On the simulation of quantum circuits
read the original abstract
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an explicit class of efficiently simulable circuits (log depth circuits with 2-qubit gates of limited range) to the following: let C be any poly sized quantum circuit (generally of poly depth too) on n qubits comprising 1- and 2- qubit gates and 1-qubit measurements (with 2-qubit gates acting on arbitrary pairs of qubit lines). For each qubit line j let D_j be the number of 2-qubit gates that touch or cross the line j i.e. the number of 2-qubit gates that are applied to qubits i,k with i \leq j \leq k. Let D=max_j D_j. Then the quantum process can be classically simulated in time n poly(2^D). Thus if D=O(log n) then C may be efficiently classically simulated.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Cylindrical Matter: A beyond-quantum many-body system for efficient classical simulation of quantum pure-Ising like systems
Cylindrical matter is a new beyond-quantum model that faithfully reproduces measurement statistics of some quantum pure-Ising systems with interactions decaying faster than 1/r^{3D/2}, allowing classical simulation.
-
Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements
Explicit computation of the classical simulation threshold λ for arbitrary diagonal two-qubit gates, identifying families of states with simulable phases on finite-degree graphs.
-
Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
Systematic numerical study of QAOA parameter transfer on heavy-hex Ising models with local cubic terms shows transferred angles from small instances yield improving expectation values up to 49 layers on instances up t...
-
Quantum-inspired tensor networks in machine learning models
Tensor networks developed for quantum states are reviewed as tools for machine learning models, with assessment of their potential computational, explanatory, and privacy advantages alongside remaining challenges.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.