Overhead for simulating a non-local channel with local channels by quasiprobability sampling

Quantum ◽

10.22331/q-2021-01-28-388 ◽

2021 ◽

Vol 5 ◽

pp. 388

Author(s):

Kosuke Mitarai ◽

Keisuke Fujii

Keyword(s):

Quantum Computing ◽

Linear Combination ◽

Upper Bound ◽

First Generation ◽

Quantum Devices ◽

Non Local ◽

The Cost ◽

Non Locality

As the hardware technology for quantum computing advances, its possible applications are actively searched and developed. However, such applications still suffer from the noise on quantum devices, in particular when using two-qubit gates whose fidelity is relatively low. One way to overcome this difficulty is to substitute such non-local operations by local ones. Such substitution can be performed by decomposing a non-local channel into a linear combination of local channels and simulating the original channel with a quasiprobability-based method. In this work, we first define a quantity that we call channel robustness of non-locality, which quantifies the cost for the decomposition. While this quantity is challenging to calculate for a general non-local channel, we give an upper bound for a general two-qubit unitary channel by providing an explicit decomposition. The decomposition is obtained by generalizing our previous work whose application has been restricted to a certain form of two-qubit unitary. This work develops a framework for a resource reduction suitable for first-generation quantum devices.

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Evaluating probabilistic forecasts of football matches: the case against the ranked probability score

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2019-0089 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Edward Wheatcroft

Keyword(s):

Scoring Rules ◽

Brier Score ◽

Sporting Events ◽

Forecast Performance ◽

Scoring Rule ◽

Probability Score ◽

Probabilistic Forecasts ◽

Non Local ◽

Evaluating Forecasts ◽

Non Locality

Abstract A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is ‘sensitive to distance’, that is it takes into account the ordering in the outcomes (a home win is ‘closer’ to a draw than it is to an away win). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the Ignorance score, which is local and insensitive to distance. The Ignorance score outperforms both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.

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Upper bound for loss in practical topological-cluster-state quantum computing

Physical Review A ◽

10.1103/physreva.90.052316 ◽

2014 ◽

Vol 90 (5) ◽

Cited By ~ 10

Author(s):

Adam C. Whiteside ◽

Austin G. Fowler

Keyword(s):

Quantum Computing ◽

Upper Bound ◽

Cluster State

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GASOL: Gas Analysis and Optimization for Ethereum Smart Contracts

Tools and Algorithms for the Construction and Analysis of Systems - Lecture Notes in Computer Science ◽

10.1007/978-3-030-45237-7_7 ◽

2020 ◽

pp. 118-125 ◽

Cited By ~ 5

Author(s):

Elvira Albert ◽

Jesús Correas ◽

Pablo Gordillo ◽

Guillermo Román-Díez ◽

Albert Rubio

Keyword(s):

Upper Bound ◽

Cost Model ◽

Gas Analysis ◽

Smart Contracts ◽

Cost Models ◽

Automatic Optimization ◽

Gas Consumption ◽

The Cost ◽

Storage Patterns ◽

Program Line

Abstract We present the main concepts, components, and usage of Gasol, a Gas AnalysiS and Optimization tooL for Ethereum smart contracts. Gasol offers a wide variety of cost models that allow inferring the gas consumption associated to selected types of EVM instructions and/or inferring the number of times that such types of bytecode instructions are executed. Among others, we have cost models to measure only storage opcodes, to measure a selected family of gas-consumption opcodes following the Ethereum’s classification, to estimate the cost of a selected program line, etc. After choosing the desired cost model and the function of interest, Gasol returns to the user an upper bound of the cost for this function. As the gas consumption is often dominated by the instructions that access the storage, Gasol uses the gas analysis to detect under-optimized storage patterns, and includes an (optional) automatic optimization of the selected function. Our tool can be used within an Eclipse plugin for which displays the gas and instructions bounds and, when applicable, the gas-optimized function.

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Diluted mass gap in strongly coupled non-local Yang-Mills

Journal of High Energy Physics ◽

10.1007/jhep07(2021)226 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Marco Frasca ◽

Anish Ghoshal

Keyword(s):

Field Theory ◽

Particle Physics ◽

Mass Scale ◽

Local Theory ◽

Quantum Field ◽

Strongly Coupled ◽

Yang Mills ◽

Mass Gap ◽

Non Local ◽

Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

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Branching Space-Times

10.1093/oso/9780190884314.001.0001 ◽

2021 ◽

Author(s):

Nuel Belnap ◽

Thomas Müller ◽

Tomasz Placek

Keyword(s):

Single Case ◽

Formal Analysis ◽

Rigorous Theory ◽

Quantum Non Locality ◽

Foundations Of Physics ◽

Local Contexts ◽

Rigorous Framework ◽

Non Local ◽

Spatio Temporal ◽

Non Locality

This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.

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The Meta-Dynamic Nature of Consciousness

10.20944/preprints202003.0178.v3 ◽

2020 ◽

Author(s):

John Barnden

Keyword(s):

Mathematical Formulation ◽

Physical Universe ◽

Time Flow ◽

Non Local ◽

Physical Interactions ◽

Key Aspects ◽

Physical Laws ◽

The Universe ◽

Non Locality ◽

Do So

How, if at all, consciousness can be part of the physical universe remains a baffling problem. This article outlines a new, developing philosophical theory of how it could do so, and offers a preliminary mathematical formulation of a physical grounding for key aspects of the theory. Because the philosophical side has radical elements, so does the physical-theory side. The philosophical side is radical, first, in proposing that the productivity or dynamism in the universe that many believe to be responsible for its systematic regularities is actually itself a physical constituent of the universe, along with more familiar entities. Indeed, it proposes that instances of dynamism can themselves take part in physical interactions with other entities, this interaction then being “meta-dynamism” (a type of meta-causation). Secondly, the theory is radical, and unique, in arguing that consciousness is necessarily partly constituted of meta-dynamic auto-sensitivity, in other words it must react via meta-dynamism to its own dynamism, and also in conjecturing that some specific form of this sensitivity is sufficient for and indeed constitutive of consciousness. The article proposes a way for physical laws to be modified to accommodate meta-dynamism, via the radical step of including elements that explicitly refer to dynamism itself. Additionally, laws become, explicitly, temporally non-local in referring directly to quantity values holding at times prior to a given instant of application of the law. The approach therefore implicitly brings in considerations about what information determines states. Because of the temporal non-locality, and also because of the deep connections between dynamism and time-flow, the approach also implicitly connects to the topic of entropy insofar as this is related to time.

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Least upper bound on the cost of optimum binary search trees

Acta Informatica ◽

10.1007/bf00289510 ◽

1972 ◽

Vol 1 (4) ◽

pp. 307-310 ◽

Cited By ~ 8

Author(s):

T. C. Hu ◽

K. C. Tan

Keyword(s):

Upper Bound ◽

Binary Search ◽

Binary Search Trees ◽

Search Trees ◽

The Cost

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Locality bounds on Hamiltonians for stabilizer codes

Quantum Information and Computation ◽

10.26421/qic9.5-6-9 ◽

2009 ◽

Vol 9 (5&6) ◽

pp. 487-499

Author(s):

S.S. Bullock ◽

D.P. O'Leary

Keyword(s):

Quantum Computing ◽

Error Correction ◽

Energy Gap ◽

Stabilizer Codes ◽

Adiabatic Quantum Computing ◽

Group A ◽

Stabilizer Code ◽

Stabilizer Group ◽

The Cost ◽

Insight Into

In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of $k$-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations.

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Quantum Algorithms

Limitations and Future Applications of Quantum Cryptography - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-7998-6677-0.ch005 ◽

2021 ◽

pp. 82-101

Author(s):

Renata Wong ◽

Amandeep Singh Bhatia

Keyword(s):

Quantum Computing ◽

Fault Tolerance ◽

Quantum Computation ◽

Quantum Computer ◽

Quantum Algorithms ◽

Computer Hardware ◽

Quantum Mechanical ◽

Computational Power ◽

Quantum Devices ◽

The Core

In the last two decades, the interest in quantum computation has increased significantly among research communities. Quantum computing is the field that investigates the computational power and other properties of computers on the basis of the underlying quantum-mechanical principles. The main purpose is to find quantum algorithms that are significantly faster than any existing classical algorithms solving the same problem. While the quantum computers currently freely available to wider public count no more than two dozens of qubits, and most recently developed quantum devices offer some 50-60 qubits, quantum computer hardware is expected to grow in terms of qubit counts, fault tolerance, and resistance to decoherence. The main objective of this chapter is to present an introduction to the core quantum computing algorithms developed thus far for the field of cryptography.

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