the structure and operation method of a quantum processor according to various embodiments. [Figure 2] This is a schematic diagram illustrating a method according to one embodiment. [Figure 3] This is a schematic diagram illustrating a method according to one embodiment. [Figure 4A] This is a schematic diagram showing the operation sequence according to one embodiment. [Figure 4B] This is a schematic diagram showing the operation sequence according to one embodiment. [Figure 5]This is a schematic diagram showing the operation sequence according to one embodiment. [Figure 6] This is a schematic diagram illustrating a method according to one embodiment. [Figure 7] This is a schematic diagram illustrating a method according to one embodiment. [Figure 8] This is a schematic diagram illustrating a method according to one embodiment. [Figure 9] This is a schematic diagram showing the operation sequence according to one embodiment. [Figure 10] This is a schematic diagram illustrating a method according to one embodiment. [Modes for carrying out the invention]

[0029] The following detailed description relates to the accompanying drawings illustrating specific details and embodiments of the present disclosure that may enable the execution of the present invention. Structural, logical, and electrical modifications can be carried out using other embodiments without departing from the scope of the rights protected by the present invention. The various embodiments of the present disclosure are not necessarily mutually exclusive, for some embodiments of the present disclosure can be combined with one or more other embodiments of the present disclosure to form new embodiments.

[0030] Various examples are explained in detail below.

[0031] Figure 1 shows schematic diagrams of the structure and operation of a quantum processor ("quantum process unit" or QPU) 100 according to various embodiments. The QPU has a QR 102 and a drive unit 104. The concept of a "quantum register" (QR) is a set of multiple (for example, n) qubits (here, exemplarily q1 to q nThis represents a device capable of implementing (referred to as QR102). Exemplary components of QR102 include one ion trap, multiple (e.g., superconducting) circuit resonators, multiple quantum dots, one optical system, one laser, one electromagnetic coil, etc. The drive device 104 is configured to drive (e.g., activate) QR102 according to, for example, sequence 106 (also referred to as operation sequence). An exemplary process of operation sequence 106 includes starting QR 101 (i.e., transitioning QR to its initial state Z0), driving and controlling QR102 103, and / or reading out QR102 110. In the initial state Z0 of QR102, each qubit may be unentangled and / or in its ground state (here, exemplarily |0)), but not necessarily all qubits.

[0032] The specific implementation of the drive unit 104 or the operation sequence 106 depends on the type and architecture of the qubits. The drive unit 104 may have one or more transducers configured to interact with QR102 or its environment, for example, configured to change and / or detect at least its state Z. Exemplary implementations of the transducers of the drive unit include actuators (e.g., regulating elements), sensors, transceivers, etc. Exemplary transducers of the drive unit are configured to transmit and / or detect to QR102 one or more of optical radiation, magnetic fields, electric fields, electric charges, and particle radiation. 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 mathematically represented by two basis vectors in a two-dimensional Hilbert space (expanded here exemplarily by |0) and |1). Qubits can be realized in various types and architectures. Examples include energy levels in trapped ions, polarization states of photons, spin in quantum dots or silicon, and energy levels in superconducting circuit resonators.

[0034] Overall, the drive control 103 of QR102 is tuned to excite a change in the state of QR102 (also called a state transition). The drive control 103 of QR102 is performed according to one or more quantum gates 108 (see also Figure 5). The concept of a "quantum gate" (also called a quantum logic gate or gate) represents a quantum mechanical analogue to a logic gate in an electrical circuit. The quantum gate 108 corresponds to a process of influence on QR102 that changes the state Z of QR102, for example, the state Z of one or more qubits in QR102. By using the quantum gate 108, unitary functions can be realized similarly to logic gates, specifically similarly to their Boolean functions. Mathematically, a quantum gate changes a qubit from state |x) to state

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[0035] The concept of a "quantum algorithm" (also called a quantum circuit) generally refers to a set of processes (e.g., quantum gates) or processes within QR102 that interact with QR102 (e.g., at least one of its qubits) to trigger or at least excite a change in state Z of QR102. For good understanding, quantum circuits are represented as circuit diagrams, similar to electronic circuits, with one axis (here, the left-to-right axis) representing the passage of time. Similar to electrical circuits, the sum of multiple quantum circuits can also be considered a quantum circuit. From this perspective, the entire operation sequence 106 can be understood as a quantum circuit, and similarly, the components of a quantum circuit can be understood as processes, for example, drive-control 103 or readout 110. From a data processing perspective, each quantum circuit transitions the state of QR102 (also called the input state of the quantum circuit) to another state of QR102 (also called the output state of the quantum circuit). Here, the output state of the drive-control 103 process (also called the drive-control process 103) is, for example, |x i )|x j Although exemplified as a superposition state having (1≦i,j≦n), it does not necessarily have entangled qubits. If the output state of a quantum circuit is a superposition state (for example, having entangled qubits), the quantum circuit is also referred to herein as a start circuit (or preparation circuit). In general, a superposition state can have, with respect to individual qubits, a superposition of the states of individual qubits, and / or, with respect to multiple qubits, an entanglement of multiple qubits and / or a superposition of their states. Therefore, a start circuit can be configured to transition qubits to a superposition state, which does not necessarily result in entanglement of qubits, but is still entirely possible.

[0036] The start circuit is preferably configured to change the square of the absolute value of the amplitude and the phase of the qubit. The quantum circuit optionally has or consists of one or more quantum gates (e.g., multi-qubit quantum gates) parameterized using, for example, at least one parameter (also called a variation parameter) (in the case of a start circuit, it is also called a variational circuit or abbreviated as VQC). The start circuit optionally also has one or more unparalleled quantum gates and / or one or more multi-qubit quantum gates. The parameterization of a quantum circuit is denoted in this specification by a vector for the sake of brevity (in this case, also called a parameter vector), which may have two or more parameters as components, but does not necessarily have to. Thus, the output state of a parameterized quantum circuit is a function of the parameter vector, and its vector components are the parameters of the quantum circuit.

[0037] The process of reading QR102 110 (also referred to as the read process 110) includes, for example, detecting the state of QR102, which may be the superposition state and / or result thereof of the drive control process 103, by sensor technology (i.e., using sensors). During the read 110, the state of QR102 is the measurement-based ground state of the read process (here, exemplarily Z AIt collapses into (assuming). To improve the accuracy of the expected value, the readout process 110 (also called the quantum mechanical measurement process or simply measurement) can be repeated multiple times, for example, for each parameter vector and / or term of the Hamiltonian. The input state of the readout process 110 may be the output state of the drive control process 103. The sensor may be part of a measurement chain having corresponding infrastructure (e.g., including a processor, storage medium and / or bus system). The measurement chain can be configured to drive and control the sensor, process the detected state as an input quantity, and output data representing the input quantity based on this. The measurement chain is realized or can be realized by, for example, a drive device 104. The sensor may have one or more measurement bases, one of which is the measurement base for performing the readout process 110. A measurement base is, simply put, a characteristic of the sensor on which the readout process 110 is performed. Mathematically speaking, the measurement base unfolds the Hilbert space of states on which the state of QR is projected during readout. Depending on the technical embodiment, the QPU can implement one or more measurement bases. As an optional means, the QPU can implement multiple measurement bases, thereby allowing the selection of measurement bases to be parameterized in place of and / or in addition to parameterized quantum gates.

[0038] FIG. 2 schematically shows a method according to various embodiments 200 that can be executed by, for example, a control device 202. The concept of a "control device" can be understood as any type of entity (e.g., a processor) that can process data or signals. The data or signals can be processed, for example, according to at least one (i.e., one or more) special functions executed internally by the control device or processor. The control device, for example, its processor, can include an analog circuit, a digital circuit, a logic circuit, a microprocessor, a microcontroller, a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an integrated circuit of a programmable gate array (FPGA), or any combination thereof, or can be composed of these. Any other method of realizing each function described in detail herein can also be understood as a processor or a logic circuit. One or more of the individual method steps described herein can be executed (e.g., realized) by one or more special functions executed by the processor. The processor of the control device can be, for example, a classical (i.e., non-quantum mechanical, e.g., transistor-based) processor.

[0039] A process sequence 602 of the method (also referred to as an optimization process sequence 602) is shown. The process sequence 602 has an operation sequence 106 that can be realized by a QPU (e.g., according to embodiment 100), and, for example, has an adjustment process 213 that can be realized by, for example, a control device 202 (e.g., exactly one). The QPU includes a plurality of qubits (here, exemplified as q1 to q nThe QPU has a QR102 configured to achieve the following. Not all components of the tuning process 213 necessarily have to be performed by a classical processor; rather, depending on the performance of the QPU, it may be possible to perform at least partially the QPU itself. The method may optionally include repeating the optimization process sequence 602 multiple times (e.g., K times) (see also Figure 6).

[0040] Operation sequence 106 is the first execution 201(m) of the read process 110. S The process involves performing a first read process 201 (or a first read process 201), thereby calculating a first data 252 representing a first state 204a of QR102 (for example, at a first time point t1) (here, Z1 = Z(t1) as an example), performing drive control 205 (also called start preparation 205) of QR102 in the first state 204a, and executing a second read process 207 (m E The process includes performing a second readout process (also referred to as a second readout process 207), thereby calculating a second data 254 that represents a second state 204b of QR102 (for example, at a second time point t2 > t1) obtained from the drive control 205 (here, Z2 = Z(t2) as an example). Depending on the specific implementation (see also Figures 4A and 4B), the first state 204a is, for example, the output state of the first readout process 201, or at least based thereon, the ground state (i.e., a state without superposition), or, for example, the output state of an additional drive control 211 of QR102 (also referred to as thermalization 211), or at least based thereon, the superposition state. If the operation sequence 106 has a thermalization 211 of QR102, preferably, if the thermalization 211 is in the initial state and / or before the first time point t1, this facilitates the initialization of the quantum mechanical state at a temperature above 0K, because 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 base of the quantum gate 108.

[0041] The start preparation 205 has one or more quantum gates 108 (for example, per qubit) and / or at least one parameter (for example, per qubit)

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[0042] For each optimization process sequence 602, the parameter vector of that optimization process sequence 602 (also called the adjustment process)

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[0043] The adjustment process 213 can be performed, for example, so that the objective function, which depends on the first and second data, is optimized, for example, so that its output is minimized. The objective function (for example, its output) can represent, for example, QS, for example, its state variables, which will be explained in detail below.

[0044] Figure 3 schematically illustrates various embodiments 300 that can be implemented based on a variation method (e.g., the Rayleigh-Ritz method) using a control device 202, which is here exemplary configured as a CPU. Embodiment 300 can be configured similarly to Embodiment 200, where the output 302a of the objective function 302 can be expressed, for example, as a function of the state variables of the heated QS (e.g., free energy F), preferably as a function of the entropy S and energy E of the heated QS, and more preferably according to relation (2). In this case, the first data 252 represents the entropy calculated based on the measurement of the QPU, and the second data 254 represents the energy of the heated QS, calculated based on the measurement of the QPU. The exemplary explanation here for free energy (e.g., as the output of the objective function) may similarly apply to any other state variables of the (e.g., heated) QS.

[0045] The optimization of the objective function 302 can be performed by a so-called optimization algorithm 304, which uses the output 302a of the objective function 302 to determine the parameter vector of the operation sequence 106.

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[0046] The optimization process sequence 602 is its actual parameter vector

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[0047] Figures 4A and 4B show schematic diagrams of the operation sequence 106 according to various embodiments 400a and 400b, which can also be realized in embodiments 100 to 300, for example. However, the common feature of the operation sequence 106 (in this case also referred to as "Full Quantum Variational Thermalizer" or simply FQVT) is that it has two process pairs, each of which has a VQC (VQC1 or VQC2) and a subsequent readout process 110. The VQC of each process pair is configured to provide a superposition of multiple quantum states (also referred to as a superposition state) having different amplitudes as the output state (qubit state). The readout process 110 of each process pair can be configured to act on the superposition and transition the superposition to a single ground 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 This includes detecting (measuring) the output state of VQC1, that is, reading QR102 according to VQC1 after drive control has been performed. The output state of VQC1 is measured m S Using this, a transition to the ground state can be made with a probability p (given by the amplitude of the ground state here). FQVT106 can be executed multiple times for every 602 optimization process sequences, where measurement m S Statistics regarding the output are collected. After FQVT106 is repeated at a high frequency, the measurement m S From, measurement in the new round m S The probability p of obtaining the ground state i in this state. i The probability p can be calculated. i Based on this, the entropy of a quantum mechanical system is expressed, for example, by the following relationship:

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

[0051] If the QPU cannot perform the read process 110 (also referred to as intermediate measurement) between two VQCs, or if 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, and the qubits of the first group (also referred to as the logical main register) and the qubits of the second group (also referred to as the logical auxiliary register or auxiliary qubit) are configured to become entangled with each other. n ) and auxiliary registers (here, a1 to a n For the sake of ease of understanding, in this specification, these will be treated as (logically) separate QR102s, but it should be understood that they may, but may not necessarily, be part of the same (physically) QR102. The auxiliary registers have at least the same number of qubits as the main registers, for example, multiple n qubits.

[0052] According to embodiment 400b, only the main register is driven and controlled according to VQC1 and VQC2, m E It is read out using [this method]. Furthermore, the operation sequence 106 according to embodiment 400b includes entangling the output state of VQC1 (which is, for example, a superposition state) with an auxiliary register 410 (also referred to as the entanglement process 410). The entanglement process 410 may include, for example, using at least one CNOT gate to entangle each qubit of the main register with (for example, strictly) one qubit of the auxiliary register. The output of the entanglement process 410 has a plurality of (for example, n) pairs of entangled qubits, each pair having a qubit of the main register and a qubit of the auxiliary register.

[0053] Furthermore, the operation sequence 106 according to embodiment 400b includes using VQC2 to transition only the state of the main register (which is, for example, a superposition state) resulting from the entanglement process 410 to a superposition as a second state 204b. In this case, the first read process m S This includes detecting (measuring) the state 214b of the auxiliary register resulting from the entanglement process 410. The state 214b of the auxiliary register is measured m S Using this, the transition to the ground state can be initiated with probability p (given by the amplitude of the ground state here). In this case, by measuring all qubits (for example, commonly) at the end of operation sequence 106, the energy (q) can be determined. i (measurement) and entropy (a i The measurement of and are specifically sent out. In one example, the first read process (of the auxiliary register) m S However (in terms of time), for example, the second read process m E Immediately before, or the second read process m E At the same time, or for example, a second read process m E It takes place immediately afterward.

[0054] Figure 5 schematically shows the operation sequence 106 according to various embodiments 500, illustrating an exemplary implementation of Embodiment 400a in the case of two qubits. t (θ j ) is, for example, θ which indicates the rotation angle. j Represents rotation around the t-axis (t=x, y, or z), which depends on Φ. i or

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

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[0056] Figure 6 schematically shows various embodiments 600 of the method to illustrate additional and 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, the number of rounds (also called the round counter) reaches a target number K, or until the variation of the output of the objective function falls below a threshold. Once the criteria are met, the parameter vector updated in the last executed optimization process sequence 602 is...

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[0057] The said or each optimization process sequence 602 uses a parameter vector based on the result of the adjustment process 213.

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[0058] As an optional measure, the optimization process sequence 602 or each optimization process sequence 602 may include executing the operation sequence 106 multiple times, for example, until a criterion is met, for example, until the number of rounds r reaches the target number R. In this case, the adjustment process 213 may be based on first and second data from multiple operation sequences 106. As an optional measure, at the start of the optimization process sequence 602, the method includes, in 601, parameter vector

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[0059] In the first exemplary implementation (specifically showing segmentation optimization), the method (for example, for optimizing free energy) has multiple steps, in which one or more optimization process sequences 602 are executed in each step. For this, please refer to Figure 8, which specifically shows the first exemplary implementation in a schematic diagram 800 similar to that of embodiment 600. In the first of the multiple steps, step 801 (specifically showing VQC1 optimization using a simplified Hamiltonian), the operation sequence 106 is performed on the parameter vector

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[0060] In the second exemplary implementation (specifically, the approximate FQVT), the method involves reducing VQC1 and not variationally changing all qubits. For this, please refer to Figure 9, which shows the first exemplary implementation in schematic diagram 900, similar to that of embodiment 400a. In other words, VQC1 is configured to change only a portion of QR102 and / or change fewer qubits than VQC2. As a result, only a small number of states exist after the entropy measurement. Therefore, the approximate FQVT here considers only the lowest energetically excited state and thus requires significantly fewer parameters, thereby similarly reducing the energy requirement and error vulnerability of the method. Especially for large systems, this modified form significantly reduces the required resources (e.g., computation time) without significant loss of accuracy.

[0061] Figure 7 shows schematic diagrams of methods according to various embodiments 700, where the output 701 of the objective function (exemplified here as free energy) that depends on the round counter 703 is shown. Curve 706 compares the methods described herein with theoretical values ​​(curve 702), ideal transitions with precisely calculated probabilities for each state (curve 704), and a Fake Vigo Simulator (curve 708) using an error model derived from IBM's real quantum chip, "Vigo." The solid lines represent the average of a series of trials, and the area represents the error range defined by the standard deviation.

[0062] In the first embodiment, the method (e.g., each optimization process sequence) includes executing 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 Qiskit's "memory-limited BFGS algorithm" ("L_BFGS_B") as the optimization algorithm, where a Hamiltonian operator according to relation (3) and an operation sequence 106 according to embodiment 500 using β=1 are used. In the second or third embodiment, the method according to embodiment 600 is executed at least 20 times, where the parameter vector

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

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[0064] Figure 10 schematically shows various embodiments 1000 of a method that can be executed based on a variable method (e.g., the Rayleigh-Ritz method) using a control device 202, which is here exemplary configured as a CPU. This method can be configured according to one or more embodiments 100 to 900, for example, according to at least embodiment 600 (also referred to as FQVT optimization 600). QR102 is the output vector output by FQVT optimization 600.

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[0065] While specific embodiments have been illustrated and described herein, those skilled in the art will recognize that these specific embodiments can be modified into a variety of alternative and / or equivalent realizations without departing from the scope of the invention. This application is intended to encompass any adapted or modified forms of the specific embodiments described herein. Accordingly, the invention is limited only by the claims and their equivalents.

Claims

1. A method for operating a quantum register (102), The first read process (201) is performed such that a first data (252) representing the first state of the quantum register (102) is calculated, at least one quantum gate (VQC) ２ In accordance with the above, a first drive control (205) is performed on the quantum register (102) in the first state, The second read process (207) is executed such that a second data (254) representing the second state of the quantum register (102) obtained from the first drive control (205) is calculated, To optimize the objective function which depends on the first data (252) and the second data (254), the first data (252) and the second data (254) are used to perform the at least one quantum gate (VQC ２ Adjusting at least one parameter of (213), The at least one quantum gate (VQC) obtained from the above adjustment (213) ２ The second drive control (205) of the quantum register (102) is performed in accordance with the above, A method that includes this.

2. The first reading process (201) is, Reading out the aforementioned quantum register (102), or, The additional quantum registers entangled by the aforementioned quantum register (102) are read out. The method according to claim 1, including the method described in claim 1.

3. At least one additional quantum gate (VQC) １ The adjustment (213) is performed according to the first drive control (211) of the quantum register (102), wherein the first state of the quantum register (102) is based on the additional first drive control (211), and the adjustment (213) uses the first data (252) and the second data (254) to perform the at least one additional quantum gate (VQC １ This includes adjusting or setting to an invariant at least one parameter of ) The at least one additional quantum gate (VQC) obtained from the above adjustment (213) １ In accordance with the above, an additional second drive control (211) of the quantum register (102) is performed, The method according to claim 1, further comprising:

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

5. The at least one quantum gate (VQC ２ ), and / or the at least one additional quantum gate (VQC １ ), is configured to transition the quantum register (102) to an entangled-free superposition state or an at least partially entangled superposition state, the method according to claim 3.

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

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

8. A control device (202) configured to carry out the method described in claim 1.

9. A computer program, configured to cause a processor that executes the computer program to carry out the method described in claim 1.

10. A computer-readable medium storing instructions configured to cause a processor that executes instructions to carry out the method described in claim 1.

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