Quantum Error Correction with Mixed Ancilla Qubits

TL;DR

This paper proposes a method to improve quantum error correction fidelity when ancilla qubits are initialized in mixed states, by modifying the encoding process to include error correction inverse operations, beneficial for architectures lacking projective measurement.

Contribution

It introduces a novel technique to enhance quantum error correction with mixed ancilla qubits by altering encoding operators, applicable to measurement-limited quantum architectures.

Findings

Increased fidelity with mixed ancilla qubits using the proposed method.

The method requires at most doubling the number of gates.

Applicable to architectures without projective measurement.

Abstract

Most quantum error correcting codes are predicated on the assumption that there exists a reservoir of qubits in the state $\ket{0}$, which can be used as ancilla qubits to prepare multi-qubit logical states. In this report, we examine the consequences of relaxing this assumption, and propose a method to increase the fidelity produced by a given code when the ancilla qubits are initialized in mixed states, using the same number of qubits, at most doubling the number of gates. The procedure implemented consists of altering the encoding operator to include the inverse of the unitary operation used to correct detected errors after decoding. This augmentation will be especially useful in quantum computing architectures that do not possess projective measurement, such as solid state NMRQIP.