US-12626177-B2 - Quantum operation control layout for a quantum computation

US12626177B2US 12626177 B2US12626177 B2US 12626177B2US-12626177-B2

Abstract

A method of determining a quantum operation control layout for a quantum computation on a quantum system is provided. The quantum computation is to be carried out on constituents of the quantum system arranged in accordance with a mesh. Vertices of the mesh represent possible sites for the constituents of the quantum system. Each cell of the mesh indicates that quantum interactions between constituents of the quantum system arranged in that cell are possible during the quantum computation. The method includes providing a data set including data representing hyperedges of a hypergraph. The method includes determining a set of generalized cycles. The method includes determining a mesh mapping that maps data representing the hyperedges of the hypergraph or of the enlarged hypergraph to the vertices of the mesh. The method includes generating the quantum operation control layout. The quantum operation control layout includes data indicating layout vertices of the mesh.

Inventors

Wolfgang Lechner

Assignees

Parity Quantum Computing GmbH

Dates

Publication Date: 20260512
Application Date: 20200709

Claims (16)

1 . A method of determining a quantum operation control layout for a quantum computation on a quantum system, wherein the quantum computation is to be carried out on constituents of the quantum system arranged in accordance with a mesh, wherein vertices of the mesh represent possible sites for the constituents of the quantum system and each cell of the mesh indicates that quantum interactions between constituents of the quantum system arranged in that cell are possible during the quantum computation, the method comprising: providing a data set including data representing hyperedges of a hypergraph; determining a set of generalized cycles, the generalized cycles containing hyperedges of the hypergraph or containing hyperedges of an enlarged hypergraph, the enlarged hypergraph at least including the hyperedges of the hypergraph and an additional hyperedge, wherein a maximal length of generalized cycles of the set of generalized cycles is not greater than a maximal vertex number of the cells of the mesh; determining a mesh mapping that maps data representing the hyperedges of the hypergraph or of the enlarged hypergraph to the vertices of the mesh, wherein each generalized cycle of a constraining subset of the set of generalized cycles consists of hyperedges mapped to a cell of the mesh; and generating the quantum operation control layout, the quantum operation control layout including data indicating layout vertices of the mesh, wherein each layout vertex corresponds to a hyperedge mapped according to the mesh mapping, and including data indicating layout vertex sets, each layout vertex set consisting of layout vertices within a cell of the mesh that correspond to a generalized cycle of the constraining subset of generalized cycles.
2 . The method of claim 1 , wherein the mesh is two-dimensional.
3 . The method of claim 1 , wherein the lengths of the generalized cycles of the set of generalized cycles are in the range from three to the maximal vertex number of the cells of the mesh, or are equal to the maximal vertex number of the cells of the mesh.
4 . The method of claim 1 , wherein the number of nodes of the hypergraph is N, the number of hyperedges of the hypergraph is K, and the cardinality of the constraining subset is at least K−N.
5 . The method of claim 1 , wherein the number of nodes of the hypergraph is N, the number of hyperedges of the hypergraph is K, and wherein K is smaller than N(N−1)/2.
6 . The method of claim 1 , wherein the hyperedges of the hypergraph are associated with weights, and the quantum operation control layout includes data associating the layout vertices with the weights of the hyperedges of the hypergraph or of the enlarged hypergraph that are mapped to the layout vertices by the mesh mapping, wherein additional hyperedges of the enlarged hypergraph not contained in the hypergraph are assigned a weight of zero.
7 . The method of claim 1 , wherein the quantum operation control layout is a transparent quantum operation control layout which includes at least one of: data representing the mesh mapping and data representing the generalized cycles of the constraining subset of generalized cycles.
8 . The method of claim 1 , wherein the union of generalized cycles of the constraining subset of generalized cycles contains all hyperedges of the hypergraph or of the enlarged hypergraph and/or wherein the generalized cycles of the constraining subset of generalized cycles connect all hyperedges of the hypergraph or of the enlarged hypergraph.
9 . The method of claim 1 , wherein the cardinality of at least one hyperedge of the hypergraph is odd and/or wherein the cardinality of at least one hyperedge of the hypergraph is at least three.
10 . The method of claim 1 , wherein the constraining subset includes at least one of: a regular generalized cycle and an irregular generalized cycle.
11 . The method of claim 1 , wherein the mesh mapping is constructed by mapping the hyperedges of a first generalized cycle of the set of generalized cycles on vertices of a cell of the mesh, mapping the hyperedges of a second generalized cycle of the set of generalized cycles on the vertices of a neighboring cell of the mesh, wherein the first generalized cycle and the second generalized cycle have at least one hyperedge in common and the at least one hyperedge is mapped on a corresponding at least one vertex of the mesh, and repeating this process of mapping hyperedges of generalized cycles of the set of generalized cycles until the mapped generalized cycles form the constraining subset.
12 . The method of claim 1 , comprising at least one of: (a) providing mesh data that represents the mesh or includes at least one information element about the mesh, and deriving the mesh from the mesh data, where default values are used where information about the mesh is lacking; and (b) providing information about the type of the quantum computation to be performed, wherein generating the quantum operation control layout includes adapting the format and/or content of the quantum operation control layout in dependence of the information about the type of the quantum computation to be performed.
13 . A quantum operation control layout for controlling a quantum computation on a quantum system, wherein the quantum computation is to be carried out on constituents of the quantum system arranged in accordance with a mesh, wherein vertices of the mesh represent possible sites for the constituents of the quantum system and each cell of the mesh indicates that quantum interactions between constituents of the quantum system arranged in that cell are possible during the quantum computation, the quantum operation control layout comprising: data indicating layout vertices of the mesh, and data indicating layout vertex sets, wherein each layout vertex set consists of layout vertices within a cell of the mesh.
14 . The quantum operation control layout according to claim 13 , wherein at least one of the following applies: the quantum operation control layout comprises data representing weights associated with the layout vertices; the layout vertices correspond to hyperedges of a hypergraph or of an enlarged hypergraph mapped to the layout vertices according to a mesh mapping, wherein layout vertices of each layout vertex set correspond to hyperedges forming a generalized cycle of the hypergraph or of the enlarged hypergraph; and the weights associated with the layout vertices correspond to weights of the hyperedges of the hypergraph or of the enlarged hypergraph mapped to the layout vertices by the mesh mapping.
15 . A method of performing a quantum computation on a quantum system, wherein the quantum computation is carried out on constituents of the quantum system, the method comprising: providing a quantum operation control layout for controlling the quantum computation on the quantum system, wherein the quantum computation is to be carried out on constituents of the quantum system arranged in accordance with a mesh, wherein vertices of the mesh represent possible sites for the constituents of the quantum system and each cell of the mesh indicates that quantum interactions between constituents of the quantum system arranged in the cell are possible during the quantum computation, the quantum operation control layout comprising: data indicating layout vertices of the mesh, and data indicating layout vertex sets, wherein each layout vertex set consists of layout vertices within a cell of the mesh; the method further comprising: providing the constituents of the quantum system in a spatial arrangement such that there is a constituent for every layout vertex of the mesh and, for each layout vertex set, quantum interactions are possible between constituents corresponding to layout vertices of that layout vertex set; for each layout vertex associated with a non-zero weight, applying a local field to the constituent corresponding to that layout vertex; for each layout vertex set, performing quantum interactions between constituents corresponding to the layout vertices of that layout vertex set; and measuring some or all of the constituents of the quantum system.
16 . A method of performing a quantum computation on a quantum system, wherein the quantum computation is carried out on constituents of the quantum system, the method comprising: providing a quantum operation control layout for controlling the quantum computation on the quantum system, wherein the quantum computation is to be carried out on constituents of the quantum system arranged in accordance with a mesh, wherein vertices of the mesh represent possible sites for the constituents of the quantum system and each cell of the mesh indicates that quantum interactions between constituents of the quantum system arranged in that cell are possible during the quantum computation, the quantum operation control layout comprising: data indicating layout vertices of the mesh, and data indicating layout vertex sets, wherein each layout vertex set consists of layout vertices within a cell of the mesh, wherein at least one of the following applies: the quantum operation control layout comprises data representing weights associated with the layout vertices; the layout vertices correspond to hyperedges of a hypergraph or of an enlarged hypergraph mapped to the layout vertices according to a mesh mapping, wherein layout vertices of each layout vertex set correspond to hyperedges forming a generalized cycle of the hypergraph or of the enlarged hypergraph; and the weights associated with the layout vertices correspond to weights of the hyperedges of the hypergraph or of the enlarged hypergraph mapped to the layout vertices by the mesh mapping; the method further comprising: providing the constituents of the quantum system in a spatial arrangement such that there is a constituent for every layout vertex of the mesh and, for each layout vertex set, quantum interactions are possible between constituents corresponding to layout vertices of that layout vertex set; for each layout vertex associated with a non-zero weight, applying a local field to the constituent corresponding to that layout vertex; for each layout vertex set, performing quantum interactions between constituents corresponding to the layout vertices of that layout vertex set; and measuring some or all of the constituents of the quantum system.

Description

CROSS REFERENCE TO RELATED APPLICATIONS This application is a United States National Phase Patent Application of International Patent Application Number PCT/EP2020/069416, filed on Jul. 9, 2020, and incorporates by reference herein the same in its entirety. FIELD Embodiments described herein relate to a method of determining a quantum operation control layout for a quantum computation on a quantum system, to the quantum operation control layout itself, to a computer program product including the quantum operation control layout, and to a method of performing the quantum computation on the quantum system using the quantum operation control layout. Further embodiments are directed to systems for determining the quantum operation control layout for the quantum computation on a quantum system and/or for performing the quantum computation on the quantum system using the quantum operation control layout, in particular systems configured to carry out the methods described herein, and to uses of the systems. BACKGROUND Computing devices based on classical information processing, i.e., computing devices not making use of quantum mechanical effects, once started out as hard-wired calculators which could only perform specific operations. The transition to fully programmable computers revolutionized the field and started the information age. Currently, quantum computing devices, i.e., computing devices which, possibly in addition to using classical information processing, make use of quantum mechanical effects to solve computational problems, are still mostly in stages comparable to those of hard-wired calculators in that they can only tackle computational problems for which they are particularly designed. EP 3 113 084 A1 describes a method and apparatus for solving computational problems using a quantum system. This quantum computing method/apparatus receives a computational problem, in particular an NP hard computational problem or an NP complete computational problem, such as the (classical) Ising spin model with N spins and all-to-all pairwise interactions. The quantum method/apparatus encodes the computational problem into a single-body problem Hamiltonian of the quantum system with adjustable parameters. For instance, in the case of the (classical) Ising spin model with N spins and all-to-all pairwise interactions between the N spins, each term of the single-body problem Hamiltonian may be regarded as corresponding to one of the pairwise interactions, and so there are N(N−1)/2 single-body terms of the problem Hamiltonian acting on a corresponding number of quantum bits (qubits) of the quantum system, and there is a like number of adjustable parameters. The qubits of the quantum system represent the parity of the spins of the Ising spin model, wherein the state |0> indicates anti-parallel alignment of the corresponding spins of the Ising spin model, and the state |1> indicates parallel alignment. In addition, a short-range Hamiltonian is provided in EP 3 113 084 A1 to compensate for the increased number of degrees of freedom of the quantum system as compared to the Ising spin model, the short-range Hamiltonian being a sum of at least N(N−1)/2−N constraint Hamiltonians, wherein each constraint Hamiltonian acts with a constraint strength C on at most four qubits forming a plaquette of a square lattice that contains the qubits of the quantum system. The constraint Hamiltonians ensure consistency with the Ising spin model in that they enforce the presence of an even number (zero, two, etc.) of states |0> within subsets of qubits that correspond to spins with anti-parallel alignment in closed loops over spins in the Ising spin model. The ground state of a final Hamiltonian being the sum of the problem Hamiltonian and of the short-range Hamiltonian, or at least a thermal state close to that ground state, contains information about a solution to the computational problem that is encoded in the parameters of the problem Hamiltonian. Measuring the quantum system in such a state can reveal information about the solution to the computational problem. The ground state of the final Hamiltonian, or thermal state close to the ground state, can be reached by quantum annealing, i.e. an adiabatic sweep from the ground state of an initial Hamiltonian to the ground state of the final Hamiltonian as described in EP 3 113 084 A1. Alternatively, the ground state may be reached by counter-diabatic driving using a Hamiltonian with an additional counter-diabatic part as described in PCT/EP2019/066916. The adiabatic quantum computation and the counter-diabatic quantum computation can both be regarded as an analog quantum computation. A digital version of the quantum computation using quantum gates is described in PCT/EP2019/052528. A state approximating the ground state of the final Hamiltonian can be reached by a sequence of unitary operators acting on an initial state, wherein the unitary operators are propagators of the initial Hamiltoni