Variational Quantum Simulation of General Processes

Physical Review Letters
Suguru EndoXiao Yuan

Abstract

Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks-generalized time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalized time evolution provides a unified framework for variational quantum simulation. In particular, we show its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalized time evolution. Meanwhile, assuming a tensor product structure of the matrices, we also propose another variational approach for these two tasks by combining variational real and imaginary time evolution. Finally, we introduce variational quantum simulation for open system dynamics. We variationally implement the stochastic Schrödinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a 6-qubit 2D transverse field Ising model under dissipation.

References

Aug 23, 1996·Science·S Lloyd
Apr 12, 1993·Physical Review Letters·H J Carmichael
Jul 15, 1996·Physical Review Letters·N Hatano, D R Nelson
Mar 16, 2007·Physical Review Letters·Carl M BenderBernhard K Meister
Nov 13, 2009·Physical Review Letters·Aram W HarrowSeth Lloyd
Dec 21, 2010·Annual Review of Physical Chemistry·Ivan KassalAlán Aspuru-Guzik
Sep 10, 2011·Physical Review Letters·Jutho HaegemanFrank Verstraete
Feb 14, 2012·Physical Review Letters·Tony E LeeM C Cross
Jun 2, 2012·Physical Chemistry Chemical Physics : PCCP·Dawei LuJiangfeng Du
Jul 9, 2013·Physical Review Letters·B D CladerC R Sprouse
Jul 24, 2014·Nature Communications·Alberto PeruzzoJeremy L O'Brien
Oct 11, 2014·Physical Review Letters·Patrick RebentrostSeth Lloyd
Mar 21, 2015·Physical Review Letters·Dominic W BerryRolando D Somma
Dec 15, 2016·Physical Review. E·Dominic C RoseJuan P Garrahan
Mar 25, 2017·Physical Review Letters·S PaesaniM G Thompson
Sep 15, 2017·Nature·Jacob BiamonteSeth Lloyd
Dec 9, 2017·Physical Review Letters·Kristan TemmeJay M Gambetta
Feb 2, 2018·Science Advances·Raffaele SantagatiMark G Thompson
Feb 27, 2018·Physical Review Letters·Leonard WossnigAnupam Prakash
Mar 2, 2019·Physical Review Letters·Yiğit SubaşıDavide Orsucci
May 31, 2019·Physical Review Letters·Sam McArdleSimon Benjamin

❮ Previous
Next ❯

Citations

May 29, 2021·Physical Review Letters·Zoë HolmesAndrew T Sornborger
Oct 15, 2021·Journal of Chemical Theory and Computation·Chee-Kong LeeLiang Shi

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.