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Bulletin of the American Physical Society

Quantum Optimal Control of Nuclear Spins in 87Sr for Quantum Logic with Qudits

Sivaprasad Omanakuttan, Anupam Mitra, Michael J. Martin, Ivan Deutsch

Published Mar 16, 2021• 0 citations
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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.
The realization of effective quantum error correction protocols remains a central challenge in the development of scalable quantum computers. Employing high-dimensional quantum systems (qudits) can offer more hardware-efficient protocols than qubit-based approaches. Using electron-nuclear double resonance, we implement a logical qubit encoded on the four states of a I=3/2 nuclear spin hyperfine-coupled to an S=1/2 electron spin qubit; the encoding protects against the dominant decoherence mechanism in such systems, i.e., fluctuations of the quantizing magnetic field. We explore the dynamics of the encoded state both under a controlled application of the fluctuation and under natural decoherence processes. Our results confirm the potential of these proposals for practical, implementable, fault-tolerant quantum memories.