Academic Journal
QUANTUM ALGORITHM FOR SIMULATING REAL TIME EVOLUTION OF LATTICE HAMILTONIANS.
| Τίτλος: | QUANTUM ALGORITHM FOR SIMULATING REAL TIME EVOLUTION OF LATTICE HAMILTONIANS. |
|---|---|
| Συγγραφείς: | HAAH, JEONGWAN1 jwhaah@microsoft.com, HASTINGS, MATTHEW B.1 mahastin@microsoft.com, KOTHARI, ROBIN1 robin.kothari@microsoft.com, GUANG HAO LOW1 guanghao.low@microsoft.com |
| Πηγή: | SIAM Journal on Computing. 2023, Vol. 52 Issue 6, p1-35. 35p. |
| Θεματικοί όροι: | *Algorithms, Qubits, Commutation (Electricity), Velocity, Physics |
| Περίληψη: | We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in its vicinity). This class of Hamiltonians is very general and is believed to capture fundamental interactions of physics. Our algorithm simulates the time evolution of such a Hamiltonian on n qubits for time T up to error using O (nT polylog(nT) gates with depth O (T polylog(nT). Our algorithm is the first simulation algorithm that achieves gate cost quasilinear in nT and polylogarithmic in 1. Our algorithm also readily generalizes to time-dependent Hamiltonians and yields an algorithm with similar gate count for any piecewise slowly varying time-dependent bounded local Hamiltonian. We also prove a matching lower bound on the gate count of such a simulation, showing that any quantum algorithm that can simulate a piecewise constant bounded local Hamiltonian in one dimension to constant error requires gates in the worst case. The lower bound holds even if we only require the output state to be correct on local measurements. To the best of our knowledge, this is the first nontrivial lower bound on the gate complexity of the simulation problem. Our algorithm is based on a decomposition of the time-evolution unitary into a product of small unitaries using Lieb--Robinson bounds. In the appendix, we prove a Lieb--Robinson bound tailored to Hamiltonians with small commutators between local terms, giving zero Lieb--Robinson velocity in the limit of commuting Hamiltonians. This improves the performance of our algorithm when the Hamiltonian is close to commuting. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Business Source Index |
καταχωρήστε σχόλιο πρώτοι!