Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
arXiv:2306.10758 · doi:10.1103/PhysRevA.109.012219
Abstract
The problem of simulatability of quantum processes using classical resources plays a cornerstone role for quantum computing. Quantum circuits can be simulated classically, e.g., using Monte Carlo sampling techniques applied to quasiprobability representations of circuits' basic elements, i.e., states, gates, and measurements. The effectiveness of the simulation is determined by the amount of the negativity in the representation of these basic elements. Here we develop an approach for minimizing the total negativity of a given quantum circuit with respect to quasiprobability representations, that are overcomplete, i.e., are such that the dimensionality of corresponding quasistochastic vectors and matrices is larger than the squared dimension of quantum states. Our approach includes both optimization over equivalent quasistochastic vectors and matrices, which appear due to the overcompleteness, and optimization over overcomplete frames. We demonstrate the performance of the developed approach on some illustrative cases, and show its significant advantage compared to the standard overcomplete quasistochastic representations. We also study the negativity minimization of noisy brick-wall random circuits via a combination of increasing frame dimension and applying gate merging technique. We demonstrate that the former approach appears to be more efficient in the case of a strong decoherence.
arXiv comment15 pages, 8 figures
References in corpus (43)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Quantum Computing in the NISQ era and beyond
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Variational Quantum Algorithms
- Quantum computational advantage using photons
- Noisy intermediate-scale quantum (NISQ) algorithms
- Improved Simulation of Stabilizer Circuits
- Strong quantum computational advantage using a superconducting quantum processor
- Symmetric Informationally Complete Quantum Measurements
- Contextuality supplies the magic for quantum computation
- The Resource Theory of Stabilizer Computation
- Random Quantum Circuits
- Application of a resource theory for magic states to fault-tolerant quantum computing
- Discrete phase space based on finite fields
- Negative Quasi-Probability as a Resource for Quantum Computation
- Non-convex Optimization for Machine Learning
- Hudson's Theorem for finite-dimensional quantum systems
- Improved classical simulation of quantum circuits dominated by Clifford gates
- Negativity and contextuality are equivalent notions of nonclassicality
- Simulation of quantum circuits by low-rank stabilizer decompositions
- Estimating outcome probabilities of quantum circuits using quasiprobabilities
- Quasi-probability representations of quantum theory with applications to quantum information science
- Wigner function negativity and contextuality in quantum computation on rebits
- Informationally complete measurements and groups representation
- Quantifying quantum speedups: improved classical simulation from tighter magic monotones
- Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
- Robustness of Magic and Symmetries of the Stabiliser Polytope
- Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
- Equivalence between contextuality and negativity of the Wigner function for qudits
- Phase space simulation method for quantum computation with magic states on qubits
- Introducing the Qplex: A Novel Arena for Quantum Theory
- Quorum of observables for universal quantum estimation
- Uniqueness of noncontextual models for stabilizer subtheories
- Quasiprobability representations of quantum mechanics with minimal negativity
- A hidden variable model for universal quantum computation with magic states on qubits
- Variational autoencoder reconstruction of complex many-body physics
- Probability representation of quantum dynamics using pseudostochastic maps
- Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics
- Discrete Wigner Functions from Informationally Complete Quantum Measurements
- Quantum Theory is a Quasi-stochastic Process Theory
- Minimal informationally complete measurements for probability representation of quantum dynamics
- Faster Born probability estimation via gate merging and frame optimisation
- The Extension of Unital Completely Positive Semigroups on Operator Systems to Semigroups on -algebras