Virtual quantum error detection

TL;DR

The paper introduces Virtual Quantum Error Detection (VQED), a protocol that virtually detects errors in quantum computations without the need for syndrome measurements, reducing overhead and improving robustness.

Contribution

It proposes VQED, a novel, low-depth quantum error detection method that is compatible with existing error mitigation techniques and does not require syndrome measurement circuits.

Findings

VQED can be implemented with a constant depth circuit.

Results show VQED enhances robustness against certain noise models.

VQED is compatible with other error mitigation strategies.

Abstract

Quantum error correction and quantum error detection necessitate syndrome measurements to detect errors. Performing syndrome measurements for each stabilizer generator can be a significant overhead, considering the fact that the readout fidelity in the current quantum hardware is generally lower than gate fidelity. Here, by generalizing a quantum error mitigation method known as symmetry expansion, we propose a protocol called virtual quantum error detection (VQED). This method virtually allows for evaluating computation results corresponding to post-selected quantum states obtained through quantum error detection during circuit execution, without implementing syndrome measurements. Unlike conventional quantum error detection, which requires the implementation of Hadamard test circuits for each stabilizer generator, our VQED protocol can be performed with a constant depth shallow quantum circuit with an ancilla qubit, irrespective of the number of stabilizer generators. Furthermore, for some simple error models, the computation results obtained using VQED are robust against the noise that occurred during the operation of VQED, and our method is fully compatible with other error mitigation schemes, enabling further improvements in computation accuracy and facilitating high-fidelity quantum computing.