EP-4738205-A1 - QUANTUM INFORMATION PROCESSING METHOD, QUANTUM INFORMATION PROCESSING PROGRAM, CLASSIC COMPUTER, AND HYBRID SYSTEM

EP4738205A1EP 4738205 A1EP4738205 A1EP 4738205A1EP-4738205-A1

Abstract

A classical computer transmits a quantum circuit for preparing a quantum state to a quantum computer. A quantum computer, with respect to a first qubit group containing n individual qubits and a second qubit group containing n individual qubits different to the qubits in the first qubit group, sets n individual pairs of a qubit in the first qubit group and a qubit in the second qubit group, uses the n individual pairs and the quantum circuit to execute Bell measurement on a tensor product of quantum states so as to acquire a result of the Bell measurement, and transmits the Bell measurement result to the classical computer. The classical computer computes respective expectation values of plural Pauli products in a quantum state based on the Bell measurement results, and computes respective expectation values of a plurality of operators based on an arbitrary combinations of Pauli products from out of the plural Pauli products.

Inventors

YANO, HIROSHI
KOHDA, Masaya
Tsutsui, Shoichiro
IMAI, RYOSUKE
KANNO, Keita
NAKAGAWA, Yuya

Assignees

QunaSys Inc.

Dates

Publication Date: 20260506
Application Date: 20230630

Claims (12)

A quantum information processing method for execution by a classical computer in a hybrid system including the classical computer and a quantum computer, the quantum information processing method comprising: the classical computer transmitting a quantum circuit for preparing a quantum state to the quantum computer; the quantum computer, with respect to a first qubit group containing n individual qubits and a second qubit group containing n individual qubits different to the qubits in the first qubit group, setting n individual pairs of a qubit in the first qubit group and a qubit in the second qubit group, using the n individual pairs and the quantum circuit to execute Bell measurement on a tensor product of quantum states so as to acquire a result of the Bell measurement, and transmitting the Bell measurement result to the classical computer; and the classical computer computing respective expectation values of a plurality of Pauli products in a quantum state based on the Bell measurement results, and computing respective expectation values of a plurality of operators based on an arbitrary combinations of Pauli products from out of the plurality of Pauli products.
The quantum information processing method of claim 1, wherein: each of a plurality of operators O i (wherein i is an index to identify an operator) is computable by following Equation (A) based on coefficients c k (i) and Pauli products P k (i) (wherein k is an index to identify a Pauli product); O i = ∑ k c k i P k i the Bell measurement result for a tensor product of the quantum state ρ is expressed by the following Equation (B1); and Φ 1 ± = 1 2 0 ρ ⊗ 0 ρ ± 1 ρ ⊗ 1 ρ Φ 2 ± = 1 2 0 ρ ⊗ 1 ρ ± 1 ρ ⊗ 0 ρ the classical computer computes squares (Tr (ρP k (i) )) 2 of respective expectation values of a plurality of Pauli products P k (i) in a quantum state ρ based on | φ 1 ± > and | φ 2 ± > from out of the Bell measurement result, computes absolute values |Tr (ρP k (i) )| of respective expectation values of a plurality of Pauli products P k (i) by computing square roots of the squares (Tr (ρP k (i) )) 2 , computes respective expectation values Tr (ρP k (i) ) of the plurality of Pauli products P k (i) based on a sign of the expectation values predetermined for each of the plurality of Pauli products P k (i) and based on the absolute values |Tr (ρP k (i) )| of the respective expectation values of the plurality of Pauli products P k (i) , and computes respective expectation values of a plurality of operators O i according to above Equation (A) based on a predetermined plurality of coefficients c k (i) and on the expectation values Tr (ρP k (i) ) of the plurality of Pauli products P k (i) .
The quantum information processing method of claim 2, wherein: the quantum computer acquires the expectation value signs by approximate computation of an expectation value Tr (ρP k (i) ) for each of the plurality of Pauli products P k (i) . and the classical computer computes the respective expectation values Tr (ρP k (i) ) of the plurality of Pauli products P k (i) based on the expectation value signs obtained by the quantum computer and on the absolute values |Tr (ρP k (i) )| of the respective expectation values of the plurality of Pauli products P k (i) .
The quantum information processing method of claim 2, wherein the classical computer: computes an expectation value Tr (ρ'P k (i) ) related to a state p' approximating to the quantum state p; and computes an expectation value Tr (ρP k (i) ) of each of the plurality of Pauli products P k (i) based on a sign of the computed expectation value Tr (ρ'P k (i) ) and on the absolute values |Tr (ρP k (i) )| of the respective expectation values of the plurality of Pauli products P k (i) .
The quantum information processing method of claim 2, wherein: the operator is a Hamiltonian operator H; a variational quantum eigensolver (VQE) is employed when computing expectation values of the Hamiltonian operator H; the quantum state ρ is a parameter θ appended quantum state ρ (0); and the classical computer, in repeated computation of the VQE when searching for a parameter θ* so as to minimize Tr (ρ(θ)H) that is an expectation value of the Hamiltonian operator H, computes respective expectation values Tr (ρP k (i) ) for the plurality of Pauli products P k (i) by reusing a sign of the expectation value obtained at a previous step as a sign of the expectation value for a next step onwards in a specific period.
The quantum information processing method of claim 1, wherein: each of a plurality of operators O i (wherein i is an index to identify an operator) is computable by following Equation (A) based on coefficients c k (i) and Pauli products P k (i) (wherein k is an index to identify a Pauli product); O i = ∑ k c k i P k i the Bell measurement result for a tensor product of the quantum state ρ and the quantum state σ is expressed by the following Equation (B2); Φ 1 ± = 1 2 0 ρ ⊗ 0 σ ± 1 ρ ⊗ 1 σ Φ 2 ± = 1 2 0 ρ ⊗ 1 σ ± 1 ρ ⊗ 0 σ the classical computer computes values (Tr (ρP k (i) )) (Tr (σP k (i) )) related to respective expectation values of a plurality of Pauli products P k (i) based on | φ 1 ± > and | φ 2 ± > from out of the Bell measurement result, computes an expectation value (Tr (σP k (i) ) of a Pauli product P k (i) in a quantum state σ, computes respective expectation values Tr (ρP k (i) ) of the plurality of Pauli products P k (i) by dividing the values (Tr (ρP k (i) )) (Tr (σP k (i) )) related to the expectation values by the expectation value (Tr (σP k (i) ), and computes respective expectation values of a plurality of operators O i according to above Equation (A) based on a predetermined plurality of coefficients c k (i) and on the expectation values Tr (ρP k (i) ) of a plurality of Pauli products P k (i) .
The quantum information processing method of claim 6, wherein: the quantum state σ is a superimposed state of quantum states of qubit numbers k1, k2, ···, km; k 1 + k 2 + ⋯ + km = n ; and n is a total number of qubits for computing the quantum state σ.
The quantum information processing method of claim 6, wherein the classical computer: predetermines the quantum state σ by executing optimization computation so as to minimize an objective function expressing variation in computation results of the expectation values (Tr (ρP k (i) ); and transmits information of the quantum state σ to the quantum computer.
A quantum information processing program for execution by a classical computer in a hybrid system including the classical computer and a quantum computer, the quantum information processing program causing the classical computer to execute processing comprising: the classical computer transmitting a quantum circuit for preparing a quantum state to the quantum computer; the quantum computer, with respect to a first qubit group containing n individual qubits and a second qubit group containing n individual qubits different to the qubits in the first qubit group, setting n individual pairs of a qubit in the first qubit group and a qubit in the second qubit group, using the n individual pairs to execute Bell measurement on a tensor product of quantum states so as to acquire a result of the Bell measurement, and transmitting the Bell measurement result to the classical computer; and the classical computer computing respective expectation values of a plurality of Pauli products in a quantum state based on the Bell measurement results, and computing respective expectation values of a plurality of operators based on an arbitrary combinations of Pauli products from out of the plurality of Pauli products.
A classical computer in a hybrid system including the classical computer and a quantum computer, wherein: the classical computer transmits a quantum circuit for preparing a quantum state to the quantum computer; the quantum computer, with respect to a first qubit group containing n individual qubits and a second qubit group containing n individual qubits different to the qubits in the first qubit group, sets n individual pairs of a qubit in the first qubit group and a qubit in the second qubit group, uses the n individual pairs to execute Bell measurement on a tensor product of quantum states so as to acquire a result of the Bell measurement, and transmits the Bell measurement result to the classical computer; and the classical computer computes respective expectation values of a plurality of Pauli products in a quantum state based on the Bell measurement results, and computes respective expectation values of a plurality of operators based on an arbitrary combinations of Pauli products from out of the plurality of Pauli products.
A hybrid system including a classical computer and a quantum computer, wherein: the classical computer transmits a quantum circuit for preparing a quantum state to the quantum computer; the quantum computer, with respect to a first qubit group containing n individual qubits and a second qubit group containing n individual qubits different to the qubits in the first qubit group, sets n individual pairs of a qubit in the first qubit group and a qubit in the second qubit group, uses the n individual pairs to execute Bell measurement on a tensor product of quantum states so as to acquire a result of the Bell measurement, and transmits the Bell measurement result to the classical computer; and the classical computer computes respective expectation values of a plurality of Pauli products in a quantum state based on the Bell measurement results, and computes respective expectation values of a plurality of operators based on an arbitrary combinations of Pauli products from out of the plurality of Pauli products.
A hybrid system comprising a plurality of classical computers and a plurality of quantum computers, wherein in the hybrid system: at least one classical computer from out of the plurality of classical computers transmits a quantum circuit for preparing a quantum state to the quantum computer; at least one quantum computer from out of the plurality of quantum computers, with respect to a first qubit group containing n individual qubits and a second qubit group containing n individual qubits different to the qubits in the first qubit group, sets n individual pairs of a qubit in the first qubit group and a qubit in the second qubit group, uses the n individual pairs to execute Bell measurement on a tensor product of quantum states so as to acquire a result of the Bell measurement, and transmits the Bell measurement result to the classical computer; and at least one classical computer from out of the plurality of classical computers computes respective expectation values of a plurality of Pauli products in a quantum state based on the Bell measurement results, and computes respective expectation values of a plurality of operators based on an arbitrary combinations of Pauli products from out of the plurality of Pauli products.

Description

Field Technology disclosed herein relates to a quantum information processing method, a quantum information processing program, a classical computer, and a hybrid system. Background Art Executing a task of "measuring an expectation value of an operator" with good efficiency is important when executing some computation processing using a quantum computer. For example, when executing a quantum computation using a quantum computer, a ground state energy may be obtained by measuring an expectation value of a Hamiltonian operator for a ground state. Normally, when measuring an expectation value of a complicated operator such as a Hamiltonian operator using a comparatively shallow quantum circuit, there is a need to repeatedly execute plural types of quantum circuit. Note that an operator may be represented by a linear sum of arbitrary Pauli products. Note that a Pauli product is an operator expressed by a direct product of a Pauli operator. A method for computing a value related to an arbitrary Pauli product using a quantum circuit having 2n individual qubits is known in Document 1 (Hsin-Yuan Huang, Richard Kueng, John Preskill, "Information-theoretic bounds on quantum advantage in machine learning", Phys. Rev. Lett. 126, 190505 (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.190505)) and Document 2 (Zhang Jiang, Amir Kalev, Wojciech Mruczkiewicz, Hartmut Neven, "Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning", Quantum 4, 276 (2020) (https://quantum-journal.org/papers/q-2020-06-04-276/)). For example, Document 1 discloses technology for computing an absolute value of an expectation value of an arbitrary Pauli product using a quantum circuit having 2n individual qubits. Moreover, Document 2 discloses technology for computing an arbitrary Pauli product expectation value itself using a quantum circuit having 2n individual qubits. Appropriate processing of Pauli product expectation values is needed to obtain an expectation value of an operator. However, such a method is not disclosed in Document 1 or Document 2. SUMMARY OF INVENTION Technical Problem In consideration of the above circumstances, technology disclosed herein provides a quantum information processing program, a classical computer, and a hybrid system that are capable of efficiently obtaining an expectation value of an operator. Solution to Problem In order to achieve the above object, a quantum information processing method of the present disclosure is a quantum information processing method for execution by a classical computer in a hybrid system including the classical computer and a quantum computer. In the quantum information processing method, the classical computer transmits a quantum circuit for preparing a quantum state to the quantum computer. The quantum computer, with respect to a first qubit group containing n individual qubits and a second qubit group containing n individual qubits different to the qubits in the first qubit group, sets n individual pairs of a qubit in the first qubit group and a qubit in the second qubit group, uses the n individual pairs and the quantum circuit to execute Bell measurement on a tensor product of quantum states so as to acquire a result of the Bell measurement, and transmits the Bell measurement result to the classical computer. The classical computer computes respective expectation values of plural Pauli products in a quantum state based on the Bell measurement results, and computes respective expectation values of plural operators based on an arbitrary combinations of Pauli products from out of the plural Pauli products. Advantageous Effects Technology disclosed herein exhibits the advantageous effect of enabling an expectation value of an operator to be obtained efficiently. BRIEF DESCRIPTION OF DRAWINGS Fig. 1 is a diagram illustrating an example of a schematic configuration of a hybrid system 100 of the present exemplary embodiment.Fig. 2 is a schematic block diagram of a computer functioning as a classical computer 110, a control device 121, and a user terminal 130.Fig. 3 is a diagram to explain Bell measurement.Fig. 4 is a diagram illustrating an example of a sequence of executions by a hybrid system 100 of an exemplary embodiment.Fig. 5 is a diagram illustrating an example of a sequence of executions by a hybrid system 100 of an exemplary embodiment. DESCRIPTION OF EMBODIMENTS Detailed explanation follows regarding exemplary embodiments of technology disclosed herein, with reference to the drawings. Hybrid System 100 According to First Exemplary Embodiment Fig. 1 illustrates a hybrid system 100 according to a first exemplary embodiment. The hybrid system 100 of the present exemplary embodiment includes a classical computer 110 serving as an example of an information processing device, a quantum computer 120, and a user terminal 130. As illustrated in Fig. 1, the classical computer 110, the quantum computer 120, and the user termi