Quantum Subspace Expansion for Logical Qubit Error Correction

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Solution Overview

Problem

Existing quantum error correction methods require complex syndrome measurements and additional qubits, which are cumbersome and challenging to implement, especially on noisy intermediate-scale quantum computers, limiting the exploration and optimization of quantum codes.

Innovation Solution

A post-processing technique using quantum subspace expansion to correct errors in logical qubits by measuring projective corrections with symmetry operators, eliminating the need for on-the-fly syndrome measurements and additional ancilla qubits, and allowing for the use of approximate symmetries and non-commuting operators.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If syndrome measurements are used to diagnose errors, then error detection capability is improved, but device complexity increases due to additional qubits and measurement circuits

Engineering Contradiction:
Improveerror detection capabilityVSAvoidcomplexity of syndrome measurements
Core Design Contradiction:
ReliabilityVSDevice complexity

Solution Approach 1:

The patent extracts the error detection function from the traditional syndrome measurement process and implements it through post-processing techniques. Instead of requiring additional qubits and real-time syndrome measurements, the method extracts error information from existing computational results through classical post-processing, thereby maintaining error detection capability while eliminating the need for complex measurement circuits

Inventive Principle:
Principle #2Taking out (Extraction)

Solution Approach 2:

The patent applies preliminary action by performing error correction post-processing after the quantum computation is complete. Rather than requiring real-time syndrome measurements during computation, the method prepares the quantum state with embedded error information and then applies classical post-processing to correct errors, thereby avoiding the need for complex real-time measurement infrastructure

Inventive Principle:
Principle #10Preliminary action

2Measurement precision

If additional ancilla qubits are used for syndrome measurements, then error correction accuracy is improved, but the feasibility on noisy intermediate-scale quantum computers deteriorates

Engineering Contradiction:
Improveerror correction accuracyVSAvoidfeasibility on NISQ devices
Core Design Contradiction:
Measurement precisionVSEase of manufacture

Solution Approach 1:

The patent applies self-service by enabling the quantum computational system to correct its own errors using only the qubits already involved in the computation. The method extracts error information from the computational results themselves and applies corrections through classical post-processing, thereby achieving error correction without requiring additional ancilla qubits that would be needed for traditional syndrome measurements

Inventive Principle:
Principle #25Self-service

3Reliability

If fast feedback mechanism with unitary recovery operators is applied, then error propagation is reduced, but the complexity of real-time decoding and recovery increases

Engineering Contradiction:
Improveerror propagation controlVSAvoidcomplexity of decoding and recovery
Core Design Contradiction:
ReliabilityVSDevice complexity

Solution Approach 1:

The patent replaces the mechanical system of real-time quantum operations (unitary recovery operators applied during computation) with a classical post-processing system. Instead of requiring fast feedback mechanisms that apply quantum corrections in real-time, the method uses classical algorithms to analyze computational results and apply corrections after the fact, thereby reducing the complexity of real-time decoding while maintaining error propagation control

Inventive Principle:
Principle #28Mechanics substitution (Replace mechanical system)

4Adaptability or versatility

If strict stabilizer measurements are performed, then quantum code optimization is improved, but the resource requirements and control complexity increase

Engineering Contradiction:
Improvequantum code optimizationVSAvoidresource requirements
Core Design Contradiction:
Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent applies partial action by performing error correction post-processing on a subset of computational results rather than requiring complete syndrome measurements for all qubits. The method selectively applies classical post-processing to correct errors in relevant portions of the computational output, thereby achieving quantum code optimization without the full resource requirements of strict stabilizer measurements

Inventive Principle:
Principle #16Partial or excessive action

Data Source

PatentEP4679338A1Decoding errors using quantum subspace expansion
Publication Date: 2026.01.14 GOOGLE LLC
  • EP4679338A1 patent drawingFigure 1
  • EP4679338A1 patent drawingFigure 2A~2B
  • EP4679338A1 patent drawingFigure 3A~3B

AI summary

Methods, systems and apparatus for correcting a result of a quantum computation. In one aspect, a method includes selecting a quantum error correcting code for the quantum computation, wherein the quantum error correcting code is defined by multiple stabilizer generators; determining a set of symmetry operators, comprising: selecting a subset of the stabilizer generators, determining, for each selected stabilizer generator, a sum between an identity operator and the stabilizer generator, and multiplying the determined sums together to form a summation of terms, wherein each term in the summation is equal to a respective symmetry operator; measuring a projective correction of a physical observable over an output quantum state of the quantum computation using the determined set of symmetry operators, wherein the physical observable corresponds to the result of the quantum computation; and determining a corrected result of the quantum computation using the measured projective correction of the physical observable.