Efficiency of open quantum walk implementation of dissipative quantum computing algorithms

Abstract

An open quantum walk formalism for dissipative quantum computing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on the open quantum walk formalism are more efficient than the canonical dissipative quantum computing approach. In particular, the open quantum walks can be designed to converge faster to the desired steady state and to increase the probability of detection of the outcome of the computation.

Special Issue: Quantum Walks

References in corpus (13)

• Quantum random walks - an introductory overview
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Universal computation by quantum walk
• Preparation of Entangled States by Quantum Markov Processes
• Universal quantum computation using the discrete time quantum walk
• Dissipative preparation of entanglement in optical cavities
• Decoherence can be useful in quantum walks
• Open Quantum Random Walks
• Quantum stochastic walks: A generalization of classical random walks and quantum walks
• Dynamics of nonequilibrium thermal entanglement
• Cooling atoms into entangled states
• Nonequilibrium thermal entanglement for three-spin chain
• Microscopic derivation of Open Quantum Walks

Cited by in corpus (29)

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• Quantum walks on graphs representing the firing patterns of a quantum neural network
• Dissipative preparation of large W states in Optical Cavities
• Homogeneous Open Quantum Random Walks on a lattice
• Simulation of single-qubit open quantum systems
• From classical to quantum walks with stochastic resetting on networks
• Open Quantum Walks: a short introduction
• Microscopic derivation of Open Quantum Walks
• Quantum Hidden Markov Models based on Transition Operation Matrices
• Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
• Open quantum random walks with decoherence on coins with $n$ degrees of freedom
• Non-Commutative Resistance Networks
• Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks
• On a generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks
• Dissipative preparation of generalised Bell states
• A quantum collisional classifier driven by information reservoir
• Lazy Open Quantum Walks
• Microscopic derivation of open quantum walk on two node graph
• Quantum techniques for eigenvalue problems
• Mean hitting times of quantum Markov chains in terms of generalized inverses
• Preparing Renormalization Group Fixed Points on NISQ Hardware
• Dynamics and computation in linear open quantum walks
• A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks
• Open Quantum Random Walks: reducibility, period, ergodic properties
• Dissipative realization of a quantum distance-based classifier using open quantum walks
• A Generalized Quantum Optical Scheme for Implementing Open Quantum Walks
• Shannon Entropy and Diffusion Coeffcient in Parity-Time Symmetric Quantum Walks