Quantum Subspace Expansion for Logical Qubit Error Decoding
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Solution Overview
Problem
Existing quantum computing technologies face challenges in accurately mitigating errors without complex syndrome measurements and additional qubits, particularly in near-term devices, limiting the exploration and optimization of quantum codes under realistic noise conditions.
Innovation Solution
A post-processing technique using quantum subspace expansion (QSE) for decoding errors on logical qubits, which employs projectors from quantum error correcting codes to correct observables without requiring strict stabilizer measurements or feed-forward mechanisms, allowing for the study and optimization of quantum codes on real devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If syndrome measurements and fast feedback mechanisms are used for error correction, then error mitigation accuracy is improved, but device complexity and resource requirements increase
Solution Approach 1:
The patent extracts the error correction functionality from the real-time measurement and feedback loop, moving it to a post-processing stage. The quantum state is measured once, and error correction is applied computationally afterward, eliminating the need for complex syndrome measurements and feed-forward mechanisms during quantum computation.
Solution Approach 2:
The patent performs preliminary error correction by storing the measured quantum state and applying correction operations in advance before final readout. This allows error mitigation to be performed systematically using classical computation on the measured data, rather than requiring real-time feedback during the quantum process.
2Reliability
If additional qubits are used for syndrome measurements, then error detection capability is improved, but the number of qubits and control requirements increase
Solution Approach 1:
The patent removes the requirement for additional ancilla qubits by extracting the error syndrome information from dedicated measurement qubits and obtaining it through standard quantum state measurement. The error correction is then performed computationally rather than through additional quantum hardware.
Solution Approach 2:
The patent creates a classical copy of the quantum measurement outcomes and performs error correction operations on this classical data. This allows the error detection and correction functionality to be implemented through classical computation rather than requiring additional quantum resources.
3Ease of manufacture
If geometrically local codes are used, then implementation feasibility is improved, but code performance and error correction capability are limited
Solution Approach 1:
The patent inverts the traditional approach by not restricting code selection to geometrically local codes. Instead, it allows any quantum error correcting code to be used, and the post-processing framework adapts to the specific code structure. This enables the use of high-performance codes like surface codes and LDPC codes that may not be geometrically local but offer superior error correction capabilities.
Solution Approach 2:
The patent changes the parameter of code locality from a strict requirement to a flexible property. By using post-processing, the system can accommodate codes with various geometric properties, allowing optimization of code parameters like distance, rate, and locality based on the specific quantum hardware and error characteristics.
Data Source
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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.