Quantum variational method, apparatus, and storage medium for simulating quantum systems

Patent metadata

Field	Value
Publication number	US-11314536-B2
Application number	US-201916505179-A
Country	US
Kind code	B2
Filing date	Jul 8, 2019
Priority date	Jul 8, 2019
Publication date	Apr 26, 2022
Grant date	Apr 26, 2022

Abstract

The present disclosure discloses a method for obtaining optimal variational parameters of a ground state wavefunction for a Hamiltonian system. The method includes initializing a plurality of variational parameters and sending the variational parameters to a quantum computing portion to output a plurality of measurement results. The method includes transmitting the measurement results to a classical computing portion to update the plurality of variational parameters based on the plurality of measurement results and an update rule, and determining whether a measured energy satisfies a convergence rule. When the measured energy does not satisfy the convergence rule, the method includes sending the plurality of updated variational parameters to the quantum computing portion for a next iteration; and when the measured energy satisfies the convergence rule, the method includes obtaining a plurality of optimal variational parameters for the Hamiltonian system.

First claim

What is claimed is:

1. A method for obtaining a plurality of optimal variational parameters of a wavefunction for a Hamiltonian system, the method comprising:
initializing, by a device comprising a quantum computing portion and a classical computing portion in communication with the quantum computing portion, a plurality of variational parameters of the wavefunction for the Hamiltonian system;
sending, by the device, the plurality of variational parameters to the quantum computing portion to begin an iteration, so that the quantum computing portion performs a plurality of measurements to output a plurality of measurement results based on the plurality of variational parameters, the wavefunction, and the Hamiltonian system;
transmitting, by the device, the plurality of measurement results from the quantum computing portion to the classical computing portion, so that the classical computing portion updates the plurality of variational parameters based on the plurality of measurement results and an update rule;
determining, by the device, whether a measured energy satisfies a convergence rule;
in response to the determination that the measured energy does not satisfy the convergence rule, sending the plurality of updated variational parameters as the plurality of variational parameters to the quantum computing portion for a next iteration; and
in response to the determination that the measured energy satisfies the convergence rule, setting, by the device, the plurality of updated variational parameters so as to obtain a plurality of optimal variational parameters for the Hamiltonian system,
wherein:
the Hamiltonian system comprises a Hamiltonian H and a ground-state wavefunction Ψ(τ), the ground-state wavefunction Ψ(τ) satisfies imaginary time Schrodinger equation

∂

❘

Ψ
⁡

(
τ
)

〉

∂
τ

=

-

(

H
-

E
τ

)

❘

Ψ
⁡

(
τ
)

〉

,

 wherein τ=i*t, i is an imaginary unit, t is time, and E τ is an energy of the Hamiltonian system, and
the ground-state wavefunction Ψ(τ) includes an approximated parametrized wavefunction comprising |Ψ(τ) =|Ψ({right arrow over (θ)}(τ)) =V({right arrow over (θ)})|Ψ(0) , where V({right arrow over (θ)}) is a set of quantum operations realizable in quantum circuits, {right arrow over (θ)} includes a plurality of variational parameters.

2. The method according to claim 1 , wherein the initializing the plurality of variational parameters comprises:
initializing, by the device, the plurality of variational parameters randomly.

3. The method according to claim 1 , wherein:
the plurality of measurements comprises a plurality of gradients

∂

Ψ
⁡

[
θ
]

∂

θ
n

,

 wherein θ n is one of the plurality of variational parameters and n is an index for the plurality of variational parameters.

4. The method according to claim 3 , wherein:
the update rule comprises {right arrow over (θ)}(τ+δτ)={right arrow over (θ)}(τ)+{right arrow over ({dot over (θ)})}(τ)δτ={right arrow over (θ)}(τ)+A −1 (τ)*C(τ)δτ, wherein δτ is a timestep, A is a matrix with matrix elements

A
mn

=

Re
⁢

〈

∂

Ψ
⁡

[
θ
]

∂

θ
m

❘

∂

Ψ
⁡

[
θ
]

∂

θ
n

〉

,

 A −1 is an inverse matrix of A, C is a vector with vector elements

C
n

=

-
Re

⁢

〈

∂

Ψ
⁡

[
θ
]

∂

θ
n

❘

Assignees

• Tencent America LLC

Inventors

• Lee Chee Kong
• Sun Qiming

Classifications

• G06N3/047

  Probabilistic or stochastic networks · CPC title

• G06N3/044

  Recurrent networks, e.g. Hopfield networks · CPC title

• G06N3/0499

  Feedforward networks · CPC title

• G06N10/40

  Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control · CPC title

• B82Y10/00

  Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic · CPC title