Algorithmic quantum simulation of memory effects

Alvarez-Rodriguez, Unai; Candia, Roberto Di; Casanova, Jorge; Sanz, Mikel; Solano, E.

doi:10.1103/physreva.95.020301

Cited by 9 publications

(8 citation statements)

References 43 publications

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“…In this way, it is possible to simulate several linear integro-differential equations coming from quantum models. An example of this is a Volterra equation describing non-Markovian quantum memory effects 35 , given by…”

Section: Memristive Analog Computationmentioning

confidence: 99%

Analog simulator of integro-differential equations with classical memristors

Barrios

Retamal

Solano

2019

Sci Rep

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An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales.

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Section: Memristive Analog Computationmentioning

confidence: 99%

Analog simulator of integro-differential equations with classical memristors

Barrios

Retamal

Solano

2019

Sci Rep

Self Cite

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“…Optimal strategies of computation for quantum chemistry merge quantum simulation and classical numerical techniques. These methods, that we name as algorithmic quantum simulation 45 , allow us to employ quantum simulators for the computationally hard tasks, such as time evolution, on top of the classical algorithm, which provides flexibility for computing relevant observables. In the context of quantum chemistry, we have the example of ground state finding via a variational eigensolver 11 14 46 47 48 .…”

Section: Resultsmentioning

confidence: 99%

Quantum chemistry and charge transport in biomolecules with superconducting circuits

García-Álvarez

Heras

Mezzacapo

et al. 2016

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We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated quantum algorithms to allow the study of environmental effects.

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“…Although decoherence has been described 1 , 2 , measured 3 , 4 , simulated 5 – 7 and used for different quantum tasks 8 – 10 , it is often considered as one of the main setbacks of experimental setups based on quantum mechanics. This is evident in quantum computing, quantum simulations and quantum communication, which has triggered a race to find decoherence-resistant states and protocols, starting in the mid 1990s.…”

Section: Introductionmentioning

confidence: 99%