Pith. sign in

REVIEW 3 cited by

Quantum Algorithm for Fidelity Estimation

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2103.09076 v2 pith:RH6U4UUC submitted 2021-03-16 quant-ph

Qisheng Wang , Zhicheng Zhang , Kean Chen , Ji Guan , Wang Fang , Junyi Liu , Mingsheng Ying This is my paper · ORCID
classification quant-ph
keywords quantumalgorithmsigmacomputingfidelityproblemtimevarepsilon
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

For two unknown mixed quantum states $\rho$ and $\sigma$ in an $N$-dimensional Hilbert space, computing their fidelity $F(\rho,\sigma)$ is a basic problem with many important applications in quantum computing and quantum information, for example verification and characterization of the outputs of a quantum computer, and design and analysis of quantum algorithms. In this paper, we propose a quantum algorithm that solves this problem in $\operatorname{poly}(\log (N), r, 1/\varepsilon)$ time, where $r$ is the lower rank of $\rho$ and $\sigma$, and $\varepsilon$ is the desired precision, provided that the purifications of $\rho$ and $\sigma$ are prepared by quantum oracles. This algorithm exhibits an exponential speedup over the best known algorithm (based on quantum state tomography) which has time complexity polynomial in $N$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On estimating operator norm distance, with optimal trace distance estimation when one state is pure

    quant-ph 2026-07 accept novelty 7.0 of 10

    Rank-independent quantum estimators achieve Θ(1/ε) queries for operator-norm (and trace) distance when one state is pure, and Õ(1/ε^{3/2}) queries for general states, proving BQP-completeness.

  2. Optimal fidelity estimation when one state is pure via algorithmic Uhlmann transform

    quant-ph 2026-08 accept novelty 6.0 of 10

    When at least one of two quantum states is pure, the Uhlmann fidelity can be estimated with Θ(1/ε) queries and Θ(1/ε²) samples without knowing which state is pure, matching the optimal lower bounds.

  3. Quantum similarity learning for anomaly detection

    hep-ph 2024-11 conditional novelty 5.0 of 10

    A hybrid Transformer-quantum circuit similarity-learning network reaches AUC 96.1% on simulated di-Higgs anomaly detection, slightly above a classical baseline, with clustering mitigating shot noise.

Pith tools