  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.
