Error-mitigated initialization of surface codes with non-Pauli stabilizers

TL;DR

This paper improves surface code quantum error correction by using non-Pauli stabilizers and new initialization protocols, reducing resource overhead and enabling entanglement of logical qubits in different bases.

Contribution

It introduces non-Pauli stabilizers and protocols that enhance non-Clifford state initialization fidelity and enable logical qubit entanglement across bases, advancing fault-tolerant quantum computing.

Findings

Enhanced fidelity of non-Clifford state initialization

Reduced resource overhead for state distillation

Demonstrated entanglement of logical qubits in different bases

Abstract

Quantum error correction represents a significant milestone in large-scale quantum computing, with the surface code being a prominent strategy due to its high error threshold and experimental feasibility. However, it is challenging to implement non-Clifford logical gates in a fault-tolerant way with low overhead, through the conventional magic state distillation technique. Here, we enhance the performance of the conventional surface code by incorporating non-Pauli stabilizers and introduce two innovative initialization protocols. Our approach enhances the fidelity of the initialization of non-Clifford logical state by avoiding unprotected operations before the encoding process. This improved fidelity of the initialization of non-Clifford logical states reduces the necessary number of logical qubits for precise state distillation, ultimately decreasing the overall resource overhead. Furthermore, we demonstrate the ability to entangle logical qubits in non-Pauli and Pauli bases via the lattice surgery technique. This integration enables the use of Pauli-based surface codes for computation while non-Pauli codes are employed for auxiliary qubit initialization, thus compatible with the conventional wisdom of logical Clifford operation based on the Pauli-based surface code.