Quantum Commuting Block Circuits for Efficient Gradient Measurement

Solution Overview

Problem

Existing variational quantum algorithms face challenges in implementing commuting block circuits to facilitate the measurement of the gradient of a cost function, leading to increased processing costs and difficulty in solving problems within a practical time frame.

Innovation Solution

The implementation of a commuting block circuit is facilitated by determining a set of Pauli operators and generators for each block, ensuring mutual commutativity or anticommutativity, and incorporating base transformation circuits to optimize parameter measurement.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If a commuting block circuit is adopted to facilitate gradient measurement, then measurement efficiency is improved, but the complexity of determining the circuit structure increases

Engineering Contradiction:

Improvemeasurement efficiencyVSAvoidcircuit structure complexity

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The quantum circuit is divided into multiple commuting blocks, where each block contains rotation gates with generators that mutually commute. This segmentation allows independent optimization and measurement of each block's contribution to the gradient, improving measurement efficiency while managing complexity through modular structure.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Pauli operator sets are pre-determined and classified into commuting groups before circuit construction. By performing this classification in advance, the system establishes a structured framework that guides subsequent circuit assembly, reducing the complexity of real-time circuit determination while enabling efficient gradient measurement.

Inventive Principle:

Principle #10Preliminary action

2Measurement precision

If Pauli operators are determined for each block with mutual commutativity constraints, then gradient measurement accuracy is improved, but the processing time for circuit determination increases

Engineering Contradiction:

Improvegradient measurement accuracyVSAvoidcircuit determination time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

Pauli operator sets are pre-determined and classified into commuting groups before circuit construction. By performing this classification in advance, the system establishes a structured framework that guides subsequent circuit assembly, reducing the complexity of real-time circuit determination while enabling efficient gradient measurement.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The system transforms the problem from determining individual Pauli operators for each gate to selecting from pre-classified commuting Pauli operator sets. This parameter transformation changes the optimization space from continuous gate-by-gate determination to discrete set selection, reducing computational time while maintaining measurement precision.

Inventive Principle:

Principle #35Parameter changes

3Productivity

If rotation gates are configured with specific generators from Pauli operator sets, then the ability to measure cost function gradients is improved, but the device complexity increases

Engineering Contradiction:

Improvegradient measurement capabilityVSAvoidquantum circuit complexity

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The quantum circuit is divided into multiple commuting blocks, where each block contains rotation gates with generators that mutually commute. This segmentation allows independent optimization and measurement of each block's contribution to the gradient, improving measurement efficiency while managing complexity through modular structure.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Pauli operator sets serve multiple functions: they define the generators for rotation gates, establish commutation relationships for blocking, and provide the basis for gradient measurement. This multi-functionality reduces the need for separate circuit components, managing complexity while enhancing gradient measurement capability.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS20250272592A1Computer-readable recording medium storing information processing program, information processing method, and information processing device

Publication Date: 2025.08.28 FUJITSU LTD

AI summary

A non-transitory computer-readable recording medium storing an information processing program for causing a computer to execute processing includes acquiring a first Pauli operator set that is a set of first Pauli operators for qubits related to a target problem formed by a product of Pauli operators for qubits different from each other, acquiring a second Pauli operator set that is a set of second Pauli operators for the qubits related to the problem, which are commutative with all the first Pauli operators, and determining a commuting block circuit formed by blocks that corresponds to each rotation gate of rotation gates included in each block has a generator (G_j{circumflex over ( )}b) formed by a product of any one first Pauli operator different for each of the rotation gates in the acquired first Pauli operator set and any one second Pauli operator selected for each of the blocks in the second Pauli operator set.