Qudit entanglers using quantum optimal control

Abstract

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 well-known 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 two-qudit gate such as CPhase. Our techniques can be used to implement qudit entangling gates for any $2\le d\le 10$ 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.

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References in corpus (14)

• Surface codes: Towards practical large-scale quantum computation
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• Quantum State Engineering and Precision Metrology using State-Insensitive Light Traps
• Fidelity of quantum operations
• Quantum computing with alkaline earth atoms
• Cooling a single atom in an optical tweezer to its quantum ground state
• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Microwave potentials and optimal control for robust quantum gates on an atom chip
• Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas
• Robust quantum logic in neutral atoms via adiabatic Rydberg dressing
• Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
• Raman cooling imaging: Detecting single atoms near their ground state of motion
• The ${}^1{\mathrm{S}}_0$-${}^3{\mathrm{P}}_2$ magnetic quadrupole transition in neutral strontium

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• Towards Necessary and sufficient state condition for violation of a multi-settings Bell inequality
• Measurement of the g factor of ground-state 87Sr at the parts-per-million level using co-trapped ultracold atoms
• Fast nuclear-spin entangling gates compatible with large-scale atomic arrays
• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
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• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures
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• Qudit Noisy Stabilizer Formalism
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