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 multibody 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 very stable qubit space during the operation. We show that ${C}_{N}$-not gates can reach the same level of fidelity at a given gate time for $N\ensuremath{\le}5$ under a suitable choice of parameters, and the gate tolerance against errors in systematic parameters can be further enhanced through optimal pulse engineering. In the case of Rydberg atoms, the proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade. Our study paves an alternative way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or with superconducting circuits. It contributes to current efforts to develop scalable quantum computation with trapped atoms and fabricable superconducting devices.
Highlights
And efficiently implementing quantum gates among multiple qubits is of central task in building near-term quantum computing systems [1]
It can limit the overall fidelity of lengthy algorithms in quantum computation [41,42,43,44,45,46,47,48] and simulation [49,50,51,52], as typically the holonomic quantum computation (HQC) is implemented with concatenating multiple, universal singleand two-qubit gates
Our study paves a route to achieve optimized holonomic quantum computation with strongly interacting Rydberg atoms and superconducting circuits, and might find applications in quantum computation and simulations based on robust multiqubit gates
Summary
And efficiently implementing quantum gates among multiple qubits is of central task in building near-term quantum computing systems [1]. Efforts have been spent to combine HQC with decoherence-free subspace to protect qubits from noises [9, 18] or with error-correcting codes to eliminate qubit errors actively [35,36,37,38] With these developments, the gate errors are mainly affected by the imperfect control parameter [20, 39, 40]. Our study paves a route to achieve optimized holonomic quantum computation with strongly interacting Rydberg atoms and superconducting circuits, and might find applications in quantum computation and simulations based on robust multiqubit gates.
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