Competition of decoherence and quantum speed limits for quantum-gate fidelity in the Jaynes-Cummings model

Year: 2024

Authors: Pratapsi S.S., Buffoni L., Gherardini S.

Autors Affiliation: Univ Lisbon, Inst Super Tecn, P-1699 Lisbon, Portugal; Inst Telecomunicacoes, P-1049001 Lisbon, Portugal; Univ Florence, Dept Phys & Astron, I-50019 Sesto Fiorentino, Italy; Elettra Sincrotrone Trieste, Area Sci Pk, I-34149 Basovizza, Italy; Univ Florence, LENS, I-50019 Sesto Fiorentino, Italy; INFN, Str Costiera 11, I-34151 Trieste, Italy.

Abstract: Quantum computers are operated by external driving fields, such as lasers, microwaves, or transmission lines, that execute logical operations on multiqubit registers, leaving the system in a pure state. However, the drive and the logical system might become correlated in such a way that, after tracing out the degrees of freedom of the driving field, the output state will not be pure. Previous works have pointed out that the resulting error scales inversely with the energy of the drive, thus imposing a limit on the energy efficiency of quantum computing. In this study, focusing on the Jaynes-Cummings model, we show how the same scaling can be seen as a consequence of two competing phenomena: the entanglement-induced error, which grows with time, and a minimal time for computation imposed by quantum speed limits. This evidence is made possible by quantifying, at any time, the computation error via the spectral radius associated with the density operator of the logical qubit. Moreover, we also prove that, in order to attain a given target state at a chosen fidelity, it is energetically more efficient to perform a single driven evolution of the logical qubits rather than to split the computation in subroutines, each operated by a dedicated pulse.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 6 (2)      Pages from: 23296-1  to: 23296-12

More Information: The authors acknowledge Yasser Omar and Sebastian Deffner for the interesting discussions that led to this work. S.S.P. acknowledges the support from the la Caixa Foundation through scholarship No. LCF/BQ/DR20/11790030. S.G. acknowledges support from the PNRR MUR Project No. PE0000023-NQSTI financed by the European Union-Next Generation EU, the Royal Society funding IECR2222003, and the project QuONTENT Quantum Communications fOr NexT gEneration iNterneT Progetto Ricerca@CNR. L.B. received funding from Next Generation EU, in the context of the National Recovery and Resilience Plan, M4C2 investment 1.2, Project No. SOE0000098-ThermoQT. This resource was financed by the Next Generation EU (DD 247 19.08.2022). The views and opinions expressed are only those of the authors and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.
KeyWords: State
DOI: 10.1103/PhysRevResearch.6.023296