Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
arXiv:2401.04672 · doi:10.1103/PhysRevLett.133.030801
Abstract
The inherent irreversibility of quantum dynamics for open systems poses a significant barrier to the inversion of unknown quantum processes. To tackle this challenge, we propose the framework of virtual combs that exploit the unknown process iteratively with additional classical post-processing to simulate the process inverse. Notably, we demonstrate that an -slot virtual comb can exactly reverse a depolarizing channel with one unknown noise parameter out of potential candidates, and a 1-slot virtual comb can exactly reverse an arbitrary pair of quantum channels. We further explore the approximate inversion of an unknown channel within a given channel set. A worst-case error decay of is unveiled for depolarizing channels within a specified noise region. Moreover, we show that virtual combs can universally reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead.
5 + 14 pages, 3 figures
References in corpus (27)
- Error mitigation for short-depth quantum circuits
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Quantum Error Mitigation
- Practical Quantum Error Mitigation for Near-Future Applications
- From Classical to Quantum Shannon Theory
- Quantum Circuits Architecture
- Transforming quantum operations: quantum supermaps
- Quantum channels and memory effects
- Optimal quantum learning of a unitary transformation
- A randomized quantum algorithm for statistical phase estimation
- Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations
- Optimal resource cost for error mitigation
- Optimal quantum networks and one-shot entropies
- Optimal probabilistic storage and retrieval of unitary channels
- Probabilistic exact universal quantum circuits for transforming unitary operations
- Generating random quantum channels
- Physical Implementability of Linear Maps and Its Application in Error Mitigation
- Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
- Quantum Phase Processing and its Applications in Estimating Phase and Entropies
- Resetting uncontrolled quantum systems
- Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly
- Optimal single shot strategies for discrimination of quantum measurements
- Virtual quantum resource distillation
- Demonstration of universal time-reversal for quantum processes
- A universal quantum rewinding protocol with an arbitrarily high probability of success
- Translating Uncontrolled Systems in Time
- Higher-order quantum transformations of Hamiltonian dynamics