One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons

Abstract

In this work, we derive analytic formulae that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows our formulae are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any mixed state of the ion crystal's motion that is diagonal in the Fock state basis. Our treatment of static motional frequency shifts, trap anharmonicities, heating, and motional dephasing apply to both laser-based and laser-free gates, while our treatment of field imhomogenieties applies to laser-free systems.

References in corpus (9)

• Quantum computing with trapped ions
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Trapped-ion quantum logic gates based on oscillating magnetic fields
• High-fidelity laser-free universal control of two trapped ion qubits
• High-fidelity trapped-ion quantum logic using near-field microwaves
• Robust and resource-efficient microwave near-field entangling ${}^9$Be${}^{+}$ gate
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• Spin readout of trapped electron qubits
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• Fast multi-qubit global-entangling gates without individual addressing of trapped ions
• Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations
• Individual addressing of trapped ion qubits with geometric phase gates
• Quantum parameter estimation of nonlinear coupling in trilinear Hamiltonian with trapped ions
• Bespoke Pulse Design for Robust Rapid Two-Qubit Gates with Trapped Ions
• Modelling noise in global Molmer-Sorensen interactions applied to quantum approximate optimization
• Fano Resonance in Excitation Spectroscopy and Cooling of an Optically Trapped Single Atom
• Generalized phase estimation in noisy quantum gates
• Engineering artificial atomic systems of giant electric dipole moment
• Strong coherent ion-electron coupling using a wire data bus