Dr. Radhakrishnan Balu Profile

Dr. Radhakrishnan Balu

at DEVCOM Army Research Lab

SPIE Involvement:

Conference Program Committee | Author

Proceedings Article | 12 April 2021 Presentation + Paper

Quantum logic programming with Weyl predicates

Radhakrishnan Balu

Proceedings Volume 11726, 117260G (2021) https://doi.org/10.1117/12.2586496

KEYWORDS: Logic, Computer programming, Stochastic processes, Space operations, Quantum computing, Scattering, Quantum mechanics, Optical filters, Optical components, Optical circuits

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In our previous work we described quantized computation using Horn clauses and based the semantics, dubbed as entanglement semantics as a generalization of denotational and distribution semantics, and founded it on quantum probability by exploiting the key insight classical random variables have quantum decompositions. Towards this end we built a Hilbert space of H-interpretations and a corresponding non commutative von Neumann algebra of bounded linear operators. In this work we extend the formalism using second-quantized Horn clauses that describe processes such as Heisenberg evolutions in optical circuits, quantum walks, and quantum filters in a formally verifiable way. Our goal is to build a model of computation based on logic via Currry-Howard correspondence. Towards this end we can think of completely positive *-unital maps of Horn clauses as function types representing modus ponens (equation (19)). Recursions that result from inductive reasoning has a quantum analogue in terms of sequence of *-homomorphisms induced by completely positive *-unital maps (equation (18)). We base our system on a measure theoretic approach to handle infinite dimensional systems and demonstrate the expressive power of the formalism by casting an algebra used to describe interconnected quantum systems (QNET) in this language. The variables of a Horn clause bounded by universal or existential quantifiers can be used to describe parameters of optical components such as beam splitter scattering paths, cavity detuning from resonance, strength of a laser beam, or input and output ports of these components. Prominent clauses in this non commutative framework are Weyl predicates, that are operators on a Boson Fock space in the language of quantum stochastic calculus, martingales and conjugate Brownian motions compactly representing statistics of quantum field fluctuations. We formulate theorem proving as a quantum stochastic process in Heisenberg picture of quantum mechanics, a sequence of goals to be proved, using backward chaining.

Proceedings Article | 7 June 2017 Presentation

Time-continuous open quantum walks (Conference Presentation)

Radhakrishnan Balu, Chaobin Liu

Proceedings Volume 10193, 101931A (2017) https://doi.org/10.1117/12.2262502

KEYWORDS: Stars, Ultrafast phenomena, Photonics, Current controlled current source

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Proceedings Article | 8 May 2017 Presentation + Paper

Continuous-time limit of topological quantum walks

Radhakrishnan Balu, Daniel Castillo, George Siopsis, Christian Weedbrook

Proceedings Volume 10193, 1019319 (2017) https://doi.org/10.1117/12.2262596

KEYWORDS: Quantum computing, Motion analysis, Diffusion, Quantum physics, Xenon, Analytical research, Astatine, Physics, Astronomy, Photonics systems

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Proceedings Article | 5 May 2017 Paper

Characterizing the Nash equilibria of three-player Bayesian quantum games

Neal Solmeyer, Radhakrishnan Balu

Proceedings Volume 10212, 102120T (2017) https://doi.org/10.1117/12.2262518

KEYWORDS: Quantum information, Quantum physics, Quantum networks, Quantum computing, Quantum communications, Quantum circuits, Matrices, Quantum efficiency, Analytical research, Algorithm development

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Proceedings Article | 26 May 2016 Paper

Formal verification of communication protocols using quantized Horn clauses

Radhakrishnan Balu

Proceedings Volume 9873, 98730F (2016) https://doi.org/10.1117/12.2222590

KEYWORDS: Composites, Logic, Quantum communications, Space operations, Quantum information, Quantum computing, Computer programming, Stochastic processes, Quantum mechanics, Computing systems

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Proceedings Article | 21 May 2015 Paper

Quantum probabilistic logic programming

Radhakrishnan Balu

Proceedings Volume 9500, 950011 (2015) https://doi.org/10.1117/12.2176986

KEYWORDS: Probability theory, Logic, Computer programming, Quantum communications, Chemical species, Prisms, Scientific programming, Computer programming languages, Superposition, Quantum mechanics

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Showing 5 of 6 publications

Conference Committee Involvement (7)

Quantum Information Science, Sensing, and Computation XVI

22 April 2024 | National Harbor, Maryland, United States

Quantum Information Science, Sensing, and Computation XV

3 May 2023 | Orlando, Florida, United States

Quantum Information Science, Sensing, and Computation XIV

6 April 2022 | Orlando, Florida, United States

Quantum Information Science, Sensing, and Computation XIII

12 April 2021 | Online Only, Florida, United States

Quantum Information Science, Sensing, and Computation XII

27 April 2020 | Online Only, California, United States

Showing 5 of 7 Conference Committees

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