Power of quantum measurement in simulating unphysical operations
arXiv:2309.09963 · doi:10.1103/PhysRevResearch.7.013334
Abstract
The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations according to classically determined probability distributions. In this work, we show that using quantum measurement instead leads to lower simulation costs for general Hermitian-preserving maps. Remarkably, we establish the equality between the simulation cost and the well-known diamond norm, thus closing a previously known gap and assigning diamond norm a universal operational meaning for all Hermitian-preserving maps. We demonstrate our method in two applications closely related to error mitigation and quantum machine learning, where it exhibits a favorable scaling. These findings highlight the power of quantum measurement in simulating unphysical operations, in which quantum interference is believed to play a vital role. Our work paves the way for more efficient sampling techniques and has the potential to be extended to more quantum information processing scenarios.
11 pages, 4 figures
References in corpus (38)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Separability Criterion for Density Matrices
- Separability of Mixed States: Necessary and Sufficient Conditions
- Entanglement detection
- Quantum computational advantage using photons
- Quantum Convolutional Neural Networks
- Error mitigation for short-depth quantum circuits
- Quantum Resource Theories
- Strong quantum computational advantage using a superconducting quantum processor
- Distance measures to compare real and ideal quantum processes
- Robustness of entanglement
- Robustness of coherence: An operational and observable measure of quantum coherence
- Practical Quantum Error Mitigation for Near-Future Applications
- A random compiler for fast Hamiltonian simulation
- Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
- Direct detection of quantum entanglement
- Quantum Sampling Problems, BosonSampling and Quantum Supremacy
- How robust is a quantum gate in the presence of noise?
- Genralized Robustness of Entanglement
- Computational advantage of quantum random sampling
- Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
- Noise robustness of the nonlocality of entangled quantum states
- Circuit knitting with classical communication
- Constructing a virtual two-qubit gate by sampling single-qubit operations
- Robustness of Measurement, discrimination games and accessible information
- Quasiprobability decompositions with reduced sampling overhead
- Optimal resource cost for error mitigation
- Overhead for simulating a non-local channel with local channels by quasiprobability sampling
- Physical Implementability of Linear Maps and Its Application in Error Mitigation
- Detecting and quantifying entanglement on near-term quantum devices
- Randomizing multi-product formulas for Hamiltonian simulation
- Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
- Virtual quantum resource distillation
- Entanglement activation and the robustness of quantum correlations
- Importance sampling for stochastic quantum simulations
- Noise effects on purity and quantum entanglement in terms of physical implementability
- Single Qubit Error Mitigation by Simulating Non-Markovian Dynamics
- Information recoverability of noisy quantum states