Quantum Error Detection Without Using Ancilla Qubits
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 $|0\rangle_L=|01\rangle$ and $|1\rangle_L=|10\rangle$. If during the
final measurement a $|11\rangle$ or $|00\rangle$ 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 $U_3$ and logical $C_x$ 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 $N\in\{2,3,4,5\}$
logical qubits and $Q\in\{1,2,3,4,5\}$ 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 $Q\in\{2,3,4\}$.
Nicolas J. Guerrero David E. Weeks