Tensor-Based VQA Cost Function Landscape Generation

Solution Overview

Problem

Reconstructing the landscape of a variational quantum algorithm (VQA) cost function is computationally expensive and memory-intensive, especially when the quantum circuit has a large number of parameters, due to the curse of dimensionality.

Innovation Solution

A method involving discretization of the cost function to form a landscape tensor, random sampling of parameter values, execution of the quantum circuit to generate cost function values, and solving a low-rank tensor completion problem to estimate missing values, allowing for efficient reconstruction of the cost function landscape.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If conventional methods are used to reconstruct the VQA cost function landscape, then measurement precision is improved, but use of energy and computational cost increase exponentially due to the curse of dimensionality

Engineering Contradiction:

Improvecost function landscape reconstruction accuracyVSAvoidcomputational cost

Core Design Contradiction:

Measurement precisionVSUse of energy by moving object

Solution Approach 1:

The patent segments the high-dimensional cost function landscape into multiple low-dimensional slices or projections. Instead of reconstructing the entire high-dimensional landscape directly, the method divides it into manageable lower-dimensional subspaces that can be reconstructed individually with fewer quantum samples, then combines these segments to form the complete landscape reconstruction.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent transforms the high-dimensional reconstruction problem into a series of low-dimensional problems by projecting the cost function onto lower-dimensional subspaces. This dimensionality reduction allows the use of fewer quantum samples while still capturing the essential features of the cost function landscape through techniques like random projections or slicing methods.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

2Measurement precision

If conventional methods are used to reconstruct the VQA cost function landscape, then measurement precision is improved, but device complexity and memory requirements increase

Engineering Contradiction:

Improvecost function landscape reconstruction accuracyVSAvoidquantum resource requirements

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent segments the high-dimensional cost function landscape into multiple low-dimensional slices or projections. Instead of reconstructing the entire high-dimensional landscape directly, the method divides it into manageable lower-dimensional subspaces that can be reconstructed individually with fewer quantum samples, then combines these segments to form the complete landscape reconstruction.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent transforms the high-dimensional reconstruction problem into a series of low-dimensional problems by projecting the cost function onto lower-dimensional subspaces. This dimensionality reduction allows the use of fewer quantum samples while still capturing the essential features of the cost function landscape through techniques like random projections or slicing methods.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

3Adaptability or versatility

If the number of parameters in the quantum circuit increases, then adaptability and problem-solving capability are improved, but the curse of dimensionality causes exponential increase in computational cost

Engineering Contradiction:

Improvequantum circuit parameter flexibilityVSAvoidlandscape reconstruction efficiency

Core Design Contradiction:

Adaptability or versatilityVSProductivity

Solution Approach 1:

The patent transforms the high-dimensional reconstruction problem into a series of low-dimensional problems by projecting the cost function onto lower-dimensional subspaces. This dimensionality reduction allows the use of fewer quantum samples while still capturing the essential features of the cost function landscape through techniques like random projections or slicing methods.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Solution Approach 2:

The patent changes the parameter representation by working with projections or slices of the original parameters rather than the full parameter set. This allows the method to handle high-dimensional parameter spaces efficiently by transforming the problem into lower-dimensional parameter spaces that require fewer quantum evaluations.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS20250165825A1Systems and methods for tensor-based variational quantum algorithm cost function landscape generation

Publication Date: 2025.05.22 JPMORGAN CHASE BANK NA

AI summary

In some aspects, the techniques described herein relate to a method including: receiving a cost function, where the cost function is a function of parameters of a quantum circuit; discretizing the cost function to determine a number of dimensions and a number of elements in each dimension; formulating a landscape tensor, wherein the landscape tensor is formulated based on, and includes, the number of dimensions and the number of elements in each dimension; randomly sampling values of the parameters of the quantum circuit; executing the quantum circuit with the values of the parameters, wherein executing the quantum circuit generates values of the cost function; inserting the values of the cost function as values of corresponding elements in the number of elements included in the landscape tensor; and solving a low-rank tensor completion problem to estimate the values of empty elements in the landscape tensor.