2022/04/23 by Guerrero, Nicolas J., Weeks, David E.
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2204.11114
In this paper, we describe and experimentally demonstrate an error detection scheme that does not employ ancilla qubits or mid-circuit measurements. This is achieved by expanding the Hilbert space where a single logical qubit is encoded using several physical qubits. For example, one possible two qubit encoding identifies |0⟩L=|01⟩ and |1⟩L=|10⟩. If during the final measurement a |11⟩ or |00⟩ is observed an error is declared and the run is not included in subsequent analysis. We provide codewords for a simple bit-flip encoding, a way to encode the states, a way to implement logical U3 and logical Cx gates, and a description of which errors can be detected. We then run Greenberger-Horne-Zeilinger circuits on the transmon based IBM quantum computers, with an input space of N∈\2,3,4,5\ logical qubits and Q∈\1,2,3,4,5\ physical qubits per logical qubit. The results are compared relative to Q=1 with and without error detection and we find a significant improvement for Q∈\2,3,4\.