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Bulletin of the American Physical Society

Analytic optimal control theory for high-fidelity Rydberg-blockade entangling gates

Lukas Theis, Felix Motzoi, Frank K. Wilhelm, Mark E. Saffman

Published Mar 7, 2018• 0 citations
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We show that the use of shaped pulses improves the fidelity of a Rydberg-blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical derivative removal by adiabatic gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade, we generate Bell states with a fidelity of F>0.9999F>0.9999F>0.9999 in a 300 K environment for a gate time of only 50ns50\phantom{\rule{0.28em}{0ex}}\mathrm{ns}50ns, which is an order of magnitude faster than previous protocols. These results establish the potential of neutral atom qubits with Rydberg-blockade gates for scalable quantum computation.
We study the generation of two-qudit entangling quantum logic gates using two techniques in quantum optimal control.We take advantage of both continuous, Lie algebraic control and digital, Lie group control.In both cases, the key is access to a time-dependent Hamiltonian, which can generate an arbitrary unitary matrix in the group SU(d 2 ).We find efficient protocols for creating high-fidelity entangling gates.As a test of our theory, we study the case of qudits robustly encoded in nuclear spins of alkaline earth atoms and manipulated with magnetic and optical fields, with entangling interactions arising from the wellknown Rydberg blockade.We applied this in a case study based on a d = 10 dimensional qudit encoded in the I = 9/2 nuclear spin in 87 Sr, controlled through a combination of nuclear spin resonance, a tensor ac-Stark shift, and Rydberg dressing, which allows us to generate an arbitrary symmetric entangling twoqudit gate, such as CPhase.Our techniques can be used to implement qudit entangling gates for any 2 ≤ d ≤ 10 encoded in the nuclear spin.We also studied how decoherence due to the finite lifetime of the Rydberg states affects the creation of the CPhase gate and found, through numerical optimization, a fidelity of 0.9985, 0.9980, 0.9942, and 0.9800 for d = 2, d = 3, d = 5, and d = 7, respectively.This provides a powerful platform to explore the various applications of quantum information processing of qudits, including metrological enhancement with qudits, quantum simulation, universal quantum computation, and quantum error correction.