Systematic error tolerant multiqubit holonomic entangling gates

TL;DR

This paper proposes a method for implementing high-fidelity, error-tolerant multiqubit holonomic gates using Rydberg atoms or superconducting circuits, enhancing robustness for scalable quantum computing.

Contribution

It introduces a systematic error-tolerant protocol for multiqubit holonomic gates that remains stable against laser fluctuations and motional dephasing, differing from traditional Rydberg schemes.

Findings

Achieves high-fidelity controlled gates for N≤5 qubits.

Demonstrates robustness against systematic errors.

Shows potential for scalable quantum computation.

Abstract

Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic $(N+1)$-qubit controlled gates using Rydberg atoms confined in optical arrays or superconducting circuits. We identify the scheme, deduce the effective multi-body Hamiltonian, and determine the working condition of the multiqubit gate. Uniquely, the multiqubit gate is immune to systematic errors, i.e., laser parameter fluctuations and motional dephasing, as the $N$ control atoms largely remain in the much stable qubit space during the operation. We show that $C_N$-NOT gates can reach same level of fidelity at a given gate time for $N\leq5$ under a suitable choice of parameters, and the gate tolerance against errors in systematic parameters can be further enhanced through optimal pulse engineering. In case of Rydberg atoms, the proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade. Our study paves a new route to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or with superconducting circuits. It contributes to current efforts in developing scalable quantum computation with trapped atoms and fabricable superconducting devices.