Quantum Error Detection Without Using Ancilla Qubits

TL;DR

This paper introduces and experimentally demonstrates a quantum error detection method that encodes logical qubits in multiple physical qubits without using ancilla qubits or mid-circuit measurements, improving error detection capabilities.

Contribution

The authors present a novel error detection scheme that expands the Hilbert space for encoding logical qubits, avoiding ancilla qubits and mid-circuit measurements, with experimental validation on IBM quantum computers.

Findings

Significant error detection improvement for 2-4 physical qubits per logical qubit.

Effective implementation of logical gates within the expanded Hilbert space.

Experimental validation on transmon-based IBM quantum hardware.

Abstract

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 $Q\in\{2,3,4\}$.