Digital quantum simulation of fermi-bose subsystems in two-dimensional quantum computing systems

Abstract

One aspect of the present disclosure relates to a method for configuring a quantum computing system, where the quantum computing system includes a plurality of qubits arranged on a two-dimensional (2D) lattice, and is configured to perform a plurality of quantum computing operations. A method of the present disclosure includes receiving a selection of a first plurality of qubits and a second plurality of qubits of a plurality of qubits representing two different degrees of freedom associated with respective components of a physical system to be mapped to the first plurality of qubits and the second plurality of qubits. Adjacent qubits of a first aspect are configured to transmit quantum information between each other. A number of chains of the first plurality of qubits and a number of ladders of the second plurality of qubits are configured to perform a plurality of quantum computing operations.

Description

Technical Field

[0001] This specification relates to methods for configuring quantum computing systems. Related aspects relate to quantum computing systems and remote computing systems. Background Art

[0002] There is growing interest in implementing quantum computing on various physical systems to solve a variety of real-world problems, such as those involving computations in chemistry, biology, solid-state physics, and cryptography systems (see, for example, E. Grumbling and M. Horowitz, “Quantum Computing: Progress and Prospects,” Washington, DC: The National Academies Press, 2019; https: / / doi.org / 10.17226 / 25196). The goal is to speed up computations compared to classical computers and / or solve a class of problems that cannot be solved even on supercomputers performing classical computations based on classical algorithms. In the field of physical simulations on quantum computers, there are some applications, such as in solid-state physics and chemistry, that require the joint quantum simulation of fermion baths and non-interacting baths on quantum computers. These can be physical problems in which the non-interacting bath takes the form of bosonic patterns or non-interacting fermion patterns.

[0003] Some known prior art techniques involve implementing both fermionic degrees of freedom and bosonic modes, as well as their possible interactions, on the qubits of a quantum computer. However, the number of quantum computing operations required for quantum simulations of physical problems involving interacting fermions and bosons performed on some prior art quantum computer architectures is so large that the overall quantum simulation becomes time-consuming, such that the qubits may lose coherence within a time interval smaller than that required to complete the quantum computing task.

[0004] Therefore, new and efficient techniques need to be developed to reduce the number of quantum computing operations required to perform quantum simulations of fermion-boson interacting systems on quantum computers. Summary of the Invention

[0005] A first aspect of the present disclosure relates to a method for configuring a quantum computing system, wherein the quantum computing system includes a plurality of qubits arranged on a two-dimensional (2D) lattice and configured to perform a plurality of quantum computing operations. The method of the present disclosure includes receiving a selection of a first plurality of qubits from the plurality of qubits, wherein the first plurality of qubits includes a plurality of qubit chains. In the method of the first aspect, each qubit in the plurality of chains of the first plurality of qubits represents a first degree of freedom associated with a corresponding component of a physical system to be mapped to the plurality of chains of the first plurality of qubits. Furthermore, each qubit in the first plurality of qubits is configured to transmit quantum information of the qubit to another qubit in the first plurality of qubits adjacent to the qubit, wherein the another qubit in the first plurality of qubits is configured to receive quantum information of the qubit in the first plurality of qubits. The method also includes receiving a selection of a second plurality of qubits from the plurality of qubits, wherein the second plurality of qubits includes a plurality of qubit ladders, wherein each qubit ladder represents a second degree of freedom associated with a corresponding component of a physical system to be mapped to the plurality of ladders of the second plurality of qubits. The second degree of freedom of the first aspect is different from the first degree of freedom. In a first aspect of the present disclosure, each qubit in the second plurality of qubits is configured to send quantum information of the qubit to another qubit in the second plurality of qubits adjacent to the qubit, wherein the another qubit in the second plurality of qubits is configured to receive quantum information of the qubit in the second plurality of qubits. In the method of the first aspect, one or more qubits in the chains of the first plurality of qubits are adjacent to corresponding one or more qubits in the ladders of the second plurality of qubits and are configured to send quantum information to and / or receive quantum information from corresponding one or more qubits in the ladders of the second plurality of qubits. The chains of the first plurality of qubits and the ladders of the second plurality of qubits are configured to perform a plurality of quantum computing operations.

[0006] A second aspect provides a quantum computing system configured according to any of the steps of the technology of the first aspect.

[0007] A third aspect provides a quantum computing system configured to perform a plurality of quantum computing operations and adapted to perform any of the steps of the technique according to the first aspect.

[0008] A fourth general aspect of the present disclosure relates to a remote computing system comprising a quantum computing system and configured to perform a quantum computing task, wherein the quantum computing task comprises a plurality of quantum computing operations according to the first aspect. The plurality of quantum computing operations of the fourth aspect may be performed according to any of the method steps of the first aspect. The remote computing system of the fourth aspect is further configured to transmit a result of the computing task to a computer-implemented system.

[0009] The technologies of the first to fourth aspects can have advantageous technical effects.

[0010] First, the disclosed technology relates to performing digital quantum simulations of a fermionic system (e.g., a fermion-bosonic interaction system) interacting with a non-interacting bath on a quantum computing system including a hardware architecture (e.g., one or more chips) having qubits arranged in a 2D lattice, with a reduced number of quantum computing operations required compared to some prior art techniques. For example, in some prior art techniques using quantum computers with two-dimensional connectivity, for each interaction between a fermionic degree of freedom and a bosonic mode, a number of operations are required. / fermion SWAP operation, where N is the number of qubits representing fermionic degrees of freedom, and M is the number of qubits representing bosonic modes. In some cases, the configuration of qubits on a 2D lattice of the present technology allows the number of quantum computing operations required to realize each interaction between fermionic degrees of freedom and non-interacting baths (e.g., bosonic modes) to be reduced from to O(1). Furthermore, in some embodiments of the present technology, the use of quantum exchange registers can allow for a further reduction in the fermion exchanges required during quantum simulations of fermion-boson systems. Thus, the total number of quantum computing operations can be significantly reduced compared to some prior art techniques.

[0011] Second, by using the quantum bit configuration of the present technique, the number of quantum gates required to complete a quantum computing task can be reduced, resulting in a reduction in the total decoherence or inaccuracy that occurs in the quantum computing system: each quantum gate may be a potential source of decoherence and / or inaccuracy related to the fact that the physical implementation of the quantum gate may not match the user-specified logical gate operation (this problem is known as gate infidelity). Therefore, in the present technique, when the above two factors are considered together, the gain of reducing the total number of quantum computing operations on the quantum bits of the 2D lattice and the resulting reduction in computing time becomes more significant compared to some existing techniques.

[0012] Third, the disclosed techniques enable parallel execution of some quantum computing operations that cannot be performed in parallel using some existing techniques. This can provide additional speedups in executing quantum computing operations, which can result in maintaining coherence between qubits throughout the execution time of the entire quantum computing task.

[0013] Some terms are used in this specification as follows:

[0014] The term "qubit" (or qubit) may refer to a quantum mechanical system having (at least) two quantum states or any superposition of these quantum states, which is also referred to as a two-level system for short. A two-level system is a basic unit that carries quantum information, into which quantum information can be encoded and from which it can be retrieved. For example, the spin of an electron in a magnetic field having two energy levels and corresponding spin-up and spin-down states is a physical realization of a qubit. Another physical realization involves the polarization of a single photon, where two orthogonal polarizations can be considered as two qubit states. In some cases, the two quantum states may be associated with two different energy levels, for example, two selected energy levels in the anharmonic energy spectrum (or in other words, an anharmonic energy level ladder) of a physical system that serves as a physical realization of a qubit (this may be the case, for example, of a superconducting qubit). In other cases, the two quantum states may be associated with two degenerate energy levels (i.e., they share the same energy value), which may be the case for a photonic quantum computer. The quantum state of a single qubit can be described by a wave function, which can be represented as a vector in a two-dimensional complex space, and changes in its quantum state (e.g., due to the time evolution of the qubit state and / or as a result of applying quantum gate operations) can be visualized on a Bloch sphere (see, e.g., MA Nielsen and ILChuang, "Quantum Computation and Quantum Information": 10th Anniversary Edition, Cambridge University Press, 2010). Quantum computation can include quantum computation operations on multiple qubits (see discussion below) so that their multi-qubit quantum state can be manipulated and changed. In some cases, each qubit in the multiple qubits can be processed independently of each other, in which case the multi-qubit quantum state can be written as a separable quantum state, i.e., it can be represented as a tensor product of the states of each single qubit (and ultimately as a corresponding superposition of the quantum states of the individual qubits). In other cases, when at least two qubits from the plurality of qubits cannot be processed independently of each other (or in other words, they cannot be described individually from each other), the multi-qubit quantum state represents an entangled state that cannot be represented in terms of a tensor product of the states of the individual qubits (see further discussion below, where both cases are discussed in more detail).

[0015] There are several physical implementations of systems that can be used as qubits in quantum computing contexts (i.e., as two-level systems). The qubits of the present disclosure are not limited to a specific physical implementation. One example of such a physical implementation is a quantum computer based on cavity quantum electrodynamics (cQED), in which the qubits are provided by the internal states of trapped atoms coupled to a high-fineness cavity. One example of quantum computing using circuit quantum electrodynamics is superconducting quantum computing based on superconducting qubits coupled to a microwave cavity (called a quantum bus) and radiated in the microwave region, whose quantum states are manipulated by electromagnetic pulses to control the magnetic flux, charge, or phase difference across a nanofabricated Josephson junction, see, e.g., https: / / doi.org / 10.1038 / nature07128. Another example involves a solid-state nuclear magnetic resonance (NMR) Kane quantum computer, in which the qubits are implemented as nuclear spin states of donor atoms (e.g., phosphorus donor atoms) embedded in a corresponding host lattice (e.g., in a pure silicon lattice). In some other examples, the physical implementation of a quantum computer can be based on neutral atoms in an optical lattice, where qubits are realized by the internal states of neutral atoms (e.g., Rydberg atoms) trapped in the optical lattice (e.g., interacting with each other via Rydberg interactions), see, for example, https: / / doi.org / 10.1088 / 0953-4075 / 49 / 20 / 202001. In still other examples, the quantum computer can be a quantum dot computer, where qubits are given by the corresponding spin states of trapped electrons.

[0016] The term "quantum computing operation" and the related term "quantum computing" may refer to an operation on a qubit that can change its quantum state. Quantum computing operations on one or more qubits may be performed by quantum gates that manipulate the quantum state of the qubits, or in other words, manipulate the quantum information carried by them. As further disclosed below, a single qubit may form a single-qubit quantum state (e.g., a ground state, an excited state, or a superposition of both). In some cases, multiple qubits may form a multi-qubit quantum state, which may be a tensor product state or an entangled state (see the discussion below for more details). In some cases, a quantum computing operation may be represented by a sequence of quantum gates acting on the corresponding qubits. A quantum gate may be represented by a unitary operator U (e.g., represented by a corresponding unitary matrix) that ensures conservation of the norm of the wave function of the qubit in the absence of dissipation, such that the product of the operator and its Hermitian conjugate is equal to the identity operator, in represents the Hermitian conjugation, and I is the unit operator. Thus, the quantum gate is configured to perform a unitary transformation on the qubit, that is, in other words, the unitary operator representing the quantum gate performs a unitary transformation on the quantum state of the qubit (again, see the discussion below). The Hadamard gate H, the phase gate S, the π / 8-gate, and the Pauli X-, Y-, and Z-gates are examples of single-qubit gates whose effects on the qubit can be visualized on the Bloch sphere mentioned above (see, for example, the book by MA Nielsen and IL Chuang mentioned above). Any quantum computation on one or more qubits can be generated by a finite set of qubit gates that are universal for quantum computation. In this case, any unitary operation representing this quantum computation on the qubit can be decomposed into a set of operations performed by a quantum circuit containing gates from this finite set. Any unitary operation (e.g., a unitary operation performed on any multi-qubit logic gate) can be composed of a two-qubit controlled-NOT (CNOT) gate and a corresponding number of single-qubit gates, i.e., single-qubit rotations with a number of free parameters that characterize the unitary operation under consideration. For example, any unitary operation can be approximated (to a given accuracy) by Hadamard gates, phase gates, CNOT gates, and π / 8-gates, also known as universal quantum gates (see, e.g., M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information”: 10th Anniversary Edition, Cambridge University Press, 2010). For example, in the case of superconducting qubits, a single-qubit gate can be implemented by a rotation between two energy levels of a single superconducting qubit induced by a microwave pulse sent on a transmission line coupled to the qubit, the frequency of the microwave pulse being resonant with the energy separation between the energy levels. Furthermore, a two-qubit gate can be realized by coupling two superconducting qubits, for example, via a microwave cavity or an intermediate electrically coupled circuit (see, e.g., https: / / doi.org / 10.1038 / nature02851). In the case of neutral atom quantum computing, a two-qubit gate can be realized using a controllable Rydberg interaction between neutral atoms, which is strong enough to perform two gate operations (see, e.g., https: / / doi.org / 10.1103 / PhysRevX.10.021054).

[0017] As used herein, the term "unitary transformation" as applied to a qubit should be interpreted broadly in this disclosure and may refer to a unitary transformation of the quantum state of the qubit resulting from a unitary operation acting on the qubit, which may be defined by a unitary operator acting on their quantum state. For example, a quantum computing operation, such as an operation that applies different single or multiple quantum gates (represented by corresponding unitary operators) to a qubit, may result in a unitary transformation of the quantum state of the qubit. In other words, one or more unitary transformations of the quantum state of one or more qubits associated with corresponding gates applied to the one or more qubits may be performed in a corresponding subspace of the Hilbert space of the qubit, while the unit transformation (or in other words, the unit operation) is applied to the remainder of the Hilbert space. (In this context, a Hilbert space can be understood as a complex vector space spanned by vectors representing the quantum states of qubits, with defined inner products between them.) In some cases, the quantum states of qubits can evolve unitarily according to the qubit's Hamiltonian (e.g., the Jaynes-Cummings Hamiltonian in cQED), which is a Hermitian operator that determines their interactions with external control fields (e.g., magnetic fields) as well as the qubit's coupling to a host lattice or cavity (e.g., a quantum bus in the case of superconducting quantum computing) and its possible interactions (such as dipole-dipole interactions in the case of Rydberg atoms). This unitary time evolution of the quantum state of a qubit that occurs during quantum computing (represented by a unitary time evolution operator) is also referred to in this specification as a "unitary transformation." As can be seen from the above discussion, a single-qubit rotation is a specific case of a unitary transformation.

[0018] In the present disclosure, a "quantum computing operation" performed on a quantum bit of a quantum computing system may be performed to simulate the quantum state generated by the corresponding quantum Hamiltonian. The physical system of interest "can be encoded into the qubits of the quantum computing system" so that the unitary time evolution of the components of the physical system (see the next paragraph for details) is transferred from the components to the qubits, thereby allowing the quantum computing system to simulate the unitary time evolution of the physical system under consideration. In other words, the quantum state of the qubit of the quantum computing system can be determined according to the Hamiltonian of the physical system encoded in the qubit. Unitary evolution, in which case the time evolution of the physical system can be implemented, for example, as a series of quantum gates acting on quantum bits (i.e., gates available in the specific architecture and / or quantum bit topology of the quantum computer). Therefore, the "quantum computing operations" performed on the quantum bits of the quantum computing system of the present disclosure can be referred to as "digital quantum simulations" of the physical system of interest on the quantum computing system. For example, the occupation of fermion orbitals (more precisely, the distribution of electrons in atomic or molecular orbitals) and / or bosonic modes can be represented by corresponding quantum bits (i.e., the corresponding quantum states of the quantum bits). In the present disclosure, "encoded into quantum bits" can be used together with "mapped onto quantum bits" having the same meaning.

[0019] As used herein, a "physical system" can be any system that follows a quantum Hamiltonian The invention relates to a quantum physical system that evolves and includes corresponding components (e.g., one or any combination selected from the following non-exhaustive list: atoms, ions, molecules, quantum dots, photons, holes, phonons, Cooper pairs, excitons, polaritons, magnons, polaritons) that can interact with each other. For example, components of one kind can interact with components of the same kind (e.g., electron-electron interactions) and / or components of another kind (e.g., electron-phonon interactions). In this regard, in some cases of the present disclosure, the term "degree of freedom" can be used to indicate whether the spin quantum number of the corresponding component has an integer value (e.g., 0, 1, 2, or any other integer value) or a half-odd integer value (e.g., 1 / 2, 3 / 2, 5 / 2, or any other half-odd integer value), resulting in corresponding quantum statistics of these components. For example, one or more components of a physical system may be fermionic particles (e.g., electrons or other particles) or fermionic quasiparticles (e.g., holes, polarons, or other quasiparticles) having a spin of a half-odd integer value that obeys Fermi-Dirac statistics, where "fermionic degrees of freedom" are associated with such components. Another one or more components of the physical system may be bosons, such as single particles (e.g., photons), composite particles (e.g., some real or artificial atoms), or quasiparticles (e.g., Cooper pairs, collective excitations such as phonons, excitons, magnons, etc.), that obey Bose-Einstein statistics, in which case they may be referred to as bosonic modes. In other examples of the present disclosure, bosonic modes can represent non-interacting fermionic modes, such as non-interacting fermionic modes of a dynamical mean field theory (DMFT) bath: an example of a fermionic system in contact with a non-interacting fermionic bath involves providing a single-electron nanoelectronic circuit with electrons (fermionic degrees of freedom) and their conductive contacts acting as non-interacting fermionic baths (in some cases, such non-fermionic baths can be equivalent to bosonic modes for the purposes of this specification), see, for example, https: / / doi.org / 10.1109 / 5.752518.

[0020] An example of a physical system comprising fermionic degrees of freedom interacting with bosonic modes is a physical system comprising electrons and phonons interacting with each other, the evolution of which can be expressed as or the Holstein Hamiltonian description (see, e.g., G.D. Mahan, “Many Particle Physics”, Springer, New York, 2000; https: / / 10.1103 / PhysRevLett.109.200501). A non-exhaustive list of further examples includes physical systems comprising fermions in contact with a bosonic bath in the case of the tunneling problem for deriving the so-called P(E) theory (see, e.g., https: / / arxiv.org / pdf / cond-mat / 0508728.pdf), the interaction of electron systems with electromagnetic radiation fields (see, e.g., https: / / arxiv.org / pdf / 1804.07142.pdf or https: / / arxiv.org / pdf / 1501.00803.pdf), the interaction of bosonic-mediated fermionic modes common in high-energy physics (see, e.g., http: / / arxiv.org / abs / 1404.2868), ultracold fermion-bosonic mixtures (see, e.g., https: / / arxiv.org / pdf / 1212.3535.pdf), and various other physical systems arising in the context of solid-state physics and quantum chemistry.

[0021] In this specification, "transferring quantum information" between qubits of the same or different kinds (or "exchanging quantum information" as used in similar contexts in some cases) should be interpreted in a broad sense. In some cases, transferring / exchanging quantum information between two adjacent qubits may include applying a unitary transformation to the qubits, for example using one or more two-qubit gates, or in some examples, using one or more single-qubit gates or multi-qubit gates in addition to the two-qubit gates. It should be noted that "transferring quantum information" between two adjacent qubits involving a unitary transformation may include direct (physical) interaction between the qubits and / or interaction of the qubits via, for example, a host lattice / quantum bus (in the sense described above). In some examples of this specification, "quantum information" may be transferred / exchanged between distant qubits by applying corresponding unitary transformations between adjacent qubits arranged between the distant qubits. In the present technology, "quantum information" may be transferred / exchanged between adjacent qubits - this may be part of a quantum computing operation performed on a quantum computing system. In some cases, "quantum information" can be transmitted / exchanged one or more times, for example, during the course of a quantum computing operation, such as simulating the unitary time evolution of a physical system (or, in other words, its quantum Hamiltonian) over a (pre-given) time step on a quantum computing system (see further discussion below). Furthermore, when "quantum information" can be transmitted from one qubit to another adjacent qubit in the sense described above, the qubit to which the "quantum information" is transmitted can be said to be configured to receive the "quantum information."

[0022] In the present disclosure, one type of the above-mentioned “degree of freedom” (“first degree of freedom”), for example, “fermionic degree of freedom” can be encoded (or in other words, mapped) by a number of qubits representing the “first degree of freedom”, while another number of qubits can represent another type of “degree of freedom” (“second degree of freedom”), for example, “bosonic mode”. This division of qubits into different types encoding different degrees of freedom can be interpreted as that the “quantum computing operation” performed on the qubits representing, for example, “fermionic degree of freedom” is (at least partially) associated with the “fermionic degree of freedom” (which is determined by the quantum Hamiltonian of the system). ), while “quantum computing operations” performed on other qubits representing, for example, “bosonic modes” are (at least in part) associated with “bosonic modes.” In some cases, adjacent qubits of different kinds (e.g., when one qubit represents a “fermionic degree of freedom” and another adjacent qubit represents a “bosonic mode”) can involve “quantum computing operations” associated with both degrees of freedom.

[0023] In this specification, the encoding of "degrees of freedom" can be non-local in nature, that is, a number of qubits representing a "degree of freedom" of the type under consideration (e.g., two or more qubits or all qubits from the number of qubits) can include "at least partial information" about a single degree of freedom of this type (e.g., the quantum state of the number of qubits can depend on the single degree of freedom). For example, the Jordan-Wigner transformation (see, e.g., https: / / doi.org / 10.1103 / PhysRevLett.120.110501) for encoding "fermionic degrees of freedom" on qubits is non-local, so that the fermionic parity of a single orbital can be encoded into a number of qubits (e.g., all qubits of that type representing the "fermionic degree of freedom"). In some cases, the encoding of "bosonic modes" can also involve non-locality, in which case, for example, all qubits of a ladder (e.g., n qubits) together encode the "bosonic mode": for example, in binary encoding, the occupation number of the bosonic mode is expressed in Fock states |n> b (n represents any integer or zero, and the subscript b represents the bosonic mode) is a unit and can be expressed as 2 n The binary number represented in the qubit state. In other examples related to unary encoding, from |0> b to|n> b The occupation number of the bosonic mode of can be expressed for n qubits such that for the occupation number |k> b , one qubit nk is in state |1> and all other qubits are in state |0>. Binary, unary, and other possible encodings are described in https: / / doi.org / 10.1038 / s41534-020-0278-0. The term "qubit ladder" (for encoding, for example, "bosonic modes") is also used below and is a synonym for the term "ladder of qubits."

[0024] In the present disclosure, in the process of performing a "quantum computing operation" on quantum bits representing, for example, a "first degree of freedom" (e.g., implemented as a sequence of corresponding quantum gates), an entangled multi-qubit state can be established (see further discussion above), although the initial quantum states of these quantum bits are selected to be separable quantum states. In this case, each quantum bit participating in the formation of the multi-qubit state can include "at least partial information" about several first degrees of freedom (e.g., two or more first degrees of freedom). Similar considerations can also apply to the "second degree of freedom". In some cases, when adjacent quantum bits of different kinds exchange quantum information, entangled states can be formed on quantum bits of different kinds, for example, those representing both the "first degree of freedom" and the "second degree of freedom". In this case, each quantum bit participating in the formation of this multi-qubit state can be said to include "at least partial information" about two degrees of freedom (e.g., one or more fermionic degrees of freedom and one or more bosonic modes).

[0025] In this disclosure, the term "proximity" (or the qualifier "adjacent") with respect to qubits (e.g., arranged on a two-dimensional lattice) should be interpreted broadly, such that two qubits may be classified as adjacent if a universal quantum gate acting on the two qubits can be implemented without requiring one or more separate quantum gates between either of the two qubits and a third qubit. For example, if the quantum computer provides all unitary operations associated with the set of universal gates acting on the two qubits without involving a third qubit, or if they are physically coupled in hardware, or if a hardware-native two-qubit gate acting on the two qubits can be implemented without requiring a separate quantum gate between each individual qubit in the two qubits and a third qubit. In some examples, qubits may be classified as adjacent if, for example, they are nearest neighbor qubits of the same or different kinds of qubits (e.g., one kind may represent qubits representing fermionic degrees of freedom, while another kind may be a qubit, e.g., a qubit ladder representing a bosonic mode), or if the distance between the qubits under consideration is equal to or less than a predetermined characteristic distance (see discussion below). The spatial separation of qubits may be a decisive factor when they interact directly with each other, for example, via dipole-dipole interactions, as is the case for dipole-dipole interactions of light-trapped Rydberg atoms, see, for example, https: / / doi.org / 10.1088 / 0953-4075 / 49 / 20 / 202001. In other examples, the spatial distance between qubits may not be a relevant factor, or at least not the only relevant factor in determining qubit proximity. For example, semiconductor qubits can be coupled to each other via a quantum bus to which they are coupled, such that qubit coupling can be tuned by flux control of the qubits, and their spatial separation may not be a decisive factor. For example, when the qubit coupling exceeds a predetermined critical value, such that a two-qubit gate can be implemented based on the two qubits (without involving a third qubit) or the two qubits can form an entangled state, the qubits can be considered to be adjacent qubits. In this case, their spatial separation may not be a decisive factor. In some other examples, qubit-qubit coupling of superconducting qubits can be tuned by connecting them to intermediate electrical coupling circuits, see e.g., https: / / doi.org / 10.1038 / s41586-019-1666-5.

[0026] As used herein, the term "qubit chain" should be broadly interpreted as referring in this disclosure to a one-dimensional (1D) spatial arrangement of qubits of the same species in the plane of a 2D lattice (e.g., along a 1D curve or line). In some cases, a species of qubits can include one or more connected qubit chains extending along one or more directions. Additionally or alternatively, a species of qubits can include one or more disconnected qubit chains extending along one or more directions, interrupted by, for example, one or more qubit chains of another species. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1a is a flowchart illustrating a method of configuring a quantum computing system according to the first aspect. Figure 1b to Figure 1d is a flow chart illustrating further possible method steps according to the first aspect.

[0028] Figure 2a and Figure 2b Two possible quantum computing systems 1000 of the present technology are schematically shown with qubits arranged on a 2D lattice.

[0029] Figure 2a : The plurality of connected qubit chains representing a first degree of freedom (e.g., a fermion degree of freedom) includes three qubit chains 15a aligned in the vertical direction and four qubit chains 15b aligned in the horizontal direction. The plurality of connected qubit chains are arranged in a serpentine shape extending in the vertical direction. Each of the four qubit chains 15b aligned in the horizontal direction is adjacent to a corresponding ladder of a plurality of qubit ladders 16 representing a second degree of freedom (e.g., a bosonic mode), see Figure 3a for details.

[0030] Figure 2b : A pair of horizontally aligned qubit chains 15b connected by a chain 15a extending in the vertical direction and two horizontally aligned qubit chains 15b represent the first degree of freedom. Each of the four horizontally aligned qubit chains 15b is adjacent to a corresponding ladder of a plurality of qubit ladders 16 representing the second degree of freedom (see Figure 3b For details.) Two vertical auxiliary qubit chains 15c can be used to exchange quantum information (eg, by using a SWAP operation) between the subsequently disconnected horizontally aligned qubit chains 15b.

[0031] exist Figure 2a and Figure 2b On the left side of both figures, a quantum exchange register 17 is shown, which comprises a chain that can be used to exchange quantum information between qubit ladders of different sets of qubit ladders 16, for example, by using a SWAP operation (see also Figure 4).

[0032] Figure 3a and Figure 3b Shows the specified Figure 2a and Figure 2b Two possible topologies for the arrangement of qubits are shown above: a 2D lattice with multiple square units, with four qubits located at the vertices of the square units. Figure 3a and Figure 3b Only the corresponding Figure 2a and Figure 2b The upper part ( Figure 2a and Figure 2b The lower quantum bit ladder 16 and the lower horizontal quantum bit chain 15b are Figure 3a and Figure 3b For simplicity, the quantum exchange register 17 is omitted in these figures. Figure 3a and Figure 3b The qubit arrangement can also be independent of the Figure 2a and Figure 2b . Each ladder 16, representing a corresponding second degree of freedom (e.g., a bosonic mode), includes two qubits 2a, 2b; 2c, 2d surrounded by a dashed ellipse. In total, three sets of qubit ladders are shown in these two figures, with each set comprising four ladders.

[0033] Figure 3a and Figure 3b The solid lines in indicate that quantum information may be exchanged between adjacent qubits representing the same kind of degrees of freedom, i.e., a pair of qubits q1, q2 representing a first degree of freedom (e.g., a fermionic degree of freedom), and a pair of qubits qb belonging to a corresponding qubit ladder representing a second degree of freedom. 1,1 ;qb 1,2 , and in addition Figure 3b , a pair of quantum bits qh1; qh2 belonging to the corresponding auxiliary quantum bit chain 15c. Figure 3a and Figure 3b The dashed lines between the qubits in indicate that quantum information may be exchanged between adjacent qubits representing different kinds of degrees of freedom.

[0034] Figure 4 Schematically shows the specified Figure 2a and Figure 2b 1 shows a possible topology of an arrangement of qubits with a quantum exchange register 17. In this example, the quantum exchange register 17 is a chain of six qubits qR1-qR6, which can be used to exchange quantum information between qubit ladders belonging to two different sets of ladders, e.g., in a system with qubits qb 5,1 and qb 5,2The ladder (the ladder of the lower group of quantum bit ladders) is connected to the ladder with quantum bits qb 4,1 and qb 4,2 The dashed horizontal lines indicate that quantum information can be exchanged between adjacent qubits of different adjacent qubit ladders, and between qubits qR2-qR5 of the quantum exchange register 17 and corresponding adjacent qubits qb of two quantum ladders belonging to two different groups of ladders. 1,1 、qb 1,2 、qb 8,2 and qb 8,1 Quantum information is exchanged between them (e.g., by using the SWAP operation). Other notations are similar to Figure 2a and Figure 3a Those defined in association.

[0035] Figure 5a and Figure 5b An example of implementing quantum computing operations on a quantum computing system having four quantum bits q1 to q4 and two quantum bits qb of ladder 16 is shown. 2,1 ;qb 2,2 , the four qubits q1 to q4 initially encode the fermionic degrees of freedom, and the two qubits qb of the ladder 16 2,1 ;qb 2,2 Initially, the bosonic modes are encoded, namely: (1,↑)→q1, (1,↓)→q2, (2,↓)→q3, (2,↑)→q4 and |Mode1> b →qb 2,1 qb 2,2 Here (i,σ), where i=1,2, denotes electrons with spin σ=↑,↓ in orbital i, and |Mode1> b represents the quantum state of the bosonic mode. Figure 5b Each row in represents the ordering of the fermion orbitals depicted by the circles encoded on the qubits q1 to q4. The back-and-forth arrows indicate the fermion SWAP operation (FSWAP) between adjacent orbitals in each row. The top row shows the initial ordering of the fermion orbitals defined above. In each subsequent row, starting from the top row and proceeding to the bottom row, the resulting new fermion orbital order is shown (see the discussion below for more details). After each FSWAP operation is performed within the corresponding row, the ordering of the fermion orbitals on the qubits q1 to q4, qb 2,1 and qb 2,2 Perform available quantum computing operations on Figure 5b shown above).

[0036] Figures 6a to 6c Shown for Figure 5a and Figure 5bThree examples of quantum circuits for performing possible quantum computing operations 40-48 on a quantum computing system of the type described herein, wherein the quantum computing operations involve a qubit q2 representing a first degree of freedom (e.g., a fermionic degree of freedom) and two qubits qb of a qubit ladder 16 encoding a second degree of freedom (e.g., a bosonic mode) 2,1 and qb 2,2 . Quantum bits q2 and qb 2,1 adjacent, and quantum bit qb 2,1 and qb 2,2 Also adjacent, see Figure 5a In these figures, H represents a Hadamard gate, reference numerals 42, 43, 45 and 46 designate a sequence of controlled NOT (CNOT) operations, R z (2γ) and R z (γ) is a rotation transformation around the rotation axis z by angles 2γ and γ, applied to Figure 6a The quantum bit qb 2,1 and Figure 6b and Figure 6c The quantum bit qb 2,2 . R X (π / 2) represents the basis rotation transformation, and R X (-π / 2) represents the inverse basis rotation transformation. DETAILED DESCRIPTION

[0037] First, some general aspects related to the configuration of quantum computing systems will be discussed before explaining some possible implementations. Figure 1a-Figure 1d An overview of a first general aspect of the present disclosure relating to a method of configuring a quantum computing system is given in relation to the flowcharts shown. Other aspects of the method relating to performing quantum computing operations on a quantum computing system will also be described in relation to these figures. Figure 2a 、 Figure 2b 、 Figure 3a 、 Figure 3b and Figure 4 In this paper, we discuss an exemplary topology for arranging qubits on a quantum computing system according to the technology of the present disclosure. Figure 5a and Figure 5b Relatedly, we discuss examples of implementing quantum computing operations on quantum computing systems. Finally, Figures 6a to 6c Three examples of quantum circuits for performing possible quantum computing operations on quantum computing systems are presented in [1].

[0038] Figure 1a-Figure 1d A method for configuring a quantum computing system 1000 according to a first general aspect of the present disclosure is disclosed and proposed. The quantum computing system of the present disclosure includes a plurality of quantum bits arranged on a two-dimensional (2D) lattice (see, e.g., Figure 2a 、 Figure 2b 、 Figure 3a 、 Figure 3b and Figure 4 , in which various embodiments of 2D lattices are schematically shown and discussed further). The plurality of qubits of the first aspect are configured to perform a plurality of quantum computing operations (e.g., may include performing unitary transformations on individual qubits, the unitary transformations being implemented as a series of quantum gates acting on the qubits, see further discussion above). The method steps of the corresponding independent claims are summarized in Figure 1a-Figure 1d The method steps of the dependent claims are shown in boxes drawn by solid lines, while the method steps of the dependent claims are shown in boxes drawn by dotted lines.

[0039] The present technique for configuring a quantum computing system includes receiving a selection 100 of a first plurality of qubits 15a-15c; 1a-1d; 3a-3c of a plurality of qubits, wherein the first plurality of qubits comprises a plurality of qubit chains. Furthermore, each qubit 1a-1d of the plurality of qubit chains 15a-15b of the first plurality of qubits represents a first degree of freedom associated with a corresponding component of a physical system to be mapped to the plurality of qubit chains of the first plurality of qubits. In some examples, and consistent with the above discussion, the quantum Hamiltonian is represented by One or more components of the described physical system may be fermionic particles (e.g., fermionic orbitals), in which case the first degree of freedom may be referred to as a fermionic degree of freedom. Figure 2a and Figure 3a In the example of the 2D lattice shown, the number of quantum bit chains representing the first degree of freedom (e.g., the fermionic degree of freedom) includes four horizontal chains 15b and three vertical chains 15a (in Figure 2a 15a, 15b) and are arranged in a serpentine pattern (total, Figure 3a Twenty-one quantum bits q1 to q21 representing the first degree of freedom are shown. Figure 2b and Figure 3b In an embodiment of the invention, a chain of qubits representing the first degree of freedom (in Figure 2b The black bars 15a, 15b in FIG. 1 include two unconnected horizontal chains 15b and two other horizontal chains 15b connected by a vertical chain 15a (a total of Figure 3bTwelve qubits q1 to q12 representing a first degree of freedom are shown in FIG. 1 ). In some examples, the plurality of qubit chains of the first plurality of qubits may include one or more, two or more, three or more, four or more, five or more, seven or more, ten or more, or fifty or more qubit chains. A qubit chain (e.g., one or more qubit chains) in the plurality of qubit chains of the first plurality of qubits may include two or more, five or more, ten or more, twenty or more, or fifty or more qubits. In some cases, the number of qubits in the plurality of qubit chains of the first plurality of qubits may be equal to the number of fermionic degrees of freedom mapped to (or, in other words, encoded from) the plurality of qubit chains. In some examples, and consistent with the discussion above, a qubit (e.g., each qubit) representing a first degree of freedom may include “at least partial information” about more than one first degree of freedom due to the non-local nature of the mapping of the first degree of freedom to the qubits of the plurality of qubit chains and multi-qubit entanglement that may develop during quantum computation (see further discussion below).

[0040] In the present technology, each qubit (q1) in the first plurality of qubits is configured to send quantum information of the qubit to another qubit (q2) in the first plurality of qubits that is adjacent to the qubit. In addition, the another qubit in the first plurality of qubits is configured to receive quantum information of the qubit in the first plurality of qubits. The possible adjacent qubits in the plurality of chains of the first plurality of qubits are represented by Figure 3a and Figure 3b The solid vertical and horizontal lines in are specified. Figure 3a and Figure 3b It can be seen that qubit q1 of the upper chain of the first plurality of qubits is a nearest neighbor with respect to qubit q2 of the chain, such that qubit q2 can be classified as a neighboring qubit with respect to qubit q1 according to the definition further above. For the same reason, Figure 3a and Figure 3bThe qubit q3 of qubit q1 can be considered to be adjacent to qubit q2, and so on. Thus, qubit q1 can be configured to send the quantum information it carries to qubit q2 (e.g., using a fermion SWAP operation, see further discussion), and vice versa, qubit q2 can be configured to send the quantum information it carries to qubit q1. Similarly, qubit q2 can be configured to send the quantum information it carries to qubit q3, and vice versa, qubit q3 can be configured to send the quantum information it carries to qubit q2. Furthermore, qubit q2 can be configured to receive the quantum information carried by qubit q1, and vice versa, qubit q1 can be configured to receive the quantum information carried by qubit q2. In the example, qubit q3 can be configured to receive the quantum information carried by qubit q2, and vice versa, qubit q2 can be configured to receive the quantum information carried by qubit q3. Figure 3a (qubits q4 to q21) and Figure 3b Similar considerations may also apply to the other qubits of the chains of the first plurality of qubits shown (qubits q4 to q12).

[0041] The next step of the present technology includes receiving a selection 200 of a second plurality of qubits 16; 16a-16e; 2a-2d of the plurality of qubits, wherein the second plurality of qubits comprises a plurality of qubit ladders. Here, each qubit ladder represents a second degree of freedom associated with a corresponding component of the physical system to be mapped to the plurality of ladders of the second plurality of qubits. (As discussed above, "qubit ladder" will be used interchangeably with "ladder of qubits" and they have the same meaning.) The second degree of freedom of the first aspect is different from the first degree of freedom. In some examples, and consistent with the discussion above, the second degree of freedom is determined by the quantum Hamiltonian. One or more components of the described physical system may be bosonic modes, in which case the second degree of freedom may be referred to as a bosonic mode. Figure 3a and Figure 3b In the embodiment of the 2D lattice shown, each qubit ladder includes two qubits, which are enclosed in corresponding dashed ellipses. Figure 3a and Figure 3b In the embodiment shown in FIG, twelve qubit ladders are shown (eg, the upper left qubit ladder has qubits qb 1,1 and qb 1,2 , while the lower right qubit ladder has qubit qb 12,1 and qb 12,2 ). It can also be seen from these figures that the qubits within each ladder extend in the vertical direction, while the groups of qubit ladders extend in the horizontal direction. Figure 3a and Figure 3bIn the embodiment shown in FIG, three groups of ladders are shown, each group consists of four ladders, for example, the upper ladder group has four ladders with quantum bits qb 1,1 、qb 1,2 、qb 2,1 、qb 2,2 、qb 3,1 、qb 3,2 、qb 4,1 、qb 4,2 (The first subscript enumerates the ladder, while the second subscript corresponds to the qubit number within the ladder). Figure 2a and Figure 2b , several ladders of the second plurality of qubits are shown as four filled bars 16 extending in the horizontal direction. Each horizontal bar 16 in these figures is thicker than the bars depicting the chains 15a, 15b of the first plurality of qubits to schematically illustrate that a qubit ladder extending in the vertical direction can contain more than one qubit. In some cases, the qubits (e.g., each qubit) of a ladder (e.g., each ladder) representing the second degree of freedom can include "at least partial information" about one or more second degrees of freedom due to the non-local nature of the mapping of the second degrees of freedom to the qubits of the qubit ladder and possible multi-qubit entanglement that develops during quantum computation (see above and further discussion below).

[0042] In some examples, the number of qubit ladders representing the second degree of freedom can include one or more, two or more, five or more, ten or more, fifty or more, or hundreds or more qubit ladders. Several chains of qubit ladders (e.g., one or more qubit ladders) can include two or more, five or more, ten or more, twenty or more, or fifty or more qubits. In some cases, the number of ladders of the second plurality of qubits can be equal to the number of bosonic modes mapped to (or in other words, encoded from) this number of qubit ladders. In some embodiments, as in Figure 2b and Figure 3b In those shown, the number of qubits in the chains 15a; 15b representing the first degree of freedom may be equal to the number of ladders of qubits representing the second degree of freedom. Figure 3b In the embodiment of , there are twelve qubit ladders 16, which may represent, for example, twelve bosonic modes, and there are twelve qubits q1 to q12 in three chains of the first plurality of qubits, which may represent, for example, twelve fermionic degrees of freedom. In other embodiments, such as in Figure 2a and Figure 3a In the example, the number of qubits in the chains 15a; 15b representing the first degree of freedom can be greater than the number of qubits in the ladder representing the second degree of freedom. Figure 3b In the embodiment of Figure 3a In an embodiment of, there are twelve qubit ladders 16, which can represent, for example, twelve boson modes. On the other hand, in Figure 3a the 2D lattice of, there are twenty-one qubits q1 to q21 in six chains of a first plurality of qubits, which can represent, for example, twenty-one fermionic degrees of freedom. In still other embodiments, the number of qubits in a number of chains representing a first degree of freedom can be less than the number of qubit ladders representing a second degree of freedom (not shown in the drawings). In some cases, the total number M of qubits in a number of chains of a first plurality of qubits can be less than the total number N of qubits in a number of ladders of a second plurality of qubits, M < N. For example, the corresponding ratio M / N can be a value of 9 / 10 or less, 1 / 2 or less, 1 / 4 or less, 1 / 10 or less.

[0043] In the technology of the present disclosure, each qubit 2a; 2c in a second plurality of qubits is configured to send the quantum information of the qubit to another qubit 2b; 2d in the second plurality of qubits adjacent to the qubit. In addition, the other qubit in the second plurality of qubits is configured to receive the quantum information of the qubit in the second plurality of qubits. The possible adjacent qubits in the second plurality of qubits are specified by solid lines in Figure 3a and Figure 3b . In some cases, as in those cases shown in these figures, only qubits within the same ladder can be considered adjacent to each other. In Figure 3a and Figure 3b 's embodiment, the qubit qb of the upper left qubit ladder 1,1 is the nearest neighbor to the qubit qb of the same ladder 1,2 such that, according to the further definition above, the qubit qb 1,2 can be classified as a qubit adjacent to the qubit qb 1,1 . Thus, the qubit qb 1,1 can be configured to send the quantum information it carries to the qubit qb 1,2 (for example, using a SWAP operation, see further discussion), and vice versa, the qubit qb 1,2 can be configured to send the quantum information it carries to the qubit qb 1,1 . In addition, the qubit qb 1,2 can be configured to receive the quantum information carried by the qubit qb 1,1 , and vice versa, the qubit qb 1,1 can be configured to receive the quantum information carried by the qubit qb 1,2 . Similar considerations apply to Figure 3a and Figure 3bThis also holds true for the other eleven ladder qubits presented in . In other cases, such as Figure 4 In the embodiment shown, qubits from different ladders can be adjacent to each other (in Figure 4 The possible proximity between qubits of adjacent qubit ladders is shown by dashed horizontal lines in FIG.

[0044] In a first aspect, one or more qubits 1a; 1c of the chains of the first plurality of qubits are adjacent to corresponding one or more qubits 2a; 2c of the ladders of the second plurality of qubits. Furthermore, the one or more qubits of the chains of the first plurality of qubits can be configured to send quantum information to the corresponding one or more qubits of the ladders of the second plurality of qubits. Additionally or alternatively, the one or more qubits of the chains of the first plurality of qubits can be configured to receive quantum information from the corresponding one or more qubits of the ladders of the second plurality of qubits. Figure 3a and Figure 3b In the example of FIG, several chains of the first plurality of qubits and several possible adjacent qubits of the second plurality of qubits are designated by dashed vertical lines. For example, qubit q2 of the upper chain of the first plurality of qubits is positioned relative to qubit qb of the upper ladder of qubits. 2,1 is the nearest neighbor, so that the quantum bit qb 2,1 can be classified as a qubit adjacent to qubit q2. Therefore, qubit q2 can be configured to send the quantum information it carries to qubit qb 2,1 (For example, by Figure 5a 5c, see discussion below). Additionally or alternatively, qubit q2 may be configured to receive a quantum signal generated by qubit qb. 2,1 In some cases, corresponding one or more qubits 2a; 2c of the second plurality of qubits, adjacent to one or more qubits 1a; 1c of the first plurality of qubit chains, are configured to receive quantum information from and / or send quantum information to one or more qubits 1a; 1c of the first plurality of qubit chains. Back to qubits q2 and qb 2,1 Example: qubit qb on the ladder of qubits 2,1 can be configured to send the quantum information it carries to qubit q2. Additionally or alternatively, qubit qb 2,1 can be configured to send the quantum information it carries to the quantum bit qb 2,1 Similar considerations apply to Figure 3a and Figure 3bThe eleven other ladder qubits presented in adjacent to the corresponding qubits of the chain of the first plurality of qubits are also valid (e.g., for q1 and qb 1,1 , for q3 and qb 3,1 and other qubit pairs).

[0045] In the disclosed techniques, and as further defined above, the chains of the first plurality of qubits and the ladders of the second plurality of qubits are configured to perform a plurality of quantum computing operations (see the examples and embodiments disclosed further below for details). In other words, some or all of the qubits from the chains of the first plurality of qubits and the ladders of the second plurality of qubits can participate in performing a quantum computing operation.

[0046] In with Figure 3a and Figure 3bIn the above discussion related to the embodiments of the present invention, the nearest neighbor qubits within the same or different types of qubits are referred to as adjacent qubits, which is one possible example of when a pair of qubits can be classified as adjacent (the fact that the qubit pair is adjacent is indicated by the corresponding solid or dashed lines in these figures). In other cases, other criteria can be used to determine whether a pair of qubits (within the same or different types of qubits) is adjacent. As described above, the decisive factor for classifying two qubits as adjacent is the possibility of implementing a universal quantum gate that acts on these two qubits without involving a third qubit for this purpose. For example, if the distance from the one qubit to the other qubit is equal to or less than a predetermined characteristic distance, then one qubit from the plurality of qubits on the 2D lattice can be considered to be adjacent to another qubit from the plurality of qubits, so that the above-mentioned universal gate can be implemented based only on the two qubits. In some examples, the predetermined characteristic distance can be proportional to the average distance between qubits in the plurality of qubits arranged on the 2D lattice (for example, between qubits in the first plurality of qubits and the second plurality of qubits described above). In some cases, the proportionality factor between these quantities may be selected to be 0.5 or less, 0.9 or less, 1.2 or less, 1.5 or less). In some cases, the predetermined characteristic distance may be equal to the average distance between the qubits of the plurality of qubits. For example, for the case where the 2D lattice includes square units, these two alternatives may be preferred. In still other examples, when the average distance between the qubits of the first plurality of qubits is different from the average distance between the qubits of the second plurality of qubits, a predetermined number of characteristic distances may be used to identify adjacent qubits. For example, the predetermined characteristic distance may be proportional to or equal to the corresponding average distance between qubits within the same or different plurality of qubits. In some cases, the value of the proportionality factor may be selected similarly to the case of a single predetermined characteristic distance.

[0047] In other cases, and according to the above definition, the spatial distance between qubits may not be the only relevant factor for classifying a pair of qubits as adjacent. For example, qubit-qubit coupling may be increased (e.g., by flux control or additional circuitry in the case of superconducting qubits) such that two qubits can be considered adjacent to each other in some examples despite the spatial separation. In other words, by Figure 3a and Figure 3bThe corresponding solid or dashed line in indicates the proximity between each pair of qubits to illustrate the fact that the pair of qubits under consideration are adjacent, without specifying which of the above factors is decisive for the proximity (e.g., the distance between qubits q1 and q2 of an upper chain of the first plurality of qubits may be different from the distance between qubits q2 and q3 of the same chain, but both pairs may still be classified as adjacent pairs because the other above factors come into play).

[0048] In the present technology, the qubit ladders 16 (e.g., each qubit ladder) of the plurality of ladders of the second plurality of qubits may include a plurality of qubits, wherein the plurality of qubits within the ladders extend along a first direction (e.g., in Figure 3a 、 Figure 3b 、 Figure 4 and Figure 5a In the first aspect of the present specification, each of the chains of the first plurality of qubits may be in a first direction 15a (e.g., in a vertical direction). Figure 3a and Figure 3b in the vertical direction shown) or in a second direction 15b different from the first direction (e.g., in Figure 3a and Figure 3b ) extending in the horizontal direction shown. It should be noted that in this disclosure, the extension of several ladders of the first plurality of qubits, multiple qubits within a qubit ladder (e.g., each qubit ladder), and several chains should be interpreted broadly: in some examples, the shape of a qubit chain, qubit ladder, or qubits within a qubit ladder can form a one-dimensional, 1D curve in the plane of a 2D lattice extending along the corresponding direction. In some examples, this consideration can apply to one or more (e.g., all) qubit chains, qubit ladders, and qubits within a qubit ladder.

[0049] In some cases, the plurality of ladders of the second plurality of qubits may include a set of qubit ladders 16a-16d extending along the second direction. In some cases, the set of qubit ladders may be aligned in a straight line in the second direction. Figure 5a , which shows a set of four ladders (each consisting of two qubits) aligned in a straight line in the horizontal direction. In other examples, the ladders of the second plurality of qubits can include two or more unconnected groups of qubit ladders extending along the second direction. In some cases, each of the two or more unconnected groups of qubit ladders can be aligned on a corresponding straight line in the second direction. For example, in Figure 3a and Figure 3bIn the embodiment of , three disconnected qubit ladder groups (each consisting of two qubits) are aligned in a straight line in the horizontal direction. In some cases, two groups of qubit ladders can be classified as disconnected from each other if there are no adjacent pairs of qubits (in the sense described above) belonging to two qubit ladders from different qubit ladder groups. For example, since (qb 1,2 ,qb 8,2 ), (qb 2,2 ,qb 7,2 ), (qb 3,2 ,qb 6,2 ) and (qb 4,2 ,qb 5,2 ) are not adjacent qubits, so we can Figure 3a The two upper qubit ladder groups depicted in FIG are classified as unconnected qubit ladder groups. In other cases, the plurality of ladders of the second plurality of qubits may include two or more connected qubit ladder groups extending along the second direction (not shown in the figures). It should be noted that two qubit ladder groups may be classified as connected to each other when, for example, at least one pair of adjacent qubits belonging to two qubit ladders from different qubit ladder groups can be found.

[0050] In certain cases of the first aspect, such as Figure 3a and Figure 3b As shown in the embodiment of FIG, the qubit ladders within a qubit ladder group (e.g., each individual qubit ladder group) may not be connected to each other. In this case, no adjacent qubits residing in different qubit ladders can be found, i.e., only qubit pairs within each individual ladder can be classified as adjacent qubits. For example, four pairs of adjacent qubits (qb 1,1 ,qb 1,2 ), (qb 2,1 ,qb 2,2 ), (qb 3,1 ,qb 3,2 ) and (qb 4,1 ,qb 4,2 )form Figure 3a In other cases of the first aspect, such as in Figure 4 As shown in the embodiment of , one or more adjacent qubit ladder pairs within a qubit ladder group (e.g., each individual qubit ladder group) can be connected to each other. In this case, at least one pair of adjacent qubits can be found that belong to adjacent qubit ladder pairs within the same qubit ladder group. Figure 4 In the embodiment of 1,1 ,qb 2,1 ), (qb 2,1 ,qb 3,1 ), (qb3,1 ,qb 4,1 ), (qb 1,2 ,qb 2,2 ), (qb 2,2 ,qb 3,2 ) and (qb 3,2 ,qb 4,2 ) are six adjacent qubit pairs that belong to corresponding adjacent qubit ladder pairs.

[0051] In some cases of the first aspect, the number of chains of the first plurality of qubits (representing the first degree of freedom) can include a plurality of connected qubit chains, wherein each chain in the plurality of connected qubit chains extends in one of a first direction and a second direction. In addition, one or more chains in the plurality of connected chains in the number of chains of the first plurality of qubits extending along the second direction (e.g., in the horizontal direction) can be connected to a corresponding chain in the plurality of connected qubit chains extending along the first direction (e.g., in the vertical direction). In the present technology, each chain in the plurality of connected chains of the first plurality of qubits can be aligned on a corresponding straight line in one of the first direction and the second direction. Figure 2a In the embodiment of the invention, four chains 15b of the first plurality of qubits are aligned in a straight line in the horizontal direction and are connected by three chains 15a of the first plurality of qubits aligned in a straight line in the vertical direction. Figure 2a The upper part of Figure 3a In the first aspect, three chains 15b of the first plurality of qubits are aligned in a straight line in the horizontal direction, and two qubit chains 15a connected to the first plurality of qubits are aligned in a straight line in the vertical direction. In the first aspect, the plurality of connected chains can be arranged in a serpentine shape extending in the first direction, at least partially adjacent to several ladders of the second plurality of qubits (e.g., in Figure 2a and Figure 3a 16). In some cases, multiple chains in the multiple connected chains of the first plurality of qubits aligned in the second direction may be interrupted in each first or second chain by two respective qubit ladder groups from two or more unconnected qubit ladder groups of the second plurality of qubits (see, e.g., Figure 2a , where the lowest qubit chain 15b of the serpentine is interrupted by two qubit ladder groups 16, and two subsequent horizontal qubit chains 15b of the serpentine are interrupted by two subsequent qubit ladder groups 16. In one particular case, one or more of the plurality of connected chains aligned on respective straight lines in the second direction (e.g., in the horizontal direction) may be adjacent to respective one or more of the ladders of the second plurality of qubits (e.g., in the horizontal direction). Figure 3aIn the embodiment of the invention, the upper qubit chain having qubits q1, q2, q3 and q4 aligned on a horizontal line is connected to the upper qubit chain having qubits (qb i,2 ,qb i,2 ) are adjacent to each other, where index i enumerates the ladder and runs from 1 to 4).

[0052] In an alternative embodiment of the first aspect, the plurality of chains of the first plurality of qubits (representing the first degree of freedom) may include a plurality of unconnected qubit chains aligned on corresponding straight lines in a second direction (e.g., in a horizontal direction) and / or one or more pairs of chains aligned on corresponding straight lines in the second direction. In addition, the two chains within the pair of chains may be connected to each other by corresponding chains extending in the first direction (e.g., in a vertical direction). In the present technology, the two chains within the pair of chains may be connected to each other by corresponding chains extending in the first direction. In some examples, the pair of chains may be disconnected from one or more subsequent chains of the plurality of chains of the first plurality of qubits. In Figure 2b In the embodiment of the invention, four chains 15b of the first plurality of qubits are aligned in a straight line in the horizontal direction. Two of them form a pair of qubit chains 15b connected by chains 15a of the first plurality of qubits aligned in a straight line in the vertical direction. This pair of chains and the other two qubit chains 15b ( Figure 2b The upper and lower qubit chains 15b) are disconnected. Figure 2b The upper part of Figure 3b In the embodiment, three chains 15b of the first plurality of qubits are aligned in a straight line in the horizontal direction. Two of them form a pair of qubit chains 15b connected by a chain 15a of the first plurality of qubits aligned in a straight line in the vertical direction. The pair of chains is connected by a chain 15b of the first plurality of qubits aligned in a straight line in the vertical direction. Figure 3b The third (upper) qubit chain 15b of the first plurality of qubits is shown disconnected. In some cases, each chain of the number of disconnected qubit chains, or each chain of one or more pairs of chains, can be at least partially adjacent to a corresponding one or more ladders from the number of ladders of the second plurality of qubits. For example, each of the four qubit chains of the first plurality of qubits that are aligned in a straight line in a horizontal direction is adjacent to Figure 2b In the qubit ladder. Figure 3b In an embodiment, each of the three qubit chains of the first plurality of qubits aligned in a straight line in a horizontal direction is adjacent to a corresponding four ladders of the second plurality of qubits.

[0053] In this alternative embodiment of the first aspect, the first plurality of qubits may further include one or more qubit auxiliary chains 15c; 3a-3c, configured to exchange quantum information between subsequent unconnected chains of the first plurality of qubits (e.g., using a series of SWAP operations, see discussion below). It should be noted that these qubit auxiliary chains do not represent the first degree of freedom or the second degree of freedom. Figure 3b The embodiment illustrates two qubit auxiliary chains, including qubits qh1 to qh6 in an upper auxiliary chain and qubits qh7 to qh9 in a lower auxiliary chain. (The qubits of an auxiliary chain may be referred to as auxiliary qubits.) In some cases, each chain of one or more auxiliary chains 15c of the first plurality of qubits may include a first qubit 3a; qh1 and a second qubit 3b; qh6, where the first qubit 3a; qh1 is adjacent to a qubit q4 of a corresponding chain 15b from several unconnected chains or one or more pairs of chains (this proximity is determined by Figure 3b qh6 is adjacent to qubit q5 of another chain from several unconnected chains or one or more pairs of chains, the other chain being subsequent to the corresponding chain, wherein the corresponding chain and the subsequent chain are disconnected from each other (this proximity is indicated by Figure 3b (illustrated by the dashed line between qubits qh6 and q5 in the corresponding chain). In this embodiment of the first aspect, a first qubit 3a; qh1 adjacent to a qubit of the corresponding chain can be configured to receive quantum information from and / or send quantum information to a qubit q4 of the corresponding chain in several unconnected chains or one or more pairs of chains. Additionally, a second qubit 3b; qh6 adjacent to a qubit q5 of another chain that is subsequent to the corresponding chain can be configured to receive quantum information from and / or send quantum information to a qubit of another chain in several unconnected chains or one or more pairs of chains. In some cases, conversely, a qubit q4 of the corresponding chain in several unconnected chains or one or more pairs of chains adjacent to the first qubit 3a; qh1 can be configured to send quantum information to and / or receive quantum information from the first qubit 3a; qh1. Furthermore, a qubit q5 of another chain that is subsequent to the corresponding chain can be configured to send quantum information to and / or receive quantum information from the second qubit 3b; qh6.

[0054] exist Figure 2b and Figure 3bIn the embodiment shown, the auxiliary chains 15c; 3a-3c of qubits extend in a first direction (i.e., in this example, they are aligned in a straight line in the vertical direction). Additionally or alternatively, one or more chains of auxiliary chains 15c; 3a-3c from one or more qubits may extend in a second direction (e.g., they may be aligned in a straight line in the horizontal direction). For example, when Figure 2b and Figure 3b This may be the case when one or more qubits in the qubit chain 15b representing the first degree of freedom shown in FIG are replaced by corresponding auxiliary qubits. Figure 3b In the embodiment of FIG. 1 , if qubit q4 of the upper horizontal chain is replaced by auxiliary qubit qh10 and / or qubit q5 of another horizontal chain is replaced by auxiliary qubit qh11 (not shown in the figures), auxiliary chains 15c; 3a-3c of qubits can extend in both the first and second directions. In this case, the number of qubit ladders representing the second degree of freedom (e.g., bosonic modes) can be greater than the number of qubits in the chains 15a; 15b representing the first degree of freedom (e.g., fermionic degrees of freedom).

[0055] The method of the first aspect may further include receiving a selection of a third plurality of qubits 17; 4a-4b of the plurality of qubits. In some cases, several qubits of the third plurality of qubits (qR2-qR5) may be adjacent to two or more ladders 16e; 16a of the several ladders of the second plurality of qubits and configured to receive quantum information from and / or send quantum information to two or more ladders of the several ladders of the second plurality of qubits. Two or more ladders 16e; 16a of the several ladders of the second plurality of qubits adjacent to several qubits (qR2-qR5) of the third plurality of qubits may be configured to send quantum information to and / or receive quantum information from several qubits (qR2-qR5) of the third plurality of qubits. The third plurality of qubits of the present specification may include one or more qubit chains extending in a first direction (e.g., in a vertical direction). This situation is Figure 2a and Figure 2b , where the third plurality of qubits, also referred to as quantum exchange register 17 , is represented in these figures by vertical filled bars. Figure 4 Schematically shows the Figure 2a and Figure 2b Further details of the arrangement of the qubits of the quantum exchange register 17 are shown in . Figure 4 Four of the six qubits of the quantum register 17 in the quantum register 17, namely qubits qR2, qR3, qR4 and qR5, are adjacent to qubits qb of two qubit ladders, respectively. 1,1 、qb1,2 、qb 8,2 and qb 8,1 , and configured according to the above definition. Figure 4 In one non-limiting example, the third plurality of qubits is shown as a single chain extending in a vertical direction. In other examples, the third plurality of qubits can include two or more qubit chains, three or more qubit chains, five or more qubit chains, or ten or more qubit chains; in some cases, some or all of the qubit chains can extend in the first direction (not shown in the figures).

[0056] In the disclosed technology, qubit ladders 16 (e.g., each qubit ladder) in the plurality of ladders of the second plurality of qubits may include a single qubit adjacent to a qubit of a corresponding chain 15b of the first plurality of qubits, wherein the single qubit is separated from the qubits of the corresponding chain by a first predetermined distance. For example, Figure 3a The four qubits qb of the upper ladder group are shown 1,1 、qb 2,1 、qb 3,1 and qb 4,1 qubits q1, q2, q3, and q4, respectively, are separated by the same first predetermined distance in a non-limiting example. Thus, in each of these four qubit pairs from two different qubit species, a universal quantum gate acting on the two qubits in any of these pairs can be implemented without involving the third qubit, as explained in more detail above. In some cases, when spatial separation is the determining factor for classifying a pair of qubits as adjacent, the first predetermined distance is less than a threshold. This threshold can be defined as a threshold separation distance between qubits, beyond which the two qubits become non-adjacent.

[0057] In some possible topologies of the present disclosure, the spatial arrangement of qubits and the relative distances between qubits of the same kind and / or different kinds can be similar to Figure 2a and Figure 3a In some cases, if a pair of subsequent chains from the plurality of connected chains of the first plurality of qubits is uninterrupted, the pair of subsequent chains may be separated by a second predetermined distance, e.g., Figure 3aThe second predetermined distance shown can be the distance between any of the qubit pairs (q13, q16), (q12, q17), and (q11, q18), which in some embodiments can be the same. Otherwise, when the pair of subsequent chains is interrupted, the pair of subsequent chains can be separated by a third predetermined distance: for example, the third predetermined distance can be the distance between any of the qubit pairs (q1, q14), (q3, q12), or (q5, q10), which in some embodiments can be the same. In the first aspect, the qubit ladders (e.g., each qubit ladder) of the plurality of ladders of the second plurality of qubits can have a predetermined length. In some cases, if a pair of subsequent ladder groups are uninterrupted, the pair of ladder groups can be separated by a fourth predetermined distance, for example, Figure 3a The fourth predetermined distance shown may be a quantum bit pair (qb 1,2 、qb 8,2 ), (qb 2,2 、qb 7,2 ) and (qb 4,2 、qb 5,2 ), which in some embodiments may be the same. Otherwise, when the pair of subsequent groups is interrupted, the pair of subsequent groups may be separated by a fifth predetermined distance: for example, the fifth predetermined distance may be the distance between any pair of qubits (qb 8,1 、qb 9,1 ), (qb 7,1 、qb 10,1 ) and (qb 5,1 、qb 12,1 ), which in some embodiments may be the same. In some specific examples, the first, second, and fourth predetermined distances may be equal. Additionally, the predetermined length of the qubit ladder may be equal to the product of the first predetermined distance and a value obtained by subtracting the number of qubits in the plurality of qubits in the qubit ladder from one. In some specific cases, the third predetermined distance may be equal to twice the sum of the predetermined length and the first predetermined distance plus the fourth predetermined distance. Furthermore, in an example, the fifth predetermined distance may be equal to the sum of the second predetermined distance and twice the first predetermined distance.

[0058] In one example of the present technology, the 2D lattice can be a rectangular lattice. In other examples, the 2D lattice can be a square lattice. In still other examples, the 2D lattice can have any other 2D shape (e.g., a polygon, a quadrilateral, a pentagon, a hexagon, a parallelogram, a circle, or a triangle). In some examples, multiple qubits from a plurality of qubits arranged in the 2D lattice can be equally spaced. For example, all qubits from one or more of the first, second, and third plurality of qubits can be equally spaced. In some cases, all qubits in the 2D lattice can be equally spaced. Furthermore, in some cases, a 2D lattice (e.g., a rectangular or square lattice) can include multiple square cells having four qubits located at the vertices of the square cells, where each qubit from the four qubits is a qubit from one of the first, second, and third plurality of qubits. In Figure 3a 、 Figure 3b and Figure 4 In a qubit topology of , there are square cells with qubits belonging to various combinations of one or more of (i) qubit chains of a first plurality of qubits, (ii) qubit ladders of a second plurality of qubits, and (iii) qubit chains of a third plurality of qubits (i.e., qubits from a quantum exchange register). For example, one square cell may include only qubits of the same kind (i), (ii), or (iii), while another square cell may include qubits of two or all of the listed kinds. In an alternative topology (not shown in the figures), the 2D lattice may include qubits with respect to Figure 3a A plurality of square units shown in FIG are rotated 45° about an axis perpendicular to the paper surface of the figure (see, for example, https: / / doi.org / 10.1038 / s41586-019-1666-5 Figure 1a for more details). Additionally or alternatively, the 2D lattice may include a plurality of quadrilateral (e.g., rectangular) units having four qubits at vertices of the quadrilateral (e.g., rectangular) unit cells, wherein each qubit from the four qubits is a qubit from one or more of the first, second, and third pluralities of qubits. Additionally or alternatively, the 2D lattice may include a plurality of triangular units having three qubits at vertices of the triangular unit cells, wherein each qubit from the three qubits is a qubit from one or more of the first, second, and third pluralities of qubits.

[0059] In the present technology, a first plurality of qubits, a second plurality of qubits, and a third plurality of qubits can be selected during the design phase of the quantum computing system. Additionally or alternatively, the first plurality of qubits, the second plurality of qubits, and the third plurality of qubits can be selected, for example, automatically (e.g., by a program / algorithm depending on the computational task to be performed). In other examples, the first plurality of qubits, the second plurality of qubits, and the third plurality of qubits can be selected by a user (e.g., via a suitable user interface). In the technology disclosed herein, the receiving selection steps 100, 200, 250 of the first one or more qubits and the second plurality of qubits and the third plurality of qubits are not particularly limited, and in some cases, qubits can be redistributed between the three plurality of qubits (e.g., by a user or automatically as described above): for example, for one quantum computing task (see discussion below for more details), several qubits from a plurality of qubits of a quantum computing system can be selected as members of the first plurality of qubits, while for another quantum computing task, one or more qubits (e.g., all qubits) from the plurality of qubits can be selected as belonging to the second and / or third plurality of qubits (e.g., to perform the quantum computing task more efficiently). In other examples, similar considerations apply to several qubits from the second and / or third plurality of qubits.

[0060] The next step of the method may include performing more than 300 quantum computing operations on the quantum computing system after performing the receiving selection step (related to configuring the quantum computing system). In the present technology, performing more than 300 quantum computing operations on the quantum computing system may include performing more than 400 quantum computing operations on the plurality of chains 15a-15b of the first plurality of quantum bits. Figure 2a 、 Figure 2b 、 Figure 3a 、 Figure 3b and Figure 4 Possible non-limiting arrangements of several chains of the first plurality of qubits representing the first degree of freedom are further discussed, see e.g. Figure 3a Twenty-one qubits q1 to q21 within the six chains 15a, 15b of the first plurality of qubits and Figure 3b In a first aspect, performing a plurality of quantum computing operations on the first plurality of qubits may include exchanging quantum information between two qubits (q1, q2) in one or more adjacent qubit pairs (q1, q2; q2, q3) from the first plurality of qubits in the first plurality of qubits chains 15a-15b (e.g., by applying corresponding unitary transformations implemented as one or more quantum gates according to the above definitions to the qubits). For example, from Figure 3a and Figure 3bThe qubits q1 and q2 of the upper chain of the first plurality of qubits depicted in the figures may be adjacent according to any of the criteria described above and may exchange quantum information with each other (e.g., using the fermionic SWAP operation discussed below). In some cases, any other pair or pairs of adjacent qubits of the chains of the first plurality of qubits, e.g., q2 and q3, q3 and q4, q10 and q11, and other pairs of adjacent qubits of the chains shown in these figures, may exchange quantum information with each other in a manner similar to that of the qubits q1 and q2.

[0061] The disclosed techniques may include performing more than 500 quantum computing operations on the second plurality of qubit ladders 16; 16a-16e. Possible non-limiting arrangements of the second plurality of qubit ladders 16; 16a-16e are described above in conjunction with Figure 2a 、 Figure 2b 、 Figure 3a 、 Figure 3b and Figure 4 For further discussion, see e.g. Figure 3a and Figure 3b There are three sets of quantum bit ladders extending horizontally, each set of quantum bit ladders includes four ladders with quantum bits qb i,1 、qb i,2 (each ladder extends in a vertical direction), where subscript i ranges from 1 to 12. In a first aspect, performing a plurality of quantum computing operations on the ladders of the second plurality of qubits may include performing a plurality of quantum computing operations on two qubits (qb) in one or more adjacent qubit pairs of each ladder 16; 16a-16e from the ladders of the second plurality of qubits. 2,1 、qb 2,2 ) to exchange quantum information. For example, Figure 3a and Figure 3b The qubit qb of the upper left qubit ladder of the second plurality of qubits shown in 1,1 and qb 1,2 , can be adjacent according to any of the above criteria, can exchange quantum information with each other (e.g., using one or more controlled NOT (CNOT) operations and / or similar to the following with Figures 6a to 6c In some cases, adjacent qubits within any other qubit ladder or ladders of the second plurality of qubits, i.e., qb shown in these figures, i,1 、qb i,2 (i from 2 to 12), can be compared with the quantum bit qb on the upper left ladder 1,1 and qb 1,2 They exchange quantum information with each other in a similar way.

[0062] The technology may also include exchanging 600 quantum information between two qubits from one or more pairs of adjacent qubits 1a, 2a; 1c, 2c, wherein one qubit 1a; 1c of the pair is from a first plurality of qubit chains and the other qubit 2a; 2c of the pair is from a corresponding ladder of a second plurality of qubits, the corresponding ladder being adjacent to the qubit from the chains. Figure 3a and Figure 3b In the embodiment: qubits q1 and q2 from the upper chain of the first plurality of qubits Figure 3a and Figure 3b The second qubit in the upper left qubit ladder is depicted as qubit qb 1,1 can exchange quantum information with each other (e.g., using one or more controlled NOT (CNOT) operations and / or as described below with Figures 6a to 6c In some cases, one or more pairs of adjacent qubits that are of different kinds of qubits as defined above (i.e., one qubit is from the chain of the first plurality of qubits and the other qubit belongs to the qubit ladder), e.g., q2 and qb 2,1 , q3 and qb 3,1 , q4 and qb 4,1 and other pairs of adjacent qubits shown in these figures, can be used with the qubits q1 and qb 1,1 They exchange quantum information with each other in a similar way.

[0063] In some cases of the present specification, the number of times that quantum information should be exchanged between pairs of qubits belonging to the same or different kinds of qubits during the execution of more than 300 quantum computing operations on a quantum computing system can depend on one or more of the following factors: i) the specific qubit arrangement of the quantum computing system on the 2D lattice; ii) the specific physical system mapped and simulated on the quantum computing system; iii) the specific encoding used to encode the physical system into the multiple qubits of the quantum computing system; and iv) the decomposition of the quantum computing operations to be performed for the physical system under consideration into corresponding quantum computing operations performed by native hardware gates.

[0064] According to the first aspect, the step of performing more than 400 quantum computing operations on the chains of qubits and more than 500 quantum computing operations on the ladders may further comprise performing some of the more than 410 quantum computing operations on one or more qubits 1a; 1c of the chains of the first plurality of qubits, the one or more qubits 1a; 1c being adjacent to corresponding one or more qubits 2a; 2c of the ladders of the second plurality of qubits. Figure 3aIn an embodiment, the twelve qubits q1 to q4 and q11 to q18 of the chains of the first plurality of qubits are qubits that are coupled to the qubits qb of the ladders of the second plurality of qubits. i,1 To qb i,1 adjacent, where i ranges from 1 to 4 and from 5 to 12, respectively (the proximity of these qubit pairs is indicated by dashed lines, as discussed above). Figure 3b In another embodiment shown in FIG, all twelve qubits q1 to q12 of the chains of the first plurality of qubits are coupled to qubits qb of the ladders of the second plurality of qubits. i,1 To qb i,1 adjacent, where i ranges from 1 to 12, respectively. In some cases, the steps 400, 500 of performing a plurality of quantum computing operations may include performing several of the plurality of quantum computing operations 510 on the corresponding one or more qubits 2a; 2c of the plurality of ladders of the second plurality of qubits. For example, twelve ladder qubits qb adjacent to corresponding qubits of the plurality of chains of the first plurality of qubits shown in these figures may be i,1 To qb i,1 Such quantum computing operations are performed on (i from 1 to 12).

[0065] In the present technology, the steps 400, 500 of performing the plurality of quantum computing operations may further include performing 520 of the plurality of quantum computing operations on the plurality of qubits 2b; 2d of the plurality of ladders of the second plurality of qubits for which no adjacent qubits from the plurality of chains of the first plurality of qubits are available. Figure 3a and Figure 3b In an embodiment, the second plurality of qubits comprises a plurality of ladder qubits qb i,2 (i from 1 to 12) have no neighboring qubits from the first plurality of qubits. In some cases, a qubit of each qubit ladder for which no neighboring qubits from the number of chains of the first plurality of qubits are available can exchange quantum information with a corresponding qubit of the same qubit ladder that is neighboring that qubit of the number of chains. Back Figure 3a and Figure 3b Example: Each quantum bit qb i,2 Relative to quantum bit qb i,1(i from 1 to 12) are adjacent such that they can exchange quantum information with each other. In addition, when a qubit ladder (e.g., one or more or each qubit ladder) contains more than two qubits (a situation not shown in the figures), the adjacent qubits of the qubit ladder can exchange quantum information with each other as discussed above (i.e., for example, when none of the adjacent qubits of the qubit ladder has adjacent qubits from several chains of the first plurality of qubits).

[0066] In some examples of the present disclosure, step 400 of performing a plurality of quantum computing operations on a number of qubit chains may also include performing 420 a number of quantum computing operations on a number of qubits of the number of chains in the first plurality of qubits for which adjacent qubits from the number of ladders in the second plurality of qubits are not available. For example, in Figure 3a In the embodiment of the first plurality of qubits, none of the qubits q5 to q10 and q19 to q21 of the chains have adjacent qubits that belong to one of the qubit ladders shown in the figure. In other cases, such as with Figure 3b In those cases disclosed in connection with embodiments of the present invention, each qubit q1 to q12 of the several chains of the first plurality of qubits is adjacent to a corresponding qubit from a qubit ladder in the several qubit ladders: in other words, for such embodiments, it does not matter that step 420 of performing the several quantum computing operations defined above is performed.

[0067] In some cases, the first aspect may further include receiving, by a first qubit 3a;qh1 in a chain in one or more auxiliary chains 15c of the first plurality of qubits, quantum information from a qubit q4 in a corresponding chain 15b in one or more pairs of chains or several disconnected chains. When the first plurality of qubits includes one or more auxiliary chains 15c;3a-3c of qubits, this method step may be applicable to those embodiments of the first aspect, as described above with respect to configuring a quantum computing system and Figure 3b Next, the method may further comprise: transferring quantum information from a first qubit 3a;qh1 of a chain of one or more auxiliary chains 15c of the first plurality of qubits to a second qubit 3b;qh6 by iteratively applying a number of subsequent SWAP operations between adjacent qubits of a chain qh2-qh5 of the one or more auxiliary chains 15c of the first plurality of qubits, the chains qh2-qh5 being arranged between the qubits 3a;qh1 and 3b;qh6 (see Figure 3bFinally, for embodiments in which auxiliary chains are available, the present technology may also include sending quantum information from a second qubit 3b; qh6 of a chain of one or more auxiliary chains 15c of the first plurality of qubits to a qubit q5 of another chain in one or more chain pairs or disconnected chains that is subsequent to the respective chain. It should be noted that, as discussed further above, qubits q4 and qh1 are adjacent qubits. The same applies to qubits qh6 and q5, which are also adjacent qubits.

[0068] In some examples of the present technology, the aforementioned SWAP operation can be performed by a corresponding quantum circuit for swapping two qubits (not shown in the figures). In some examples, the corresponding quantum circuit can include three CNOT quantum gates known to those skilled in the art (see, for example, MA Nielsen and ILChuang, "Quantum Computation and Quantum Information": 10th Anniversary Edition, Cambridge University Press, 2010). Additionally or alternatively, one or more SWAP operations can include decomposing the SWAP operation into corresponding quantum computing operations performed by native hardware gates.

[0069] In the disclosed technology, the second plurality of qubit ladders may include a first set of qubit ladders 16a-16d, which includes a first ladder 16a and one or more qubit ladders 16b-16d. In a non-limiting example and for further discussion, Figure 4The lower qubit ladder group in the embodiment of the invention can be referred to as the "first group of qubit ladders", the left ladder 16a from the group can be referred to as the "first ladder", and the remaining three qubit ladders 16b to 16d can be referred to as the "one or more qubit ladders". In some cases, the method of the first aspect can include transferring quantum information from the ladders 16b-16d of the one or more qubit ladders to the first ladder 16a by applying a SWAP operation between the ladders 16b-16d of the one or more qubit ladders and the first ladder 16a if the ladder 16b is adjacent to the first ladder 16a. As a result, the ladder 16b (which is adjacent to the first ladder) and the first ladder can exchange quantum information between each other. As further described above, adjacent qubit ladder pairs within the same qubit ladder group can be classified as adjacent qubit ladder pairs if at least a single pair of adjacent qubits belonging to the pair of qubit ladders can be found. In some cases, the SWAP operation between two adjacent ladders can include several SWAP operations applied to the individual qubits of the ladders. For example, the number of SWAP operations can increase as the number of qubits in the ladder under consideration increases and the number of adjacent qubit pairs in the two ladders decreases. Figure 4 The qubit ladder 16b located next to the left ladder 16a of the lower qubit ladder group can be considered as the qubit ladder adjacent to the left ladder of the qubit 16b, because there are two pairs of adjacent qubits, namely (qb 8，1 ,qb 7，1 ) and (qb 8，2 ,qb 7，2 ), which belong to these two ladders 16a, 16b. In this case, the SWAP operation between two adjacent ladders 16a, 16b (each of these ladders includes two qubits) may include the following: 8，1 ,qb 7，1 ) and (qb 8，2 ,qb 7，2 ) apply two SWAP operations between them.

[0070] Otherwise, if the ladder 16d is non-adjacent relative to the first ladder 16a, the method of the first aspect may include transferring quantum information from the ladders 16b-16d of the one or more qubit ladders to the first ladder 16a by applying a number of subsequent SWAP operations between the ladder 16d and an adjacent ladder 16b; 16c of the one or more qubit ladders, the adjacent ladder 16b; 16c being arranged between the ladder 16d and the first ladder 16a of the one or more qubit ladders. Figure 4Embodiment: Ladder 16c is not adjacent to ladder 16a (i.e., according to the terminology used above, the "first ladder"). Therefore, quantum information from ladder 16c, which is not adjacent to ladder 16a, can first be sent to its adjacent ladder 16b, for example, by 7，1 ,qb 6，1 ) and (qb 6， 2, qb 7，2 ). As a result, the two adjacent ladders 16c and 16b can exchange quantum information between each other so that the quantum information of ladder 16c is physically located on ladder 16b. In the next step, and in accordance with the above discussion, a SWAP operation can be applied between ladder 16b and the first ladder 16a to exchange the quantum information of ladders 16b and 16a. Due to the last SWAP operation between ladders 16b and 16a, the quantum information of ladder 16c, which was physically located on qubit ladder 16b as a result of the first SWAP operation between ladders 16c and 16b, will eventually be located on the first ladder 16a. Following this strategy, the quantum information of the farthest qubit ladder 16d in the lower qubit ladder group can be sent to the first ladder 16a by performing three subsequent SWAP operations between qubit ladders 16c, 16b and 16a.

[0071] In some cases, exchanging quantum information along a qubit ladder group representing a second degree of freedom (e.g., a bosonic mode) in parallel with other quantum computing operations (e.g., those involving the use of several chains of a first plurality of qubits representing a first degree of freedom (e.g., a fermionic degree of freedom) can potentially accelerate quantum computations and / or reduce the overall depth (i.e., path length, which represents the number of gates that must be executed along the path) of the quantum circuits involved in these computations. For example, if a quantum computing operation representing an interaction between a first degree of freedom and a second degree of freedom of a physical system under consideration needs to be performed, quantum information located on, for example, one of the ladders in the qubit ladder group can be exchanged along the qubit ladder group to a corresponding qubit representing the first degree of freedom.

[0072] In an embodiment of the present technology, in which there are a plurality of qubits 17; 4a-4b of a plurality of qubits (i.e., the quantum exchange register 17 described above in the context of the method steps related to configuring a quantum computing system), the method of the first aspect may further include sending quantum information from a first ladder 16a of two or more of the ladders of the plurality of qubits of the second plurality of qubits to a first plurality of qubits qR4; qR5 of the plurality of qubits of the third plurality of qubits that are adjacent to the first ladder 16a. In some cases, a SWAP operation may be applied between the first ladder 16a and the first plurality of qubits qR4; qR5, which may involve a number of SWAP operations applied to the first plurality of qubits and individual qubits of the first ladder in a manner similar to that discussed above in the context of exchanging quantum information between adjacent qubit ladders within the same set of qubit ladders. For example, in Figure 4 In the embodiment of FIG, ladder 16a may be referred to as a “first ladder”, which is adjacent to the two qubits qR4; qR5 of the third plurality of qubits (i.e., the two qubits qR4; qR5 of the quantum swap register 17). In this case, the SWAP operation between the first ladder 16a (including the two qubits) and the two qubits qR4; qR5 may include the operation between the two pairs of adjacent qubits (qb 8,1 ,qR5) and (qb 8,2 , qR4) and apply two SWAP operations between them.

[0073] In a next step, the method of the first aspect relating to an embodiment having a quantum swap register 17 may comprise sending quantum information from the first plurality of qubits qR4;qR5 to a second plurality of qubits qR2;qR3 of qubits of a third plurality of qubits that are adjacent to a second ladder 16e of two or more ladders from the plurality of ladders of the second plurality of qubits by iteratively applying a number of subsequent SWAP operations between the first plurality of qubits qR4;qR5 and the second plurality of qubits qR2;qR3. Here, the iterative application of the number of subsequent SWAP operations may comprise iteratively applying a number of subsequent SWAP operations between adjacent qubits in the third plurality of qubits that are arranged between the first plurality of qubits qR4;qR5 and the second plurality of qubits qR2;qR3, if the adjacent qubits between the qubits are available. Return Figure 4 Example: The quantum information of the first ladder 16a, which is physically located on the quantum bits qR4;qR5 of the quantum exchange register 17 (as a result of the above-mentioned sending step), can be sent to the second number of quantum bits, namely to the quantum bits qR2;qR3 adjacent to the ladder 16e. In turn, the ladder 16e can be interpreted as the "second ladder". Figure 4In the non-limiting embodiment shown, there are no available qubits between the first plurality of qubits qR4; qR5 and the second plurality of qubits qR2; qR4. In a next step, the method of the first aspect may include sending quantum information from the second plurality of qubits qR2; qR3 of the plurality of qubits of the third plurality of qubits to a second ladder 16e adjacent to the second plurality of qubits in the two or more ladders. To this end, a SWAP operation may be applied between the second plurality of qubits qR2; qR3 and the second ladder 16e, which may involve several SWAP operations applied to individual qubits of the second ladder and the second plurality of qubits, see the discussion above. Figure 4 In the example of FIG. 1 , the SWAP operation between the second ladder 16e (comprising two qubits) and the two qubits qR2; qR3 may include two pairs of adjacent qubits (qb 1,1 ,qR2) and (qb 1,2 , qR3). In this way, the qubit (qb) initially located on the first qubit ladder 16a is 8,1 ,qb 8,2 ) can be sent to the quantum bit (qb 1,1 ,qb 1,2 ).

[0074] In a non-limiting example, the following sequence of SWAP operations can be applied starting from the initial encoding of the quantum information on these qubits, qb 1,1 →qb 1,1 ,qb 1,2 →qb 1,2 ,qb 8,2 →qb 8,2 ,qb 8,1 →qb 8,1 , to exchange the quantum bits (qb) of the first quantum bit ladder 16a via the quantum exchange register 17 8,1 ,qb 8,2 ) and the qubit (qb) of the second qubit ladder 16e 1,1 ,qb 1,2 ) between quantum information:

[0075] 1)qR2→qb 1,1 ,qR3→qb 1,2 ,qR4→qb 8,2 ,qR5→qb 8,1 ;

[0076] 2)qR2→qb 1,1 ,qR3→pb 8,2 ,pR4→qb 1,2 ,pR5→qb8,1 ;

[0077] 3)qR2→qb 8,2 ,qR3→qb 1,1 ,qR4→qb 8,1 ,qR5→pb 1,2 ;

[0078] 4)qR2→qb 8,2 ,qR3→pb 8,1 ,pR4→qb 1,1 ,pR5→pb 1,2 ;

[0079] 5) pb 1,1 →qb 8,2 ,qb 1,2 →qb 8,1 ,qb 8,2 →qb 1,1 ,qb 8,1 →qb 1,2 .

[0080] In some cases, the qubit qb may be additionally performed as a sixth operation in the above example. 1,1 and qb 1,1 SWAP between them, so that after the exchange, the quantum information originally located on the first (second) qubit of the first ladder 16a is located on the first (second) qubit of the second ladder 16e, and vice versa, the quantum information originally located on the first (second) qubit of the second ladder 16e is located on the first (second) qubit of the first ladder 16a, that is: 6) qb 1,1 →qb 8,1 ,qb 1,2 →qb 8,2 ,qb 8,2 →qb 1,1 ,qb 8,1 →qb 1,2 In the above representation, the physical quantum bit is indicated on the left side of the corresponding arrow, and the quantum information of the quantum bit located at the physical quantum bit is indicated on the right side of the corresponding arrow. For example, in step 1) above, qR2→qb 1,1 Means quantum bit qb 1,1 The quantum information is physically located on the quantum bit qR2.

[0081] In some cases, exchanging quantum information between different qubit ladders representing a second degree of freedom (e.g., bosonic modes) in parallel with other quantum computing operations, involving a quantum exchange register 17, can potentially accelerate quantum computations and / or reduce the overall depth of the quantum circuits involved in those computations. For example, quantum information of a particular qubit ladder can be efficiently transferred through a 2D lattice of qubits of the present disclosure, e.g., toward a corresponding qubit representing a first degree of freedom to perform a desired quantum computing operation.

[0082] In the disclosed technology, each qubit in the chains of the first plurality of qubits (e.g., the combination of Figure 2a 、 Figure 2b 、 Figure 3a and Figure 3b In one embodiment, the quantum information carried by a qubit in a chain of qubits of the first plurality of qubits (e.g., a chain of qubits as further discussed) may include at least partial information about one or more first degrees of freedom (e.g., about fermionic degrees of freedom), or partial information about one or more first degrees of freedom and one or more second degrees of freedom (e.g., about bosonic modes). In a first aspect, the partial information carried by a qubit in the chains of the first plurality of qubits may correspond to the quantum state of the qubit. In other words, the partial information encoded in the qubit may be represented by the quantum state that the qubit has. In some cases, each qubit from a ladder in the ladders of the second plurality of qubits (e.g., the combination described above) may be a qubit that is encoded in a quantum state. Figure 2a 、 Figure 2b 、 Figure 3a and Figure 3b The quantum information carried by the qubit of a qubit ladder (as further discussed above) may include at least partial information about one or more second degrees of freedom, or partial information about one or more second degrees of freedom and one or more first degrees of freedom. In the present specification, the partial information of each qubit of a ladder from several ladders may correspond to the quantum state of the qubit of the ladder. As further discussed above, when performing quantum computing operations, multi-qubit entangled states may be formed on qubits of the same and / or different kinds, and thus the qubits participating in the formation of the multi-qubit state may include at least partial information about different degrees of freedom of the same and / or different types (e.g., one or more fermionic degrees of freedom and / or one or more bosonic modes).

[0083] In the present specification, multiple quantum computing operations can be performed to simulate the time evolution of a physical system on the quantum computing system 1000, where the time evolution of the physical system can be defined by the unitary time evolution of the quantum Hamiltonian of the physical system. In some cases, the unitary time evolution can be represented by a unitary time evolution operator. For example, the unitary time evolution of the physical system at time t in physical units, where the reduced Planck constant is It can be written as where U(t) represents the unitary time evolution operator, is the quantum Hamiltonian of the physical system, and i is the imaginary unit. In some cases, the Hamiltonian can be written as the sum of a first sub-Hamiltonian, a second sub-Hamiltonian, and a third sub-Hamiltonian. Here, the first sub-Hamiltonian can include an operator representing a first degree of freedom (e.g., a fermionic degree of freedom), the second sub-Hamiltonian can include an operator representing a second degree of freedom (e.g., a bosonic mode), and the third sub-Hamiltonian includes an operator representing both the first degree of freedom and the second degree of freedom (e.g., an interacting fermionic degree of freedom and a bosonic mode). In a specific example, the Hamiltonian can be written as Where h1, h2 and h3 are the first sub-Hamiltonian, the second sub-Hamiltonian and the third sub-Hamiltonian respectively, which are Hermitian operators.

[0084] In the present technique, the unitary time evolution of the quantum Hamiltonian of a physical system within a predetermined time interval can be decomposed into a number of time steps. For example, the predetermined time interval T can be written as T = n·τ, where τ represents the time step, and n is the number of steps (for example, n can be equal to 10 or more, 10 2 or more, 10 3 or more, 10 4 or more, 10 5 or more integers). In some cases, the multiple quantum computing operations further introduced above can be performed to simulate the unitary time evolution of the quantum Hamiltonian of the physical system on the quantum computing system 1000 within each time step. To this end, the unitary time evolution of the quantum Hamiltonian within the time step (e.g., within each time step) can be decomposed into the unitary time evolution of the first sub-Hamiltonian, the unitary time evolution of the second sub-Hamiltonian, and the unitary time evolution of the third sub-Hamiltonian. For example, the unitary time evolution of the physical system within the time step τ given by the unitary time evolution operator defined above is It can be decomposed into exp(-iτh1)·exp(-iτh2)·exp(-iτh3). This decomposition can be called a Trotter expansion known to those skilled in the art (see, for example, HFTrotter, "On the productof semi-groups of operators", Proc. Amer. Math. Soc. 10, 545-551 (1959)). In the present technology, multiple quantum computing operations may include several multiple quantum computing operations that are performed to simulate the unitary time evolution of the quantum Hamiltonian of the physical system within a predetermined time interval. In other words, multiple quantum computing operations that simulate the unitary time evolution of the physical system within a single time step τ can be repeated, for example n times, so that the unitary time evolution propagates over the time interval T = n·τ.

[0085] In the technology of the present disclosure, multiple quantum computing operations on several chains of the first plurality of qubits can be performed to simulate the unitary time evolution of the first sub-Hamiltonian and the third sub-Hamiltonian (e.g., the sub-Hamiltonians h1 and h3 introduced above). In other words, several chains of the first plurality of qubits representing the first degree of freedom can participate in quantum computing operations of those parts of the Hamiltonian of the physical system that include the first degree of freedom. Furthermore, multiple quantum computing operations on several ladders of the second plurality of qubits can be performed to simulate the unitary time evolution of the second sub-Hamiltonian and the third sub-Hamiltonian (e.g., the sub-Hamiltonians h2 and h3 introduced above). Similarly, several ladders of the second plurality of qubits representing the first degree of freedom can participate in quantum computing operations of those parts of the Hamiltonian of the physical system that include the first degree of freedom.

[0086] In the present specification, the first degree of freedom may be a fermion degree of freedom. In this case, the first sub-Hamiltonian (e.g., h1) may include an operator associated with the fermion degree of freedom, wherein the operator associated with the fermion degree of freedom is a fermion creation operator, a fermion annihilation operator, or a product thereof (e.g., such a product may include one or more, two or more, three or more fermion creation operators and / or fermion annihilation operators, as long as the product is a Hermitian operator). In some examples, the first sub-Hamiltonian may include an interaction term describing the interaction between two or more fermion degrees of freedom. Additionally or alternatively, the first sub-Hamiltonian may include a transition term describing the transition between two or more fermion degrees of freedom. In some cases, if both terms are present in the first sub-Hamiltonian, the unitary time evolution of the first sub-Hamiltonian within a time step τ may be decomposed into the unitary time evolution of the interaction term and the transition term within the time step.

[0087] In the first aspect, the second degree of freedom can be a bosonic mode. In this case, the second sub-Hamiltonian (e.g., h2) can include operators associated with the bosonic mode, wherein the operators associated with the bosonic mode are bosonic production operators, bosonic annihilation operators of the bosonic mode, or their products (e.g., such products can include one or more, two or more, three or more bosonic production operators and / or bosonic annihilation operators, as long as the product is a Hermitian operator). In addition, the third sub-Hamiltonian (e.g., h3) can include operators that are products of operators associated with fermionic degrees of freedom and bosonic modes (for which the product should also satisfy the Hermitian condition). The third sub-Hamiltonian of the first aspect can describe the interaction between the bosonic mode and the corresponding fermionic degree of freedom.

[0088] As a non-limiting example of a coupled fermion-boson system that can be simulated using the techniques of this disclosure, is a physical system governed by the following Hamiltonian:

[0089]

[0090]

[0091] Where hc represents Hermitian conjugation, and c i,σ are the fermion creation and annihilation operators of electrons with spin σ=↑,↓ in orbital i, and is a numeric operator. Here and b i The frequencies are ω i In the above expressions, V is the transition coefficient, U is the interaction strength of the fermionic degree of freedom (e.g., describing the interaction between electrons with spin σ=↑,↓ in orbitals i and i+1), and g i,σ represents the coupling strength between the corresponding fermionic degree of freedom (e.g., electrons with spin σ=↑,↓ in orbitals i and i+1) and the i-th bosonic mode. For a physical system described by the above Hamiltonian, the number of bosonic modes is less than the number of fermionic degrees of freedom. In this case, the physical system can be mapped to a system arranged in a Figure 2a For example, for N-1=10 bosonic modes, there are 2N=22 fermionic degrees of freedom. In this specific case, the physical system can be mapped to a 2D lattice arranged similar to Figure 3a On the quantum computing system on the 2D lattice shown (using twelve ladders 16 to represent bosonic modes and twenty-one quantum bits q1 to q21 to represent fermionic degrees of freedom): Figure 3aThe only difference to be implemented in the embodiment of is the insertion of an additional qubit, namely a twenty-second qubit, into the chain of the first plurality of qubits.

[0092] Another non-limiting example of a coupled fermion-boson system that can be simulated using the techniques of the present disclosure is a physical system governed by the following Hamiltonian (all notations remain similar to those used in the previous example):

[0093]

[0094] For a physical system described by the Hamiltonian (1a), the number of bosonic modes is smaller than the number of fermionic degrees of freedom. In this case, the physical system can be mapped to a system arranged in a Figure 2a [similar to the case discussed above with Hamiltonian (1)]. For example, for N = 12 bosonic modes, there are 2N = 24 fermionic degrees of freedom. In this specific case, the physical system can be mapped to a 2D lattice arranged in the same Figure 3a On a quantum computing system on a 2D lattice similar to that shown in (with twelve ladders 16 representing bosonic modes and twenty-one qubits q1 to q21 representing fermionic degrees of freedom): Figure 3a The only difference in the embodiment of the invention is that three additional qubits are inserted into the chain of the first plurality of qubits, namely the twenty-second, twenty-third and twenty-fourth qubits. In an example, the so-called jellium model describing electrons in a solid can be given by the Hamiltonian (1) with simplified on-site Coulomb repulsions and coupling to phonons with only one polarization (see, for example, "Many-Body Quantum Theory in Condensed Matter Physics. An Introduction", Bruus K. and Flensberg K., Oxford University Press 2007). (In some cases, the only possible difference from Hamiltonian (1) may be related to the influence of boundary conditions.)

[0095] A third non-limiting example of a coupled fermion-boson system that can be simulated by the methods of the present technology is a physical system described by the following Hamiltonian (all notations remain similar to those used in the previous examples):

[0096]

[0097] For a physical system governed by the above Hamiltonian, the number of bosonic modes is equal to the number of fermionic degrees of freedom. In this case, the physical system can be mapped to a system arranged in a Figure 2bFor example, for 2N=12 bosonic modes, there are 2N=12 fermionic degrees of freedom. In this specific case, the physical system can be mapped to a 2D lattice arranged in Figure 3b On a quantum computing system on a 2D lattice as shown in (with twelve ladders 16 representing bosonic modes and twelve qubits q1 to q12 representing fermionic degrees of freedom). In another example, for 2N=4 bosonic modes and 2N=4 fermionic degrees of freedom, the physical system can be mapped to a system arranged in Figure 5a A quantum computing system on a 2D lattice as shown in FIG (with four ladders 16 representing bosonic modes and four qubits q1 to q4 representing fermionic degrees of freedom).

[0098] A fourth non-limiting example of a coupled fermion-boson system that can be simulated by the methods of the present technology is a physical system described by the following Hamiltonian (all notations remain similar to those used in the previous example):

[0099]

[0100] For a physical system governed by Hamiltonian (2a), the number of bosonic modes is greater than the number of fermionic degrees of freedom. For example, for 3N = 12 bosonic modes, there are 2N = 8 fermionic degrees of freedom. In this specific case, the physical system can be mapped to a system arranged in a grid with a similar Figure 3b On a quantum computing system on a 2D lattice of the topology shown in (with twelve ladders 16 representing bosonic modes and eight qubits 15b representing fermionic degrees of freedom): Figure 3b The only difference in the implementation of the embodiment is that four qubits in the chain of the first plurality of qubits are replaced by four auxiliary qubits (e.g., the four qubits q4, q5, q11, and q12 can be replaced by four auxiliary qubits). In the example, the jellium model discussed above with respect to the Hamiltonian (1a) for the simplified on-site Coulomb repulsion of electrons in a solid can lead to Hamiltonian (2a) when considering several polarizations in the model (e.g., considering optical and acoustic modes). (In some cases, the only possible difference from Hamiltonian (2a) can be related to the influence of boundary conditions when considering coupling to phonons with three polarizations).

[0101] In some examples of the present technology, the transition coefficient v can be calculated for the Hamiltonian All transition terms of are different (e.g., for one or more Hamiltonians given by equations (1), (1a), (2), and (2a) above). In other examples, two or more (e.g., all) transition coefficients V can be the same. In some cases, all interaction coefficients U can be different, or two or more (e.g., all) interaction coefficients U can be the same. In some cases, all coupling strengths g i,σ All can be different, or two or more (eg, all) interaction coefficients g i,σ In some cases, all boson frequencies ω i can be different, or two or more (e.g., all) bosonic frequencies ω i Can be the same.

[0102] In the disclosed technology, step 300 of performing a plurality of quantum computing operations may also include initially sorting a plurality of first degrees of freedom (e.g., fermion degrees of freedom) onto a plurality of chains of a first plurality of qubits, wherein each of the plurality of first degrees of freedom is mapped to a corresponding qubit in the plurality of chains of the first plurality of qubits. For example, the fermion creation and annihilation operators introduced above c 1,σ 、 and c 2,σ The four fermionic degrees of freedom (1,↑), (1,↓), (2,↓) and (2,↑) described by (where σ=↑,↓) can be assigned to Figure 5a The qubits q1 to q4 of a single chain of the first plurality of qubits are shown as follows:

[0103] (1,↑)→q1,(1,↓)→q2,(2,↓)→q3,(2,↑)→q4(3).

[0104] In other words, the quantum information associated with these four fermionic degrees of freedom are physically located on the qubits q1 to q4 in the order defined above, which quantum information can be represented, for example, by the quantum states of these qubits (see, for example, https: / / doi.org / 10.1103 / PhysRevLett.120.110501 for further details). The ordering of the four fermionic degrees of freedom in this non-limiting example is Figure 5b This is schematically shown in the upper dashed rectangle 20a.

[0105] In the first aspect, step 300 of performing the plurality of quantum computing operations may further comprise initially mapping one or more of the second degrees of freedom (e.g., bosonic modes) to corresponding one or more of the plurality of ladders of the second plurality of qubits. Figure 5a In the embodiment, the first Bosonic mode |Mode1>b can be mapped to a quantum bit (qb 2,1 ,qb 2,2 ) on the qubits of a ladder of 16 (in this figure, this ladder is enclosed in a dotted ellipse):

[0106] |Mode1> b →qb 2,1 qb 2,2 (4).

[0107] In this non-limiting example, when only a single bosonic mode is present, the other three ladders do not participate in the quantum computation: i.e., no quantum computation operations are performed on the qubits of these remaining ladders. In the binary encoding defined above, the first bosonic mode |Mode1> b The four Fock states can be encoded into Figure 5a The two quantum bits (qb 2,1 ,qb 2,2 ). For example, such an encoding can be given in the following manner using the bra-ket notation known in the art: |00>=|0> b ,|01>=|1> b , |10>=|2> b ,|11>=|3> b (See further discussion below.) Here, the ket vector, for example |01>, can correspond to the quantum bit qb 2,1 In the excited state, the other quantum bit qb of ladder 16 2,1 In its ground state. For the case of unary encoding, the first bosonic mode |Mode1> b Only two Fock states can be encoded into Figure 5a The two quantum bits (qb 2,1 ,qb 2,2 ). In the example, this unary encoding can be written as: |01>=|0> b ,|10>=|1> b It should be noted that the specific implementation of digital quantum simulation (at the level of individual quantum operations) may depend on the chosen encoding of bosonic patterns into the qubits of the qubit ladder.

[0108] The method of the present disclosure may also include initializing one or more qubits in the several chains of the first plurality of qubits and one or more qubits in the several ladders of the second plurality of qubits to an initial quantum state. In the first aspect, one or more qubits from the several chains of the first plurality of qubits and one or more qubits from the several ladders of the second plurality of qubits can be configured to be initialized to an initial quantum state. According to the above discussion, the initial quantum state of the qubit can represent a quantum state associated with a first degree of freedom and a second degree of freedom. In some cases, the quantum state is a product quantum state of a first quantum state associated with the first degree of freedom and a second quantum state associated with the second degree of freedom, wherein the first quantum state is represented by one or more qubits (e.g., each qubit) from the several chains of the first plurality of qubits, and the second quantum state is represented by one or more qubits (e.g., each qubit) from the several ladders of the second plurality of qubits.

[0109] In some cases, the initial quantum state of the qubit can be a multi-qubit quantum state, where the multi-qubit quantum state is a tensor product state (also known as a separable quantum state) involving the tensor product of each single-qubit quantum state of one or more qubits from the chains of the first plurality of qubits and one or more qubits from the ladders of the second plurality of qubits. In one example, the quantum state of the qubit can be, for example, the zeroth quantum state corresponding to the ground state of the qubit (i.e., the state with the lowest energy, or in other words, the unexcited state). This state can be represented by, for example, the ket vector |0> in bra-ket notation known to those skilled in the art. In other examples, the quantum state of the qubit can be, for example, the first quantum state corresponding to the first excited state of the qubit (i.e., the excited state closest in energy to the ground state). This state can further be represented by the ket vector |1>. In yet other examples, the quantum state of the qubit of the first one or more qubits can be a linear superposition of the zeroth quantum state and the first quantum state. In this case, the quantum state of the qubit can be written as, for example, |ψ>=α|0>+β|1>, where α and β are some non-zero amplitudes. Back to the tensor product above: In some cases, it can be written as where L is the number of qubits participating in the tensor product state and represents a tensor product. For example, Figure 5a The two quantum bits (qb 2,1 ,qb 2,2 ), whose quantum state is the linear superposition of the zeroth quantum state and the first quantum state, and It can be written as|ψ>=α1α2|00>+α1β2|01>+α2β1|10>+β1β2|11>, where α i and β i (i=1,2) is the corresponding amplitude.

[0110] In the first aspect, and in accordance with the above discussion, the initial tensor product state can be represented as a product state of the quantum states of the fermionic degrees of freedom and the quantum states of the bosonic modes. In a specific case, the fermionic state can correspond to the ground state of the complete non-interacting fermionic part of the Hamiltonian of the physical system and the bosonic mode in an unexcited state. b In other cases, the fermionic state can correspond to the ground state of the complete interacting fermionic part of the physical system's Hamiltonian and the bosonic modes in their unexcited states. b In some cases, the ground state of the complete interacting fermion part of the Hamiltonian can be generated using corresponding quantum algorithms.

[0111] In the technology of the present disclosure, wherein the first degree of freedom is a fermionic degree of freedom and the second degree of freedom is a bosonic mode, the step 300 of performing a plurality of quantum computing operations may further include exchanging 700 quantum information between each of a plurality of odd-numbered qubits (q1; q3) from a plurality of chains of the first plurality of qubits and a corresponding adjacent even-numbered qubit (q2; q4) located on a predetermined side relative to the odd-numbered qubit, if an even-numbered qubit located on a predetermined side relative to the odd-numbered qubit exists. Here, the corresponding adjacent even-numbered qubits may be qubits of a plurality of even-numbered qubits from a plurality of chains of the first plurality of qubits. For example, the second qubit q2, which is an even-numbered qubit representing the fermionic degree of freedom (1,↓) originally encoded therein, is located to the right relative to the first qubit q1, which is an odd-numbered qubit representing the fermionic degree of freedom (1,↑) originally encoded therein. These qubits may exchange their quantum information, as indicated by Figure 5b Similarly, the fourth qubit q4, which is an even-numbered qubit representing the fermionic degree of freedom (2,↑) originally encoded into it, is located to the right relative to the first qubit q3, which is an odd-numbered qubit representing the fermionic degree of freedom (2,↓) originally encoded into it. These qubits can also exchange their quantum information, as shown by Figure 5b In the example, both exchange steps can be performed within the first step of the digital quantum simulation (see also further explanation).

[0112] In the present specification, exchanging 700 quantum information between adjacent qubits q1, q2; q3, q4 from a plurality of chains of a first plurality of qubits can be performed by applying a fermion SWAP operation (FSWAP) 21 between these adjacent qubits, wherein the fermion SWAP operation preserves the fermion anti-commutation relation between the operators associated with the fermion degrees of freedom encoded in the qubits. For example, the FSWAP operation can be defined as a unitary transformation that exchanges two fermion degrees of freedom. In the example, for the annihilation and creation operators of the fermion degrees of freedom introduced above, the FSWAP transformation can be defined as follows: Where σ∈↑,↓. In a specific case, the FSWAP operation can be given by:

[0113]

[0114] See https: / / doi.org / 10.1103 / PhysRevLett.120.110501 for further details.

[0115] In a next step, the method of the first aspect may include performing 710 several available quantum computing operations from the plurality of quantum computing operations on one or more qubits 1a-1d from the plurality of chains of the first plurality of qubits. In some cases, several available quantum computing operations may be performed on the qubits from the plurality of chains of the first plurality of qubits within a time step (e.g., within each time step) to simulate the unitary time evolution of the first sub-Hamiltonian. In an example, the unitary time evolution of the first sub-Hamiltonian within a time step τ may be written as: exp(-iτh1), consistent with the further discussion above. In some cases, the "availability" of the quantum computing operations may depend on one or more of the following factors: i) the structure of the Hamiltonian under consideration, ii) the mapping used for the fermionic degrees of freedom (e.g., a mapping based on the Jordan-Wigner transform), and iii) the step of the digital quantum simulation. In other words, several quantum computing operations may be available in the first step of the digital quantum simulation, while another several quantum computing operations may be available in the second step of the digital quantum simulation, and so on. It should be noted that after performing multiple quantum computing operations on the 2D qubit lattice of the present disclosure, as described above, the unitary time evolution of all terms of the quantum Hamiltonian of the physical system within a time step (e.g., within a time step τ) can be simulated.

[0116] For a physical system governed by Hamiltonian (2) and mapping the system to Figure 5aIn the case of the 2D lattice shown, the first step of the digital quantum simulation can describe the unitary time evolution of the interaction terms associated with the fermion degrees of freedom (1,↑), (1,↓), (2,↓) and (2,↑), while the unitary time evolution of the transition terms is not available at this stage of the digital quantum simulation (see also the initial ordering of the four fermion degrees of freedom given by equation (3)). For example, the unitary time evolution of the transition terms can be simulated in the second step of the digital quantum simulation (see further discussion below). Specifically, in the first step of the digital quantum simulation, the following unitary time evolution of the interaction terms of the first sub-Hamiltonian within the time step τ can be simulated:

[0117] exp(-i Un 1,↑ n 1,↓ τ)·exp(-i Un 2,↑ n 2,↓ τ).

[0118] In some cases of the present disclosure, and for convenience, the quantum operation describing the simulation of the first sub-Hamiltonian within the time step τ can be combined with the FSWAP operation. This quantum operation can be called the fermion simulation (FSIM) operation. In the example of Hamiltonian (2), the FSIM operation acting on the corresponding quantum bit can be written as:

[0119]

[0120] where σ = ↑,↓. Therefore, the first step of the digital quantum simulation in the example discussed above can be written as: FSIM(0,τU)q1q2 and FSIM(0,τU)q3q4 by means of FSIM operations.

[0121] The disclosed techniques may also include performing 720 a number of available quantum computing operations from a plurality of quantum computing operations involving two adjacent qubits (q1, q2) of the number of chains of the first plurality of qubits and a corresponding qubit ladder 16 having a qubit (qb) adjacent to one (q2) of the number of chains of the first plurality of qubits. 2，1). Here, the corresponding qubit ladder is a qubit ladder from the plurality of ladders of the second plurality of qubits, wherein the corresponding qubit ladder encodes the corresponding bosonic mode. In some cases, a number of available quantum computing operations involving two adjacent qubits of the plurality of chains of the first plurality of qubits and the corresponding qubit ladder can be performed to simulate the unitary time evolution of a third sub-Hamiltonian within a time step (e.g., within each time step), the qubit ladder having a qubit adjacent to one of the adjacent qubits of the plurality of chains of the first plurality of qubits. In an example, the unitary time evolution of the first sub-Hamiltonian within a time step τ can be written as: exp(-iτh3), consistent with the discussion further above.

[0122] Return to Figure 5a Example: First Bosonic Mode |Mode1> b can be mapped to a quantum bit (qb 2，1 ,qb 2，2 ) on the qubit of ladder 16. The qubit qb of this ladder 2，1 adjacent to qubit q2 of the chain of the first plurality of qubits (as before, qubit qb is illustrated in this figure by a dashed line). 2，1 and q2). For a physical system governed by the Hamiltonian (2) and mapped to Figure 5a In the case of the 2D lattice shown, the first step of the digital quantum simulation can be further described with the qubit qb being encoded into the qubit ladder 16 2，1 and qb 2，2 The unitary time evolution of the fermion-bosonic interaction associated with the first bosonic mode in and the fermionic degrees of freedom (1,↑) and (2,↑). It should be noted that the fermionic degrees of freedom (1,↑) and (2,↑) are now encoded into the qubits q2 and q3, as Figure 5b As shown schematically in the dashed rectangle 20b, two FSWAP operations have been performed, see the upper dashed rectangle 20a and the previous explanation. Specifically, in the first step of the digital quantum simulation, the following unitary time evolution of the fermion-bosonic interaction term of the third sub-Hamiltonian within the time step τ can be simulated:

[0123]

[0124] in is the creation (annihilation) operator describing the first bosonic mode, and is the coupling strength. In one non-limiting example, as will be further explained below, it can be based on Figures 6a to 6c The quantum circuit shown is used to simulate the unitary time evolution of fermion-bosonic interactions.

[0125] In the technology of the present disclosure, the step 300 of performing multiple quantum computing operations may also include exchanging 730 quantum information between each qubit in the several even-numbered qubits (q2) of the several chains of the first plurality of qubits and the corresponding adjacent odd-numbered qubit (q3) located on a predetermined side relative to the even-numbered qubit, if the odd-numbered qubit located on the predetermined side relative to the even-numbered qubit exists. Here, the corresponding adjacent odd-numbered qubits are qubits of the several odd-numbered qubits from the several chains of the first plurality of qubits. For example, the third qubit q3, which is an odd-numbered qubit representing the fermion degree of freedom (2,↑) after performing the FSWAP operation during the first step of the digital quantum simulation, is located on the right relative to the second qubit q2. Qubit q2 is an even-numbered qubit that represents the fermion degree of freedom (1,↑) after performing the FSWAP operation during the first step of the digital quantum simulation. Qubits q2 and q3 can exchange their quantum information, such as Figure 5b This is schematically indicated by the arrow 22 in the dashed rectangle 20b shown. In an example, this exchange step may be performed within the second step of the digital quantum simulation.

[0126] In a next step, the method of the first aspect may comprise performing 740 a number of available quantum computing operations from the plurality of quantum computing operations on one or more qubits 1a-1d from the number of chains of the first plurality of qubits. This method step may be performed similarly to method step 710 further elaborated above. For a physical system controlled by Hamiltonian (2) and mapped to Figure 5a For the case of the 2D lattice shown, the second step of the digital quantum simulation can describe the unitary time evolution of the transition terms associated with the fermion degrees of freedom (2, ↑) and (1, ↑), while at this stage of the digital quantum simulation, the unitary time evolution of other terms of the first sub-Hamiltonian is not available. Specifically, in the second step of the digital quantum simulation, the following unitary time evolution of the transition terms of the first sub-Hamiltonian within the time step τ can be simulated:

[0127]

[0128] Therefore, the second step of the digital quantum simulation in the example discussed above can be written as: FSIM(τV,0)q2q3 through the FSIM operation. As a result of this operation, the fermion degrees of freedom will be arranged as follows Figure 5b 20c is shown in the (third from the top) dashed rectangle 20c.

[0129] The disclosed techniques may also include performing 750 a plurality of chains involving two adjacent qubits (q1, q2) and a qubit (qb2，1 ) of the corresponding quantum bit ladder 16 from a plurality of quantum computing operations, the quantum bit (qb 2，1 ) is adjacent to one (q2) of said adjacent qubits (q1, q2) of the several chains of the first plurality of qubits. This method step may be performed similarly to the method step 720 disclosed further above. Return to the mapping to Figure 5a Hamiltonian (2) on the 2D lattice shown: The quantum computation operation describing the unitary time evolution of the fermion-bosonic interaction involving the qubit defined in method step 750 is not available in the second step of the digital quantum simulation. In this case, the digital quantum simulation can proceed to the third step, as described below.

[0130] In a next step, the method of the first aspect may include iteratively repeating 760 the steps of exchanging information and performing the plurality of available quantum computing operations until all of the plurality of available quantum computing operations from the plurality of quantum computing operations are performed. Figure 5a For the case of the 2D lattice shown, further possible steps for digital quantum simulation can be as follows:

[0131] 3) FSIM(0,0)q1q2 and FSIM(0,0)q4q3: These are two FSWAP operations (the parameters of both FSIM operations are zero) that are needed to bring the fermion degrees of freedom (1,↓) and (2,↓) to simulate the transition terms involving these fermion degrees of freedom (1,↓) and (2,↓). As a result of this operation, the fermion degrees of freedom will be arranged as follows Figure 5b (fourth from the top) is shown in dashed rectangle 20d.

[0132] Then, the fermion degrees of freedom (1,↓) and (2,↓) (which are physically located on qubits q2 and q3) can be simulated with the qubit qb encoded into the qubit ladder 16. 2，1 and qb 2，2 This can be done in a similar manner to that described above with respect to method step 720.

[0133] 4) FSIM(τV,0)q2q3. This step exchanges the fermion degrees of freedom (1,↓) and (2,↓) and simulates the transition terms involving them. As a result of this operation, the fermion degrees of freedom will be arranged as follows Figure 5b As shown in the dashed lower rectangle 20e.

[0134] The disclosed techniques may also include performing some of the 770 or more quantum computing operations on the corresponding qubit ladder 16 (e.g., on one or more of the ladders of the second plurality of qubits). In some cases, some of the quantum computing operations on the corresponding qubit ladder may be performed to simulate the unitary time evolution of the second sub-Hamiltonian within a time step (e.g., within each time step). In one example, the unitary time evolution of the second sub-Hamiltonian within a time step τ may be written as exp(-iτh2), consistent with the discussion further above. In the case of qubit qb encoded into the qubit ladder 16, the unitary time evolution of the second sub-Hamiltonian within a time step τ may be written as exp(-iτh2), consistent with the discussion further above. 2,1 and qb 2,2 In the specific case of the first bosonic mode in , this unitary time evolution within the time step τ can be written as where ω represents the frequency of the first Bosonic mode. Return to the mapping to Figure 5a Hamiltonian (2) on the 2D lattice shown: In some cases, the quantum computation operation describing the unitary time evolution of the second sub-Hamiltonian in this specific example within the time step τ can be performed as the last fifth step 5) of the digital quantum simulation (after performing the fourth step 4) of the arrangement of the fermionic degrees of freedom in Figure 5b ).

[0135] In the present disclosure, it can be said that when all the above-mentioned several available quantum computing operations and several quantum computing operations from the plurality of quantum computing operations on the corresponding qubit ladder 16 are completed, the quantum state generated by the Hamiltonian is simulated within a single time step (e.g., within the time step τ) Determining the unitary time evolution of the physical system. As further described above, the process may be repeated to propagate the unitary time evolution over a predetermined time interval (eg, over a time interval T=n·τ, where n is an integer as further disclosed above).

[0136] In this specification, each of the Bose creation operator and the Bose annihilation operator can be decomposed into a superposition of Pauli operators and / or products of Pauli operators, where each Pauli operator can act on the quantum state of one of the qubits of the corresponding qubit ladder (e.g., each qubit of the corresponding ladder), which qubit encodes the corresponding bosonic mode. Here, the Pauli operator is one of the Pauli X-, Y-, or Z-operators. In encoding Figure 5a The qubit qb of the qubit ladder 16 is shown 2,1 and qb 2,2 In the specific case of the first bosonic mode, the bosonic number operator can be represented by binary encoding as: Here Z1 represents the action on quantum bit qb 2,1 The Pauli Z-operator, and Z2 is acting on Figure 5aThe ladder 16 quantum bits qb 2,2 The Pauli Z-operator of . Therefore, the unitary time evolution in time step τ can be written in this specific example as:

[0137]

[0138] In the method of the first aspect, the above decomposition can be implemented as a sequence of single qubit rotations known to those skilled in the art.

[0139] In the disclosed technology, performing 720; 750 involves two adjacent qubits (q1, q2) of the chains of the first plurality of qubits and a qubit (qb) adjacent to one (q2) of the adjacent qubits (q1, q2) of the chains of the first plurality of qubits. 2，1 ) of the corresponding qubit ladder 16 can include using a number of quantum two-qubit gates and / or single-qubit gates arranged in a corresponding order, the qubit gates acting on two adjacent qubits (q1, q2) of the number of chains of the first plurality of qubits. In some cases of the present technology, this step allows the unitary time evolution of two adjacent qubits of the number of chains comprising the first plurality of qubits (which encode two corresponding fermionic degrees of freedom) and a fermion-boson interaction term of a bosonic mode to be represented as including only one of the two qubits and a fermion-boson interaction term of the bosonic mode. Back Figure 5a Embodiment: Two qubits q2, q3 of the chain of the first plurality of qubits are adjacent qubits. One of these qubits, qubit q2, is also adjacent to qubit qb of the qubit ladder 16. 2，1 adjacent. In a physical system governed by the Hamiltonian (2) and the system is mapped to Figure 5a In the case of the 2D lattice shown, the above-mentioned fermion-bosonic interaction term (3) with the fermionic degrees of freedom (1,↑) and (2,↑) encoded into the qubits q2 and q3 in the first step of the digital quantum simulation can be rewritten in a non-limiting example as:

[0140]

[0141] where Z f represents the Z-Pauli matrix acting on the quantum bit q2 (see Figure 5a ). It should be noted that the expression on the right side of the above equation only requires the use of qubit q2 and the two qubits qb of qubit ladder 16 2，1 and qb 2，2 In one example, this unitary time evolution within a time step τ can be written in binary as:

[0142]

[0143] In the method of the first aspect, the above decomposition can be implemented as follows Figures 6a to 6c A sequence of single-qubit rotation and controlled NOT (CNOT) operations is shown and explained in detail below.

[0144] The next step of the method may include performing a number of quantum computing operations involving i) one of the adjacent qubits (q1, q2) in the number of chains of the first plurality of qubits and a qubit (qb) of the corresponding qubit ladder; 2,1 ) adjacent one (q2), ii) a qubit (qb) in the corresponding qubit ladder that is adjacent to one (q2) of the adjacent qubits in the chains of the first plurality of qubits 2,1 ), and iii) one or more qubits (qb) in the corresponding qubit ladder that are not adjacent to one of the adjacent qubits in the chains of the first plurality of qubits 2,2 For illustrative purposes, the implementation of these three steps i), ii), and iii) will be illustrated using three non-limiting examples of quantum circuits to simulate Figure 6a 、 Figure 6b and Figure 6c The unitary transformation exp(-igτZ shown in f X1), exp(-igτZ f X1X2 / 2) and exp(-igτZ f Y1Y2 / 2).

[0145] In the present technology, performing the above-mentioned number of quantum computing operations involving i), ii), and iii) may include providing a qubit qb of the corresponding qubit ladder adjacent to one of the adjacent qubits (q2) in the number of chains of the first plurality of qubits. 2,1 Applying a basis rotation transformation 40. A next step of the method may include adding one or more qubits (qb) of the corresponding qubit ladder that are not adjacent to one of the adjacent qubits (q2) in the chains of the first plurality of qubits. 2,2 ) applies a basis rotation transformation 41, wherein the basis rotation transformation corresponds to rotating a predetermined axis on the rotation axis (e.g., z-axis) of the corresponding quantum bit. Figure 6b In the embodiment, a Hadamard gate, H, 40 can be applied to the adjacent qubit q2. Figure 5a The quantum bit qb 2,1 , and another Hadamard gate, H,41 is applied to the qubit qb that is not connected to the qubit ladder 2,1 Adjacent quantum bits qb2,2 In the example, the Hadamard gate can be converted between z-basis and x-basis. Figure 6c In the embodiment, R X (π / 2) represents a basis rotation transformation, which is a rotation operator for converting between a z-basis and a y-basis. Then, the method of the first aspect may include converting the qubits (qb) of the first plurality of qubit chains to the corresponding qubit ladder. 2,1 ) one of the adjacent qubits (q2) and the qubit (qb) of the corresponding qubit ladder 2,1 ) between applying a controlled NOT (CNOT) operation 42 (the CNOT operation is performed by Figures 6a to 6c denoted by reference numeral 42 in FIG.

[0146] The method of the first aspect may further comprise the step of: at two subsequent qubits (qb) of the corresponding qubit ladder 2,1 ;qb 2,2 ) iteratively applying a number of consecutive CNOT operations 43 between the first plurality of qubits and the adjacent qubits in the number of chains of the first plurality of qubits from the corresponding qubit ladder (qb 2,1 ), and if the one or more qubits comprise at least two qubits of the corresponding qubit ladder, then proceeding with the one or more qubits (qb 2,2 )(See Figure 6b and Figure 6c The next step in this technique may include a rotational transformation (R z (γ))44, which is applied to the last qubit qb in one or more qubits of the corresponding qubit ladder 2,2 , applying the number of CNOT operations at that qubit stops. In some cases, a rotational transformation about a rotation axis is applied to the last qubit of the one or more qubits of the corresponding qubit ladder, and the rotational transformation can be defined by a predetermined rotation angle about the rotation axis. In some examples, the predetermined rotation angle can be proportional to the time step and the product of the coupling strength between the fermionic degrees of freedom encoded by two adjacent qubits in the number of chains of the first plurality of qubits and the bosonic mode encoded by the corresponding qubit ladder. Figure 6a 、 Figure 6b and Figure 6c In the specific example of the unitary transformation simulated in , the predetermined rotation angle around the rotation axis can be given by: γ = gτ.

[0147] The next step of the technique may include iteratively performing the steps in reverse order between the two subsequent qubits (qb) of the corresponding qubit ladder. 2,2 ;qb 2,1) between the last qubit (qb 2,2 ), and if the one or more qubits include at least two qubits of the corresponding qubit ladder, proceeding to a qubit (qb) of the corresponding qubit ladder that is adjacent to one of the adjacent qubits of the number of chains of the first plurality of qubits. 2,1 )(See Figure 6b and Figure 6c 45 in the figure). A next step of the method may comprise selecting among said adjacent qubits of the chains of the first plurality of qubits a qubit (qb 2,1 ) adjacent to the qubit (q2) and the qubit (qb) of the corresponding qubit ladder 2,1 ) between applying CNOT operation 46 (see Figures 6a to 6c In a next step of the method, one or more qubits (qb) of the corresponding qubit ladder that are not adjacent to one of the adjacent qubits (q2) of the several chains of the first plurality of qubits may be processed. 2,2 ) Apply the inverse basis rotation transformation 47 (see Figure 6b and Figure 6c 47 in the figure). A next step of the present technology may include performing a step of ... a step of performing a step of a step of performing a step of a step of performing a step of a step of performing a step of a step of performing a step of a step of a step of performing a step of a step of a step of a step of a step of a step of a step of a step of a step of a step of a step of 2,1 ) Apply the inverse basis rotation transformation 48 (see Figures 6a to 6c 48 in the figure). The inverse basis rotation transformation of the first aspect can correspond to rotating the rotation axis of the corresponding qubit back to a predetermined axis. In some examples, the inverse basis rotation transformation can be defined as a transformation defined by an operator (or its corresponding matrix representation) that is Hermitian conjugate with respect to the operator defining the basis rotation transformation. In some embodiments of the present technology, the rotation axis can be the z-axis.

[0148] In some examples of the present technology, one or more CNOT operations used above can be performed by corresponding quantum CNOT gates. Additionally or alternatively, one or more CNOT operations can include decomposing the one or more CNOT operations into corresponding quantum operations performed by native hardware gates, where the native hardware gates are gates available in the qubit topology and / or the specific architecture of the quantum computer.

[0149] In the disclosed techniques, step 770 of performing several of the plurality of quantum computing operations on the respective qubit ladder 16 may include performing operations involving i) a qubit (qb) in the respective qubit ladder that is adjacent to one (q2) of the adjacent qubits (q1, q2) of the plurality of chains of qubits of the first plurality; 2,1 ), and ii) one or more qubits (qb) in the corresponding qubit ladder that are not adjacent to one of the adjacent qubits of the chains of the first plurality of qubits 2,2 ) of several quantum computing operations. In some cases, these steps i) and ii) can be performed in conjunction with steps 720; 750 and the above Figures 6a to 6c Steps ii) and iii) are performed in a similar manner as disclosed above. In some embodiments related to the implementation of step 770, the predetermined rotation angle can be proportional to the product of the time step and the frequency of the bosonic mode encoded by the corresponding qubit ladder. In a specific example, the predetermined rotation angle about the rotation axis can be given by the following formula: γ = ωτ.

[0150] The technology of the present disclosure may also include performing a quantum computing task, wherein the quantum computing task includes a plurality of quantum computing operations performed on a plurality of chains of a first plurality of quantum bits and a plurality of ladders of a second plurality of quantum bits. In addition, the quantum computing task may also include a plurality of quantum computing operations performed on one or more quantum bit auxiliary chains of the first plurality of quantum bits. In some cases, the quantum computing task may also include a plurality of quantum computing operations performed on a third plurality of quantum bits. In the technology of the present disclosure, one or more of the plurality of quantum computing operations may be performed on a quantum computing system within a time step (e.g., each time step) to simulate the unitary time evolution of the quantum Hamiltonian of the physical system. In a first aspect, the plurality of quantum computing operations may include a corresponding number of one or more quantum computing operations that are performed within a predetermined time interval to simulate the unitary time evolution of the quantum Hamiltonian of the physical system.

[0151] In some cases, quantum computing tasks may include one or more problems in the fields of quantum system simulation, computational chemistry, computational biology, solid-state physics, quantum annealing, quantum machine learning, search problems, cryptography, and the like. In some examples, one or more quantum computing operations may be performed in parallel on different pluralities of qubits. For example, a first plurality of computing operations may be performed sequentially on a first plurality of qubits from a plurality of chains of a first plurality of qubits during a first time interval, and a second plurality of computing operations may be performed in parallel on a second plurality of qubits from the plurality of chains. Alternatively or additionally, a third plurality of computing operations may be performed sequentially on a first plurality of qubits from one qubit ladder of a second plurality of qubits during the same or different time intervals, and a fourth plurality of computing operations may be performed in parallel on another qubit ladder of the second plurality of qubits.

[0152] The second aspect provides a quantum computing system 1000 configured according to any of the steps of the technology of the first aspect.

[0153] A third aspect provides a quantum computing system for performing a plurality of quantum computing operations and adapted to perform any of the steps of the technique according to the first aspect.

[0154] In some examples, the quantum computing system of the third aspect is configured according to the quantum computing system of the second aspect. The present disclosure also relates to a computer program suitable for performing any step of the technology according to the first aspect. The present disclosure also relates to a computer-readable medium (e.g., a machine-readable storage medium such as an optical storage medium or a read-only memory, e.g., a FLASH memory) and a signal storing or encoding the computer program of the present disclosure.

[0155] The quantum computing system of the second and / or third aspects may include at least one processor (e.g., a quantum processor), at least one memory (which may include a program that, when executed, performs the method steps according to the first aspect or the computer program of the present disclosure), and at least one interface for input and output. In some examples, the quantum computing system may include a hardware architecture comprising, for example, one or any combination of one or more chips, a quantum data plane, a control plane, a measurement plane, a control processor plane, a host processor, and the like. The hardware architecture of the quantum computing system of the second and / or third aspects may be based on qubits coupled to a high-fineness cavity (e.g., a superconducting qubit coupled to a microwave cavity), as further described above. In other examples, the quantum computing system may include a hardware architecture based on qubits implemented as nuclear spin states of donor atoms embedded in a corresponding host lattice. In still other examples, the quantum computing system may include a hardware architecture based on neutral atoms in an optical lattice. In some examples, the quantum computing system may be a standalone computer device. In other examples, the quantum computing system may be integrated into a system or computer device that also serves other purposes besides performing the steps of the techniques of the present disclosure. In still other examples, the quantum computing system may be a distributed system that communicates via a network (eg, the Internet).

[0156] A fourth general aspect of the present disclosure relates to a remote computing system comprising a quantum computing system and a system configured to perform a quantum computing task, wherein the quantum computing task comprises a plurality of quantum computing operations according to the first aspect. The plurality of quantum computing operations of the fourth aspect (performed by the remote computing system) may be performed according to any of the method steps of the first aspect. In some examples, the remote computing system may be configured to receive a query regarding the quantum computing task from a computer-implemented system (e.g., a system external to the remote computing system). The remote computing system of the fourth aspect is further configured to send the result of the computing task (e.g., based on the controlled quantum computing operations performed thereon) to the computer-implemented system (e.g., the computer-implemented system that sent the query). In some examples, the hardware architecture of the quantum computing system of the fourth aspect may include one or more building blocks (or component blocks) of the hardware architecture of the quantum computing system disclosed in the second and / or third aspects above. In some cases, the hardware architecture of the quantum computing system of the fourth aspect may be the same as the hardware architecture of the quantum computing system disclosed in the second and / or third aspects above.

Claims

1. A method for configuring a quantum computing system (1000), wherein the quantum computing system comprises a plurality of quantum bits arranged on a two-dimensional (2D) lattice and configured to perform a plurality of quantum computing operations, the method comprising: receiving a first plurality of qubits from the plurality of qubits (15a-15c; 1a-1d; 3a-3c) of the choice (100), wherein the first plurality of qubits comprises a plurality of qubit chains, wherein each qubit (1a-1d) of the number of qubit chains (15a-15b) of the first plurality of qubits represents a first degree of freedom associated with a respective component of a physical system to be mapped to the number of qubit chains of the first plurality of qubits, wherein each qubit (q1) of the first plurality of qubits is configured to send quantum information of the qubit to another qubit (q2) of the first plurality of qubits adjacent to the qubit, wherein the another qubit in the first plurality of qubits is configured to receive quantum information of the qubit in the first plurality of qubits; receiving a selection (200) of a second plurality of qubits (16; 16a-16e; 2a-2d) of the plurality of qubits, wherein the second plurality of qubits comprises a plurality of qubit ladders, wherein each qubit ladder represents a second degree of freedom associated with a respective component of the physical system to be mapped to the number of qubit ladders of the second plurality of qubits, wherein the second degree of freedom is different from the first degree of freedom, wherein each qubit (2a; 2c) of the second plurality of qubits is configured to transmit quantum information of the qubit to another qubit (2b; 2d) of the second plurality of qubits adjacent to the qubit, wherein the another qubit in the second plurality of qubits is configured to receive quantum information of the qubit in the second plurality of qubits, wherein one or more qubits (1a; 1c) in the qubit chains of the first plurality of qubits are adjacent to corresponding one or more qubits (2a; 2c) in the qubit ladders of the second plurality of qubits and are configured to send quantum information to and / or receive quantum information from corresponding one or more qubits in the qubit ladders of the second plurality of qubits, Wherein the plurality of qubit chains of the first plurality of qubits and the plurality of qubit ladders of the second plurality of qubits are configured to perform a plurality of quantum computing operations.

2. The method according to claim 1, wherein After performing the receiving selection step of claim 1, the method includes performing (300) a plurality of quantum computing operations on the quantum computing system, the plurality of quantum computing operations including: performing (400) a plurality of quantum computing operations on said number of qubit chains (15a-15b) of said first plurality of qubits, wherein performing the plurality of quantum computing operations on the plurality of qubit chains of the first plurality of qubits comprises exchanging the quantum information between two qubits (q1, q2) of one or more pairs of adjacent qubits (q1, q2; q2, q3) from the plurality of qubit chains (15a-15b) of the first plurality of qubits; performing (500) a plurality of quantum computing operations on said number of qubit ladders (16; 16a-16e) of said second plurality of qubits, wherein performing the plurality of quantum computing operations on the plurality of qubit ladders of the second plurality of qubits comprises performing two qubits (qb) of one or more pairs of adjacent qubits of each qubit ladder (16; 16a-16e) from the plurality of qubit ladders of the second plurality of qubits 2,1 ,qb 2,2 ) exchange the quantum information between; Quantum information is exchanged (600) between two qubits from one or more pairs of adjacent qubits (1a, 2a; 1c, 2c), wherein one qubit (1a; 1c) of the pair is from the number of qubit chains of the first plurality of qubits and the other qubit (2a; 2c) of the pair is from a corresponding ladder of the number of qubit ladders of the second plurality of qubits, the corresponding ladder being adjacent to the qubit from the number of qubit chains.

3. The method of claim 2, wherein performing (400) the plurality of quantum computing operations on the number of qubit chains and performing (500) the plurality of quantum computing operations on the number of qubit ladders further comprises: performing (410) a number of quantum computing operations of the plurality of quantum computing operations on the one or more qubits (1a; 1c) of the number of qubit chains of the first plurality of qubits that are adjacent to the corresponding one or more qubits (2a; 2c) of the number of qubit ladders of the second plurality of qubits, performing (510) several quantum computing operations of the plurality of quantum computing operations on the corresponding one or more qubits (2a; 2c) of the several qubit ladders of the second plurality of qubits, Performing (520) some of the plurality of quantum computing operations on some of the qubits (2b; 2d) in the some of the qubit ladders of the second plurality of qubits for which no adjacent qubits from the some of the qubit chains of the first plurality of qubits are available.

4. The method of claim 3, wherein performing (400) the plurality of quantum computing operations on the plurality of qubit chains further comprises: Performing (420) a number of the plurality of quantum computing operations on a number of qubits of the number of qubit chains of the first plurality of qubits for which no adjacent qubits from the number of qubit ladders of the second plurality of qubits are available.

5. The method according to any one of claims 1 to 4, wherein a qubit ladder (16) in the number of qubit ladders of the second plurality of qubits comprises a plurality of qubits, wherein the plurality of qubits within the ladder extend along a first direction, Each of the quantum bit chains of the first plurality of quantum bits extends along the first direction (15a) or along a second direction (15b) different from the first direction.

6. The method according to any one of claims 1 to 5, further comprising receiving a selection (250) of a third plurality of qubits (17; 4a-4b) of the plurality of qubits, wherein several qubits (qR2-qR5) of the third plurality of qubits are adjacent to two or more qubit ladders (16e; 16a) of the number of qubit ladders of the second plurality of qubits and are configured to receive quantum information from and / or transmit quantum information to the two or more qubit ladders of the number of qubit ladders of the second plurality of qubits, wherein the two or more qubit ladders (16e; 16a) from the number of qubit ladders of the second plurality of qubits adjacent to the number of qubits (qR2-qR5) in the third plurality of qubits are configured to send quantum information to and / or receive quantum information from the number of qubits (qR2-qR5) in the third plurality of qubits, Optionally, the third plurality of qubits comprises one or more qubit chains extending in the first direction.

7. The method according to any one of claims 1 to 6, wherein the quantum information carried by each qubit of the several qubit chains of the first plurality of qubits comprises at least partial information about one or more first degrees of freedom, or at least partial information about the one or more first degrees of freedom and one or more second degrees of freedom, wherein the portion of information carried by a qubit of the plurality of qubit chains of the first plurality of qubits corresponds to the quantum state of the qubit, wherein the quantum information carried by each qubit of a qubit ladder from the number of qubit ladders of the second plurality of qubits comprises at least partial information about one or more second degrees of freedom, or at least partial information about the one or more second degrees of freedom and the one or more first degrees of freedom, The partial information of each qubit of a qubit ladder from the plurality of qubit ladders corresponds to the quantum state of the qubit of the qubit ladder.

8. The method according to any one of claims 1 to 7, wherein performing (300) the plurality of quantum computing operations comprises: initially ordering a first plurality of degrees of freedom onto said number of qubit chains of said first plurality of qubits, wherein each of the plurality of first degrees of freedom is mapped to a corresponding qubit from the number of qubit chains of the first plurality of qubits, One or more of the second degrees of freedom are initially mapped onto corresponding one or more of the number of qubit ladders of the second plurality of qubits.

9. The method of any one of claims 1 to 8, further comprising initializing one or more qubits from the number of qubit chains of the first plurality of qubits and one or more qubits from the number of qubit ladders of the second plurality of qubits to an initial quantum state, wherein the one or more qubits from the number of qubit chains of the first plurality of qubits and the one or more qubits from the number of qubit ladders of the second plurality of qubits are configured to be initialized to the initial quantum state, wherein the initial quantum state of the qubit represents a quantum state associated with the first degree of freedom and the second degree of freedom, Optionally wherein the quantum state is a product quantum state of a first quantum state associated with the first degree of freedom and a second quantum state associated with the second degree of freedom, wherein the first quantum state is represented by the one or more qubits from the qubit chains of the first plurality of qubits, and the second quantum state is represented by the one or more qubits from the qubit ladders of the second plurality of qubits.

10. The method according to any one of claims 1 to 9, wherein the first degree of freedom is a fermionic degree of freedom and the second degree of freedom is a bosonic mode, Wherein executing (300) the plurality of quantum computing operations further comprises: exchanging (700) quantum information between each of a number of odd-numbered qubits (q1; q3) of the number of qubit chains of the first plurality of qubits and a corresponding adjacent even-numbered qubit (q2; q4) located on a predetermined side relative to the odd-numbered qubit, if the even-numbered qubit located on the predetermined side relative to the odd-numbered qubit exists, wherein the corresponding adjacent even-numbered qubits are qubits from several even-numbered qubits of the several qubit chains of the first plurality of qubits, performing (710) a number of available quantum computing operations from the plurality of quantum computing operations on one or more qubits (1a-1d) from the number of qubit chains of the first plurality of qubits, Performing (720) two adjacent qubits (q1; q2) of said number of qubit chains involving said first plurality of qubits and a qubit (qb 2,1 ) of a corresponding quantum bit ladder (16) of a plurality of available quantum computing operations from the plurality of quantum computing operations, the quantum bit (qb 2,1 ) is adjacent to one (q2) of said adjacent qubits (q1; q2) of said several qubit chains of said first plurality of qubits, wherein the corresponding qubit ladder is a qubit ladder from the number of qubit ladders of the second plurality of qubits, where the corresponding bosonic mode is encoded by the corresponding qubit ladder, exchanging (730) quantum information between each qubit of the plurality of even-numbered qubits (q2) of the plurality of qubit chains of the first plurality of qubits and a corresponding adjacent odd-numbered qubit (q3) located on the predetermined side relative to the even-numbered qubit, if the odd-numbered qubit on the predetermined side relative to the even-numbered qubit exists, wherein the corresponding adjacent odd-numbered qubits are qubits from odd-numbered qubits of the qubit chains of the first plurality of qubits, performing (740) a number of available quantum computing operations from the plurality of quantum computing operations on the one or more qubits (1a-1d) of the number of qubit chains of the first plurality of qubits, Performing (750) the two adjacent qubits (q1, q2) of the plurality of qubit chains involving the first plurality of qubits and the qubit (qb 2,1 ) of the corresponding quantum bit ladder (16) of the plurality of quantum computing operations, the quantum bit (qb 2,1 ) is adjacent to said one (q2) of said adjacent qubits (q1, q2) of said several qubit chains of said first plurality of qubits, iteratively repeating (760) the steps of exchanging information and performing the number of available quantum computing operations until all of the number of available quantum computing operations from the plurality of quantum computing operations have been performed; Several of the plurality of quantum computing operations are performed (770) on the respective qubit ladders (16).

11. The method of claim 10 , wherein performing ( 720 ; 750 ) the two adjacent qubits ( q1 , q2 ) of the plurality of qubit chains involving the first plurality of qubits and the qubit ( qb 2,1 ) of the corresponding quantum bit ladder (16) comprising the following steps: using a number of quantum two-qubit gates and / or single-qubit gates arranged in a corresponding order acting on said two adjacent qubits (q1, q2) of said number of qubit chains of said first plurality of qubits; performing a number of quantum computing operations involving the following qubits: i) adjacent qubits (q1, q2) of the qubit chains of the first plurality of qubits and the qubit (qb) of the corresponding qubit ladder; 2,1 ) adjacent to said one (q2), ii) said qubit (qb) of said corresponding qubit ladder adjacent to said one (q2) of said adjacent qubits of said plurality of qubit chains of said first plurality of qubits 2,1 ), and iii) one or more qubits (qb) of the corresponding qubit ladder that are not adjacent to said one of the adjacent qubits of the several qubit chains of the first plurality of qubits 2,2 ).

12. The method of any one of claims 1 to 11, further comprising performing a quantum computing task, wherein the quantum computing task comprises the plurality of quantum computing operations performed on the plurality of qubit chains of the first plurality of qubits and the plurality of qubit ladders of the second plurality of qubits.

13. A quantum computing system (1000) configured according to the method steps of any one of claims 1 to 12.

14. A quantum computing system (1000) configured to perform a plurality of quantum computing operations and adapted to perform the method steps of any one of claims 2 to 12.

15. A remote computing system comprising a quantum computing system (1000), the remote computing system being adapted to: performing a quantum computing task, wherein the quantum computing task comprises a plurality of quantum computing operations according to the method of claim 12; wherein the plurality of quantum computing operations are performed according to the method steps of any one of claims 2 to 12; The results of the computing task are sent to a computer-implemented system.

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