126 citations · 425 across the 33 of their papers we have counts for
37 papers
Stochastic Security as a Performance Metric for Quantum-enhanced Generative AI
Noah A. Crum, Leanto Sunny, Pooya Ronagh +3
Motivated by applications of quantum computers in Gibbs sampling from continuous real-valued functions, we ask whether such algorithms can provide practical advantages for machine…
Quantitative approach to Grover's quantum walk on graphs
Gamal Mograby, Radhakrishnan Balu, Kasso A. Okoudjou +1
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graph…
Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs
Gamal Mograby, Radhakrishnan Balu, Kasso A. Okoudjou +1
We study the spectral theory of a class of piecewise centrosymmetric Jacobi operators defined on an associated family of substitution graphs. Given a finite centrosymmetric matrix…
Quantum walks on regular graphs with realizations in a system of anyons
Radhakrishnan Balu
We build interacting Fock spaces from association schemes and set up quantum walks on the resulting regular graphs (distance-regular and distance-transitive). The construction is v…
Spectral decimation of a self-similar version of almost Mathieu-type operators
Gamal Mograby, Radhakrishnan Balu, Kasso A. Okoudjou +1
We introduce self-similar versions of the one-dimensional almost Mathieu operators. Our definition is based on a class of self-similar Laplacians instead of the standard discrete L…
Covariant Ergodic Quantum Markov Semigroups via Systems of Imprimitivity
Radhakrishnan Balu
We construct relativistic quantum Markov semigroups from covariant completely positive maps. We proceed by generalizing a step in Stinespring's dilation to a general system of impr…
Covariant Fermionic Fields of Space-like Particles
Radhakrishnan Balu
We develop covariant fermionic fields of space-like particles. As an application of the formalism we discuss the example of superluminous tachyons with imaginary rest mass and spin…
Quantum Probabilistic Spaces on Graphs for Topological Evolutions
Radhakrishnan Balu
We start with the consideration of fusion rules of anyonic particles evolving on a 2D surface and the a hypergroup comes with it to construct entangled quantum Markov chains. The f…
Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer
C. Huerta Alderete, Shivani Singh, Nhung H. Nguyen +5
The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the…
Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware
Shivani Singh, Cinthia H. Alderete, Radhakrishnan Balu +3
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. H…
Covariant Quantum White Noise from Light-like Quantum Fields
Radhakrishnan Balu
We derive covariant Weyl operators for light-like fields, with the massless Weyl fermion as an illustrative example, in such a way that they correspond to quantum white noises in v…
Covariant Quantum Fields via Lorentz Group Representation of Weyl Operators
Radhakrishnan Balu
The building blocks of Hudson-Parthasarathy quantum stochastic calculus start with Weyl operators on a symmetric Fock space. To realize a relativistically covariant version of the…
Quantum structures from association schemes
Radhakrishnan Balu
Starting from an association scheme induced by a finite group and the corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC), their entangled versions, and inte…
Bayesian Networks based Hybrid Quantum-Classical Machine Learning Approach to Elucidate Gene Regulatory Pathways
Radhakrishnan Balu, Ajinkya Borle
We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random…
Equiangular quantum key distribution in more than two dimensions
Radhakrishnan Balu, Paul J. Koprowski, Kasso A. Okoudjou +2
We extend the spherical code based key distribution protocols to qudits with dimensions 4 and 16 by constructing equiangular frames and their companions. We provide methods for equ…
Accelerated quantum walk, two-particle entanglement generation and localization
Shivani Singh, Radhakrishnan Balu, Raymond Laflamme +1
We present a scheme to describe the dynamics of accelerating discrete-time quantum walk for one- and two-particle in position space. We show the effect of acceleration in enhancing…
Formal Verification using Second-Quantized Horn Clauses
Radhakrishnan Balu
In our previous work [1] we described quantized computation using Horn clauses and based the semantics, dubbed as entanglement semantics as a generalization of denotational and dis…
The Geometry of a Quantum Circuit and its Impact on Electromagnetic Noise
Raina J. Olsen, Mohammadreza Rezaee, Radhakrishnan Balu
Here we show that to quantize any lumped element circuit, the circuit geometry must be included in a mathematical model of either the circuit fluxes or the circuit charges. By geom…
Kinematics and Dynamics of Quantum Walks in terms of Systems of Imprimitivity
Radhakrishnan Balu
We build systems of imprimitivity (SI) in the context of quantum walks and provide geometric constructions for their configuration space. We consider three systems, an evolution of…
Quantum games: a review of the history, current state, and interpretation
Faisal Shah Khan, Neal Solmeyer, Radhakrishnan Balu +1
We review both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999. We will also offer a narrative on the controver…
Demonstration of Bayesian quantum game on an ion trap quantum computer
Neal Solmeyer, Norbert M. Linke, Caroline Figgatt +4
We demonstrate a Bayesian quantum game on an ion trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the s…
Quantum Prisoners' Dilemma under Enhanced Interrogation
George Siopsis, Radhakrishnan Balu, Neal Solmeyer
In the quantum version of prisoners' dilemma, each prisoner is equipped with a single qubit that the interrogator can entangle. We enlarge the available Hilbert space by introducin…
Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation
N. Pradeep Kumar, Radhakrishna Balu, Raymond Laflamme +1
We study the dynamics of discrete-time quantum walk using quantum coin operations, and in time-dependent periodic sequence. For the two-period quantum…
Physical realization of topological quantum walks on IBM-Q and beyond
Radhakrishnan Balu, Daniel Castillo, George Siopsis
We discuss an efficient physical realization of topological quantum walks on a finite lattice. The -point lattice is realized with qubits, and the quantum circuit uti…