Variational consistent histories as a hybrid algorithm for quantum foundations

Arrasmith, Andrew; Cincio, Łukasz; Sornborger, Andrew; Zurek, Wojciech H.; Coles, Patrick J.

doi:10.1038/s41467-019-11417-0

Cited by 78 publications

(77 citation statements)

References 51 publications

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“…were prepared on a quantum computer) it is known that their Hilbert-Schmidt distance is efficiently computable (logarithmic in matrix dimension) on a quantum computer [7,8]. Because of the latter, the Hilbert-Schmidt distance is employed as a cost function in recent variational hybrid quantum-classical algorithms [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…2. The Hilbert-Schmidt distance is often employed as a cost function in variational hybrid quantumclassical algorithms (often with the low-rank assumption already made) [9][10][11][12], since it can be efficiently computed on a quantum computer. Because of our bound, minimizing the cost in these algorithms implies that one is also minimizing a function of the trace distance.…”

Section: Introductionmentioning

confidence: 99%

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Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states

2019

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The trace distance between two quantum states, ρ and σ, is an operationally meaningful quantity in quantum information theory. However, in general it is difficult to compute, involving the diagonalization of ρ − σ. In contrast, the Hilbert-Schmidt distance can be computed without diagonalization, although it is less operationally significant. Here, we relate the trace distance and the Hilbert-Schmidt distance with a bound that is particularly strong when either ρ or σ is low rank. Our bound is stronger than the bound one could obtain via the norm equivalence of the Frobenius and trace norms. We also consider bounds that are useful not only for low-rank states but also for low-entropy states. Our results have relevance to quantum information theory, quantum algorithms design, and quantum complexity theory.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states

2019

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“…This can be accomplished by preparing superpositions of the eigenvectors of the form (|r i + |r j )/ √ 2 (by means of VQSD's eigenstate preparation circuit [23]) and computing the inner product of this superposition with σ via a Swap Test. (For example, see [24] for the precise circuit.) For a fixed m, one needs to measure m(m + 1)/2 matrix elements.…”

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confidence: 99%

Variational Quantum Fidelity Estimation

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Cincio

et al. 2020

Quantum

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Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F(ρ, σ) based on the "truncated fidelity" F(ρ m , σ), which is evaluated for a state ρ m obtained by projecting ρ onto its m-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps:(1) variationally diagonalize ρ, (2) compute matrix elements of σ in the eigenbasis of ρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that a classical algorithm cannot efficiently solve this problem. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations. arXiv:1906.09253v1 [quant-ph]

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“…[25,26] A most recent report, from the Physics of Condensed Matter and Complex Systems group at Los Alamos National Laboratory, discusses the quantum-to-classical transition -when the quantum effects go away and the system starts to behave more classically, an observation that seems to parallel the above-discussed research, of change from quantum inflationary state into quantum deflationary state, with the appearance of 'physicalities', demonstrating more 'classical'/physical behavior of 'particles and waves'. [27] The geometry of counterclockwise/spiral movement, from a galaxy to planet Earth and living entities, e.g. trees, organogenesis (that's why hearts of vertebrates moves to the left from original midline location), and even DNA with left-handed amino acids, indicate a profound quantum space-time connection to Life with directionality of quantum energy vortex.…”

Section: Discussionmentioning

confidence: 99%

From a Quantum State to a Quantum State. <i>Life as a Temporary Emergence of a Differentiated Physicality</i>

Janecka¹

2019

EDUCATION

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Introduction: Neither Life nor a quantum state are isolated phenomena; both are interrelated systems with mutual dependency and shared doctrines. Material/Method: Public domain records were searched for identifiable observations that were considered relevant to Life principles of systems science; similarities with quantum space-time were explored. Results/Conclusions: A quantum state has directionality within its cycle, from a very long expansion/inflation to a very short contraction/deflation through singularities of reversals in a Black Hole, all followed by a new Big Bang with a new inflationary phase. Living systems represent recapitulation of their evolutionary history and carry it within own coded genome. Sun, Earth, and Life are estimated to have emerged almost simultaneously, within a plateau of about 600 million years (4.6-4 billion years ago), at the transition from the inflationary/expanding quantum state of the Universe to the deflationary/contracting one with the appearance of a definable manifestation of quantum system's output, the emergence, in the physicality of Sun, Earth, Life, etc. Life has its own Big Bang, symbolized by the unwinding of the nuclear DNA spiral during embryogenesis; within its scale, it is just as massive and rapid as the inflation following the Big Bang in the Universe that is generally dated to about 14 billion years ago. A pathway is also explored to consider 'how we know that we know', an outcome of translation of signal processing to cognitive understanding that impact measurements and observations.

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Variational consistent histories as a hybrid algorithm for quantum foundations

Cited by 78 publications

References 51 publications

Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states

Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states

Variational Quantum Fidelity Estimation

From a Quantum State to a Quantum State. <i>Life as a Temporary Emergence of a Differentiated Physicality</i>

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