Arrow of time and its reversal on the IBM quantum computer

Lesovik, G. B.; Sadovskyy, Ivan; Suslov, M. V.; Лебедев, А. В.; Vinokur, V. M.

doi:10.1038/s41598-019-40765-6

Cited by 45 publications

(47 citation statements)

References 35 publications

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“…Quantum processors must maintain coherence between several entangled quantum-bits (qubits) for long durations in order to employ complex quantum algorithms without error accumulation through decoherence or noise. Recently, publicly accessible quantum processors were made available online as part of the IBM-Q project, and these can be used for novel research into quantum processing 30 . Although the technology remains imperfect, with error rates per gate operation of O(0.1%) and per qubit read of O(5%) prohibiting very lengthy calculations, the platform provides a test bed for exploring quantum solutions to computational problems, and finding ways to re-express calculations in the language of quantum circuits.…”

mentioning

confidence: 99%

Neutrino oscillations in a quantum processor

Argüelles

Jones

2019

Phys. Rev. Research

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Quantum computing technologies promise to revolutionize calculations in many areas of physics, chemistry, and data science. Their power is expected to be especially pronounced for problems where direct analogs of a quantum system under study can be encoded coherently within a quantum computer. A first step toward harnessing this power is to express the building blocks of known physical systems within the language of quantum gates and circuits. In this paper, we present a quantum calculation of an archetypal quantum system: neutrino oscillations. We define gate arrangements that implement the neutral lepton mixing operation and neutrino time evolution in two-, three-, and four-flavor systems. We then calculate oscillation probabilities by coherently preparing quantum states within the processor, time evolving them unitarily, and performing measurements in the flavor basis, with close analogy to the physical processes realized in neutrino oscillation experiments, finding excellent agreement with classical calculations. We provide recipes for modeling oscillation in the standard three-flavor paradigm as well as beyond-standard-model scenarios, including systems with sterile neutrinos, non-standard interactions, Lorentz symmetry violation, and anomalous decoherence.

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mentioning

confidence: 99%

Neutrino oscillations in a quantum processor

Argüelles

Jones

2019

Phys. Rev. Research

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“…While certain terms such as field or on-site terms can be inverted efficiently in the current experiments, the inversion of off-site couplings or tunneling terms still remain challenging [32,33]. To highlight this non-triviality, we note that only recently was such inversion realised even in a simplified model [34]. In the next section we focus on describing how ARB would operate on an analogue device, where our analysis involves classically simulating the process, including modelling and implementing the error channels.…”

Section: Systematically Inverting Unitariesmentioning

confidence: 92%

“…If the errors behave like a depolarising channel due only to averaging with this kind of simple noise model then we can not trust the ARB protocol in a regime where we have more complex noise (though still adhering to noise assumptions). For the average error-rate we obtained (with 95% confidence bounds): r l = 0.003264 (0.003321, 0.003380) (33) r g = 0.003350 (0.003227, 0.003301) , (34) for locally (r l ) and globally (r g ) disordered unitaries, respectively. Where, from Lem.…”

Section: A Xy Hamiltonian With Transverse Field (Nearest-neighbours)mentioning

confidence: 96%

Randomized benchmarking in the analogue setting

Derbyshire

Malo

Daley

et al. 2020

Quantum Sci. Technol.

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Current development in programmable analogue quantum simulators (AQS), whose physical implementation can be realised in the near-term compared to those of large-scale digital quantum computers, highlights the need for robust testing techniques in analogue platforms. Methods to properly certify or benchmark AQS should be efficiently scalable, and also provide a way to deal with errors from state preparation and measurement (SPAM). Up to now, attempts to address this combination of requirements have generally relied on model-specific properties. We put forward a new approach, applying a well-known digital noise characterisation technique called randomized benchmarking (RB) to the analogue setting. RB is a scalable experimental technique that provides a measure of the average errorrate of a gate-set on a quantum hardware, incorporating SPAM errors. We present the original form of digital RB, the necessary alterations to translate it to the analogue setting and introduce the analogue randomized benchmarking protocol (ARB). In ARB we measure the average error-rate per time evolution of a family of Hamiltonians and we illustrate this protocol with two case-studies of simple analogue models; classically simulating the system by incorporating physically motivated noise. We find that for both case-studies the data fit with the theoretical model and we gain values for the average error rate for differing unitary sets. We compare our protocol with digital RB, where both advantages (more realistic assumptions on noise) and disadvantages (difficulty in reversing the time-evolution) are discussed.

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“…No information about the quantum state is being lost. Equation (18) can be inverted so we could use the state |ψ(t) at any time t to reconstruct precisely the initial state |ψ(0) . The con-stant purity of the state is precisely reflected in the unchanging value of the von Neumann entropy S vN .…”

Section: B Unitary Free Expansionmentioning

confidence: 99%

“…We now use this state as an initial state, |ψ(0) = |ψ 0 and solve (18) forward in time. The resultant S x (t) is shown in Figure 9.…”

Section: Second Law Of Thermodynamicsmentioning

confidence: 99%

Quantum operator entropies under unitary evolution

Lent

2019

Phys. Rev. E

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For a quantum state undergoing unitary Schrödinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum operator entropy, which is the Shannon entropy of the probability distribution for the eigenvalues of a Hermitian operator. These entropies characterize the missing information about a particular observable inherent in the quantum state itself. The von Neumann entropy is the quantum operator entropy for the case when the operator is the density matrix. We examine pure state unitary evolution in a simple model system comprised of a set of highly-interconnected topologically disordered states and a time-independent Hamiltonian. An initially confined state is subject to free expansion into available states. The time development is completely reversible with no loss of quantum information and no course graining is applied. The positional entropy increases in time in a way that is consistent with both the classical statistical mechanical entropy and the second law. arXiv:1901.08956v4 [quant-ph]

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Arrow of time and its reversal on the IBM quantum computer

Cited by 45 publications

References 35 publications

Neutrino oscillations in a quantum processor

Neutrino oscillations in a quantum processor

Randomized benchmarking in the analogue setting

Quantum operator entropies under unitary evolution

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