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

Journal Article · Wed Feb 23 00:00:00 UTC 2022 · Physical Review A

DOI: https://doi.org/10.1103/physreva.105.022437 · OSTI ID:1870069

Sutherland, R. Tyler  ^[1]; Yu, Qian  ^[2]; Beck, Kristin M.  ^[3]; Häffner, Hartmut ^[4]

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1. Univ. of Texas, San Antonio, TX (United States)
2. Univ. of California, Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States). Challenge Institute for Quantum Computation
3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
4. Univ. of California, Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States). Challenge Institute for Quantum Computation; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

In this work, we derive analytic formulas 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 that our formulas 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 inhomogeneities applies to laser-free systems.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1870069
• Report Number(s): LLNL-JRNL-828517; 1043993
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 2 Vol. 105; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English