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Streaming quantum state purification

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arxiv 2309.16387 v4 pith:RN2VMJDW submitted 2023-09-28 quant-ph

Andrew M. Childs , Honghao Fu , Debbie Leung , Zhi Li , Maris Ozols , Vedang Vyas This is my paper · ORCID
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keywords quantumstateerrorparameterpurificationdimensioninitialnoisy
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Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum computation with imperfect devices, but has only been studied previously for the case of qubits. We derive an efficient purification procedure based on the swap test for qudits of any dimension, starting with any initial error parameter. Treating the initial error parameter and the dimension as constants, we show that our procedure has sample complexity asymptotically optimal in the final error parameter. Our protocol has a simple recursive structure that can be applied when the states are provided one at a time in a streaming fashion, requiring only a small quantum memory to implement.

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Cited by 3 Pith papers

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

  1. A distillation-teleportation protocol for fault-tolerant QRAM

    quant-ph 2025-05 accept novelty 8.0 of 10

    An adaptive distillation-teleportation protocol implements a fault-tolerant QRAM query with poly(n) quantum resources and 1/poly(n) device fidelity, at the cost of an exponential classical dataset update each round.

  2. Quantum Simulation of Random Unitaries from Clebsch-Gordan Transforms

    quant-ph 2025-09 accept novelty 7.0 of 10

    Clebsch-Gordan transforms give exact compressed oracles for Haar-random unitary group actions, with efficient circuits for U(d).

  3. Constructing Non-Hermitian Theories with Tunable Exceptional Points and Controlled State Purification

    quant-ph 2026-08 conditional novelty 5.0 of 10

    Momentum-space deformation of quadratic fermionic Hamiltonians is presented as a design principle for creating exceptional points and for purifying mixed states under non-Hermitian evolution.

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