Genus-1 Virasoro Conjecture along Quantum Volume Direction

Quantum systems in a mechanical embedding, the breathing mode of a small particles, optomechanical system, etc. are far not the full list of examples in which the volume exhibits quantum behavior. Traditional consideration suggests strain in small systems as a result of a collective movement of particles, rather than the dynamics of the volume as an independent variable. The aim of this work is to show that some problem here might be essentially simplified by introducing periodic boundary conditions. At this case, the volume is considered as the independent dynamical variable driven by the internal pressure. For this purpose, the concept of quantum volume based on Schrödinger’s equation in [Formula: see text] manifold is proposed. It is used to explore several 1D model systems: An ensemble of free particles under external pressure, quantum manometer and a quantum breathing mode. In particular, the influence of the pressure of free particle on quantum oscillator is determined. It is shown also that correction to the spectrum of the breathing mode due to internal degrees of freedom is determined by the off-diagonal matrix elements of the quantum stress. The new treatment not using the “force” theorem is proposed for the quantum stress tensor. In the general case of flexible quantum 3D dynamics, quantum deformations of different type might be introduced similarly to monopole mode.

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A volumetric framework for quantum computer benchmarks

Quantum ◽

10.22331/q-2020-11-15-362 ◽

2020 ◽

Vol 4 ◽

pp. 362

Author(s):

Robin Blume-Kohout ◽

Kevin C. Young

Keyword(s):

Quantum Computer ◽

Pareto Frontier ◽

Large Family ◽

Test Suite ◽

Large Set ◽

Common Structure ◽

Time Space ◽

Trade Offs ◽

Graphical Summary ◽

Quantum Volume

We propose a very large family of benchmarks for probing the performance of quantum computers. We call them volumetric benchmarks (VBs) because they generalize IBM's benchmark for measuring quantum volume \cite{Cross18}. The quantum volume benchmark defines a family of square circuits whose depth d and width w are the same. A volumetric benchmark defines a family of rectangular quantum circuits, for which d and w are uncoupled to allow the study of time/space performance trade-offs. Each VB defines a mapping from circuit shapes — (w,d) pairs — to test suites C(w,d). A test suite is an ensemble of test circuits that share a common structure. The test suite C for a given circuit shape may be a single circuit C, a specific list of circuits {C1…CN} that must all be run, or a large set of possible circuits equipped with a distribution Pr(C). The circuits in a given VB share a structure, which is limited only by designers' creativity. We list some known benchmarks, and other circuit families, that fit into the VB framework: several families of random circuits, periodic circuits, and algorithm-inspired circuits. The last ingredient defining a benchmark is a success criterion that defines when a processor is judged to have ``passed'' a given test circuit. We discuss several options. Benchmark data can be analyzed in many ways to extract many properties, but we propose a simple, universal graphical summary of results that illustrates the Pareto frontier of the d vs w trade-off for the processor being benchmarked.

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Demonstration of quantum volume 64 on a superconducting quantum computing system

Quantum Science and Technology ◽

10.1088/2058-9565/abe519 ◽

2021 ◽

Vol 6 (2) ◽

pp. 025020 ◽

Cited By ~ 2

Author(s):

Petar Jurcevic ◽

Ali Javadi-Abhari ◽

Lev S Bishop ◽

Isaac Lauer ◽

Daniela F Bogorin ◽

...

Keyword(s):

Quantum Computing ◽

Computing System ◽

Quantum Volume

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