Global Estimates of Errors in Quantum Computation by the Feynman–Vernon Formalism

Aurell, Erik

doi:10.1007/s10955-018-2037-6

Cited by 5 publications

(2 citation statements)

References 61 publications

(149 reference statements)

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“…The main used tool is the Feynman-Vernon influence functional [30], which allows to capture an influence of the environment on the studied system. This approach proved useful both from practical [31][32][33] as well as fundamental point of view [34][35][36], and still provides insights into problems encountered in fields such as open systems [37], quantum thermodynamics [38][39][40][41][42][43][44] or quantum computing [45]. As we show here it encapsulates decoherence of OTOCs in therms of the microscopic parameters of the considered model, allows to gain better insight into differences between the two considered backward time evolution schemes as well as has useful applications e.g.…”

Section: Introductionmentioning

confidence: 81%

Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach

Tuziemski

2019

Phys. Rev. A

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Recent theoretical and experimental studies have shown significance of quantum information scrambling (i.e. a spread of quantum information over a system degrees of freedom) for problems encountered in high-energy physics, quantum information, and condensed matter. Due to complexity of quantum many-body systems it is plausible that new developments in this field will be achieved by experimental explorations. Since noise effects are inevitably present in experimental implementations, a better theoretical understanding of quantum information scrambling in systems affected by noise is needed. To address this problem we study indicators of quantum scramblingout-of-time-ordered correlation functions (OTOCs) in open quantum systems. As most experimental protocols for measuring OTOCs are based on backward time evolution we consider two possible scenarios of joint system-environment dynamics reversal: In the first one the evolution of the environment is reversed, whereas in the second it is not. We derive general formulas for OTOCs in those cases as well as study in detail the model of a spin chain coupled to the environment of harmonic oscillators. In the latter case we derive expressions for open systems OTOCs in terms of Feynman-Vernon influence functional. Subsequently, assuming that dephasing dominates over dissipation, we provide bounds on open system OTOCs and illustrate them for a spectral density known from the spin-boson problem. In addition to being significant for quantum information scrambling, our results also advance understating of decoherence in processes involving backward time evolution.

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Section: Introductionmentioning

confidence: 81%

Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach

Tuziemski

2019

Phys. Rev. A

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“…Stepping first back a bit, the calculation of G if (ν) proceeds by representing U and U † as path integrals. Path integrals for spins are known in general [33], and have recently been used by one of us to estimate the errors in quantum computing [34]. For the problem at hand a much simpler representation is however sufficient, where the spin paths X and Y representing U and U † are piecewise constant, taking values ± 1 2 [20].…”

Section: Thermal Power At Strong Couplingmentioning

confidence: 99%

Thermal power of heat flow through a qubit

Aurell¹,

Montana

2019

Phys. Rev. E

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In this paper we consider thermal power of a heat flow through a qubit between two baths. The baths are modeled as set of harmonic oscillators initially at equilibrium, at two temperatures. Heat is defined as the change of energy of the cold bath, and thermal power is defined as expected heat per unit time, in the long-time limit. The qubit and the baths interact as in the spin-boson model, i.e. through qubit operator σz. We compute thermal power in an approximation analogous to "noninteracting blip" (NIBA) and express it in the polaron picture as products of correlation functions of the two baths, and a time derivative of a correlation function of the cold bath. In the limit of weak interaction we recover known results in terms of a sum of correlation functions of the two baths, a correlation functions of the cold bath only, and the energy split.

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Not-quite-free shortcuts to adiabaticity

Calzetta

2018

Phys. Rev. A

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Given the increasing use of shotcuts to adiabaticity (STA) to optimize power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from the adiabatic path. This not only induces transitions to unwanted final states but also changes the system energy, so that using the STA has a definite cost in terms of conventional work definitions. This may be the ultimate cost of an adiabatic shortcut, in the sense that it is present even for a frictionless, zero temperature driving. We estimate the effect, to lowest nontrivial order in the derivatives of the time-dependent frequency, on a parametric harmonic oscillator, thus providing a consistency condition for the validity of the classical approximation. * calzetta@df.uba.ar arXiv:1807.00926v2 [quant-ph]

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Global Estimates of Errors in Quantum Computation by the Feynman–Vernon Formalism

Cited by 5 publications

References 61 publications

Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach

Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach

Thermal power of heat flow through a qubit

Not-quite-free shortcuts to adiabaticity

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