One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons
Abstract
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.
- Authors:
-
[1];
[2];
[3];
- Univ. of Texas, San Antonio, TX (United States)
- Univ. of California, Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States). Challenge Institute for Quantum Computation
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- 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)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)
- OSTI Identifier:
- 1870069
- Report Number(s):
- LLNL-JRNL-828517
Journal ID: ISSN 2469-9926; 1043993; TRN: US2306490
- Grant/Contract Number:
- AC52-07NA27344; FA9550-20-1-016; OMA-2016245
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 2; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; Atomic & molecular processes in external fields; Coherent control; Light-matter interaction; Quantum benchmarking; Quantum computation; Quantum correlations in quantum information; Quantum entanglement; Quantum gates; Quantum information architectures & platforms; Quantum optics; Quantum protocols; Atomic systems; Trapped ions; Cooling & trapping; First-principles calculations; Jaynes-Cummings model; Perturbative methods; Quantum theory; Rotating wave approximation; Schroedinger equation; Two-level models
Citation Formats
Sutherland, R. Tyler, Yu, Qian, Beck, Kristin M., and Häffner, Hartmut. One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons. United States: N. p., 2022.
Web. doi:10.1103/physreva.105.022437.
Sutherland, R. Tyler, Yu, Qian, Beck, Kristin M., & Häffner, Hartmut. One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons. United States. https://doi.org/10.1103/physreva.105.022437
Sutherland, R. Tyler, Yu, Qian, Beck, Kristin M., and Häffner, Hartmut. Wed .
"One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons". United States. https://doi.org/10.1103/physreva.105.022437. https://www.osti.gov/servlets/purl/1870069.
@article{osti_1870069,
title = {One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons},
author = {Sutherland, R. Tyler and Yu, Qian and Beck, Kristin M. and Häffner, Hartmut},
abstractNote = {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.},
doi = {10.1103/physreva.105.022437},
journal = {Physical Review A},
number = 2,
volume = 105,
place = {United States},
year = {Wed Feb 23 00:00:00 EST 2022},
month = {Wed Feb 23 00:00:00 EST 2022}
}
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