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International Journal of Circuit Theory and Applications

On the circuit paradigm in quantum networks

Günter Mahler A, Alexander Otte, Marcus Stollsteimer

Published Jan 1, 2003• 7 citations
Publisher

Abstract

Abstract Physics is not scale invariant. As we reach the quantum domain not only new computational modes, but also fundamental control limits, are expected to appear. We investigate, to what extent some variant of the circuit paradigm may remain applicable, despite the qualitative change in function. Copyright © 2003 John Wiley & Sons, Ltd.

DOI
10.1002/cta.220

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Abstract Physics is not scale invariant. As we reach the quantum domain not only new computational modes, but also fundamental control limits, are expected to appear. We investigate, to what extent some variant of the circuit paradigm may remain applicable, despite the qualitative change in function. Copyright © 2003 John Wiley & Sons, Ltd.
Abstract Physics is not scale invariant, and today the scale of atoms and molecules challenges designers of machines in which quantum effects have dominant sway. What role could circuit theory play in designing machines described by quantum‐classical models? Classical equivalent circuits do exist for systems composed of metal contacted and wired devices, such as resonant tunneling diodes, single electron transistors, metal–insulator–metal diodes, etc. circuits, but not for quantum‐entangled networks, such as multi‐quantum‐state atoms. If devices were not contacted and wired by macroscopic metals, i.e. devices were classically field coupled, then generalized circuit models can be introduced. Case studies have been presented on the role of circuit models in quantum‐classical systems. However, there are no ideal circuit elements capable of capturing the port properties of quantum‐mechanical and/or quantum‐optical subsystems and their coupling to classical waveguides or cavities. Copyright © 2007 John Wiley & Sons, Ltd.
Present-day information processing is based on the rules of classical physics. If the ubiquitous superposition principle of quantum mechanics could be harnessed, quite different and surprising rules would be at our disposal. They would give rise to the celebrated quantum parallelism allowing, e.g. for an increased efficiency of quantum over classical computing. To achieve this goal there are at least two different paradigms which could be exploited: ‘selective control’ and ‘collective control’. The latter should be an interesting alternative for nanoscopic quantum networks. Copyright © 2001 John Wiley & Sons, Ltd.
Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.
Abstract Since quantum systems interact with their environment permanently or within a measurement process, there is much interest in concepts of open quantum system modelling. In this paper we give an overview on three different concepts in order to address this problem in the context of the network paradigm. Furthermore the modelling of spatially localized decoherence processes within the stochastic diffusion wave equation approach of Gisin et al. is briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.