Quantum Probabilistic Dyadic Second-Order Logic

Baltag, Alexandru; Bergfeld, Jort M.; Kishida, Kohei; Sack, Joshua; Smets, Sonja; Zhong, Shengyang

doi:10.1007/978-3-642-39992-3_9

Cited by 7 publications

(8 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a previous research, 34 Baltag et al present a decidable logic for reasoning about the correctness of quantum programs. It captures system properties through probabilistic predication formulas, stating that a given quantum state will collapse to a state which satisfies a given condition with a given probability.…”

Section: Resultsmentioning

confidence: 99%

Quantum software testing: State of the art

Barrera

Guzmán

Polo

et al. 2021

J Software Evolu Process

View full text Add to dashboard Cite

Quantum computing is expected to exponentially outperform classic computing on a broad set of problems, including encryption, machine learning, and simulations. It has an impact yet to explore on all software lifecycle's processes and techniques. Testing quantum software raises a significant number of challenges due to the unique properties of quantum physics-such as superposition and entanglementand the stochastic behavior of quantum systems. It is, therefore, an open research issue. In this work, we offer a systematic mapping study of quantum software testing engineering, presenting a comprehensive view of the current state of the art. The main identified trends in testing techniques are (1) the statistic approaches based on repeated measurements and (2) the use of Hoare-like logics to reason about software correctness.Another relevant line of research is reversible circuit testing, which is partially applicable to quantum software unitary testing. Finally, we have observed a flourishing of secondary studies and frameworks supporting testing processes from 2018 onwards. | INTRODUCTIONQuantum computing (QC) processes information using quantum mechanics principles. In comparison to classic computing (CC), this paradigm has the potential to solve specific problems with exponential speedup. 1 QC has a wide number of applications and is expected to outperform CC in two particular kinds of computations 2 :• Applications that involve large amounts of parallel computing such as encryption, 3 big data, 4 optimization, 5 or machine learning. 6• Simulation of quantum natural phenomena, such as chemistry, 7 physics, 8 and materials science. 9With the growing accessibility of quantum computers and simulators, many concerns have arisen related to quantum software and its lifecycle and quality. Quantum software will be developed in a large-scale industrial context in the same way that classic software is nowadays produced. This implies that quantum software must be developed, operated, and maintained in a systematic, disciplined, and quantifiable manner; that is, quantum software development must be supported by a yet nonexisting body of knowledge on quantum software engineering (QSE) that must be developed to avoid a quantum software crisis. Some authors have already voiced the need to "build a community for QSE that focuses on devising methods, tools, and processes for developing quantum software systems efficiently" 10 and the need for an agenda that sets out a solid, rigorous software engineering (SE) discipline for quantum systems. 11 Others are convinced that QC could bring a "new SE golden age", 12 identifying several priority areas to be developed in QSE.

show abstract

Section: Resultsmentioning

confidence: 99%

Quantum software testing: State of the art

Barrera

Guzmán

Polo

et al. 2021

J Software Evolu Process

View full text Add to dashboard Cite

show abstract

“…This view equips quantum logic with an operational dimension, linking every physical property or proposition about a physical system to the experimental procedures that can be performed on those systems. Inspired by the work of C. Piron, [33,34], the operational view has lead to new axiomatic systems that are now studied in the context of Dynamic Quantum Logic [7][8][9][12][13][14]. In contrast to the traditional work on quantum logic (following [24,39]), the dynamic logical approach has several advantages.…”

Section: Dynamic Quantum Logicmentioning

confidence: 99%

“…In [7], we first illustrate how Hilbert spaces can be structured as QTS's. The work in [7] was the start of a new semantic approach, which was later further developed in a series of papers [8,9,[12][13][14]. In the next paragraph we introduce the setting of Quantum Transition Systems (QTS) as part of our quantum semantics for the language of P DL.…”

Section: Formalism Of Dynamic Quantum Logicmentioning

confidence: 99%

See 1 more Smart Citation

Logics of Informational Interactions

Baltag

Smets

2015

J Philos Logic

Self Cite

View full text Add to dashboard Cite

The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions (in the form of measurements and entanglement) between subsystems of a global physical system. Similarly, (multi-agent) epistemic logic is the logic of sociallyconstrained informational interactions (in the form of direct observations, learning, various forms of communication and testimony) between "subsystems" of a social system. Dynamic Epistemic Logic (DEL) provides us with a unifying setting in which these informational interactions, coming from seemingly very different areas of research, can be fully compared and analyzed. The DEL formalism comes with a powerful set of tools that allows us to make the underlying dynamic/interactive mechanisms fully transparent.

show abstract

“…Recent work toward the development of quantum logics for computation yielded probabilistic dynamic quantum logics that are decidable, such as Baltag et al (2013Baltag et al ( , 2014, and the correctness of many quantum protocols can be expressed in these languages. However, an axiomatization of these probabilistic systems is lacking.…”

Section: Introductionmentioning

confidence: 99%

Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs

Bergfeld

Sack

2015

Soft Comput

Self Cite

View full text Add to dashboard Cite

This paper presents a sound axiomatization for a probabilistic modal dynamic logic of quantum programs. The logic can express whether a state is separable or entangled, information that is local to a subsystem of the whole quantum system, and the probability of positive answers to quantum tests of certain properties. The power of this axiomatization is demonstrated with proofs of properties concerning bases of a finite-dimensional Hilbert space, composite systems, entangled and separable states, and with proofs of the correctness of two probabilistic quantum protocols (the quantum leader election protocol and the BB84 quantum key distribution protocol).

show abstract

Quantum Probabilistic Dyadic Second-Order Logic

Cited by 7 publications

References 17 publications

Quantum software testing: State of the art

Quantum software testing: State of the art

Logics of Informational Interactions

Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs

Contact Info

Product

Resources

About