A simple formula for the average gate fidelity of a quantum dynamical operation [rapid communication]

By Morten Nielsen. 2002

572 citations recorded by the source corpus.

This Letter presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al. [Phys. Lett. A 294 (2002) 258]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula due to Horodecki et al. [Phys. Rev. A 60 (1999) 1888], connecting average gate fidelity to entanglement fidelity.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7620d1f2872da4c2b09aa0090c3289291edebed2

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Geometry of Quantum States: Index (2007, unknown): “18 This trace determines the mean operation fidelity 〈F (ρψ , ρψ )〉ψ averaged over random pure states ρψ [691, 994].”
Quantum error correction below the surface code threshold (2024, unknown): “As shown in Ref.”
Quantum-assisted quantum compiling (2018, unknown): “Indeed, it can be shown [38, 39] that”
NMR techniques for quantum control and computation (2004, methodology): “Similar simple formulas can be obtained for higher dimensional systems (123).”
A Race-Track Trapped-Ion Quantum Processor (2023, unknown): “for any d-dimensional trace-preserving error [114].”
Parametrically Activated Entangling Gates Using Transmon Qubits (2017, methodology): “In using QPT to estimate the gate fidelities [37, 38] we compensated for the known readout infidelities [32, 39] and applied complete-positivity (CP) constraints.”
Fast universal control of an oscillator with weak dispersive coupling to a qubit (2021, methodology): “To quantify the quality of the optimized logical gates, we numerically calculate their average fidelity [90], defined as”
Quantum channels and memory effects (2012, background): “(51) it follows that Fe(1 /d,Φ) = 1 d2 ∑ j |Tr(Kj)|2 , (54) which can be put in correspondence with the average fidelity (49) through the identity (Horodecki et al., 1999; Nielsen, 2002) F̄ (Φ) = dFe(1 /d; Φ) + 1 d+ 1 .”
Performance and structure of single-mode bosonic codes (2017, unknown): “[135]), ∫ dψ〈ψ |E(|ψ〉〈ψ |)|ψ〉 = dFE + 1 d + 1 , (A1)”
Goal-Directed Planning via Hindsight Experience Replay (2022, methodology): “We exploited average gate fidelity (AGF) (Nielsen, 2002) as a metric to evaluate the distance between the target gate U and the current sequence of gates U n .”
A Survey on Quantum Channel Capacities (2018, background): “Nielsen in 2002 [396] defined a connection between the different fidelity measures.”
Midcircuit Operations Using the omg Architecture in Neutral Atom Arrays (2023, background): “These process fidelities can be converted to average state fidelities as Fav = (dFp + 1)/(d + 1) [103, 106].”