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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Szilard engine reversibility as quantum gate function

F. Matthew Mihelic

Published May 1, 2012• 3 citations
Publisher

Abstract

A quantum gate is a logically and thermodynamically reversible situation that effects a unitary transformation of qubits of superimposed information, and essentially constitutes a situation for a reversible quantum decision. A quantum decision is a symmetry break, and the effect of the function of a Szilard engine is a symmetry break. A quantum gate is a situation in which a reversible quantum decision can be made, and so if a logically and thermodynamically reversible Szilard engine can be theoretically constructed then it would function as a quantum gate. While the traditionally theorized Szilard engine is not thermodynamically reversible, if one of the bounding walls of a Szilard engine were to be constructed out of the physical information by which it functions in such a manner as to make that information available to both sides of the wall simultaneously, then such a Szilard engine would be both logically and thermodynamically reversible, and thus capable of function as a quantum gate. A theoretical model of the special case of a reversible Szilard engine functioning as a quantum gate is presented and discussed, and since a quantum decision is made when the shutter of a Szilard engine closes, the coherence of linked reversible Szilard engines should be considered as a state during which all of the shutters of linked Szilard engines are open simultaneously.

DOI
10.1117/12.918687

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A quantum gate is a logically and thermodynamically reversible situation that effects a unitary transformation of qubits of superimposed information, and essentially constitutes a situation for a reversible quantum decision. A quantum decision is a symmetry break, and the effect of the function of a Szilard engine is a symmetry break. A quantum gate is a situation in which a reversible quantum decision can be made, and so if a logically and thermodynamically reversible Szilard engine can be theoretically constructed then it would function as a quantum gate. While the traditionally theorized Szilard engine is not thermodynamically reversible, if one of the bounding walls of a Szilard engine were to be constructed out of the physical information by which it functions in such a manner as to make that information available to both sides of the wall simultaneously, then such a Szilard engine would be both logically and thermodynamically reversible, and thus capable of function as a quantum gate. A theoretical model of the special case of a reversible Szilard engine functioning as a quantum gate is presented and discussed, and since a quantum decision is made when the shutter of a Szilard engine closes, the coherence of linked reversible Szilard engines should be considered as a state during which all of the shutters of linked Szilard engines are open simultaneously.
The best design for practical quantum computing is one that emulates the multi-agent quantum logic function of natural biological systems. Such systems are theorized to be based upon a quantum gate formed by a nucleic acid Szilard engine (NASE) that converts Shannon entropy of encountered molecules into useful work of nucleic acid geometric reconfiguration. This theoretical mechanism is logically and thermodynamically reversible in this special case because it is literally constructed out of the (nucleic acid) information necessary for its function, thereby allowing the nucleic acid Szilard engine to function reversibly because, since the information by which it functions exists on both sides of the theoretical mechanism simultaneously, there would be no build-up of information within the theoretical mechanism, and therefore no irreversible thermodynamic energy cost would be necessary to erase information inside the mechanism. This symmetry breaking Szilard engine function is associated with emission and/or absorption of entangled photons that can provide quantum synchronization of other nucleic acid segments within and between cells. In this manner nucleic acids can be considered as a natural model of topological quantum computing in which the nonabelian interaction of genes can be represented within quantum knot/braid theory as anyon crosses determined by entropic loss or gain that leads to changes in nucleic acid covalent bond angles. This naturally occurring biological form of topological quantum computing can serve as a model for workable man-made multi-agent quantum computing systems.
The Szilárd engine is a mechanism (akin to Maxwell's demon) for converting information into energy, which seemingly violates the second law of thermodynamics. Originally a classical thought experiment, it was extended to a quantized treatment by Zurek. Here, we examine a new, elegant model of a quantum Szilárd engine by replacing the traditional rigid box with a harmonic potential, extending the scope of the model. Remarkably, almost all calculations are exact. This article is suitable for students, researchers, and educators interested in the conceptual links among information, entropy, and quantum measurement.
Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell's Demon where Landauer's principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell's demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but the erasure and related heat dissipation still take place implicitly. We explore a quantum Szilard engine considering quantum size effects. We see that insertion of the partition does not localize the particle to one side, instead creating a superposition state of the particle being in both sides. To be able to extract work from the system, particle has to be localized at one side. The localization occurs as a result of quantum measurement on the particle, which shows the importance of the measurement process regardless of whether one uses the acquired information or not. In accordance with Landauer's principle, localization by quantum measurement corresponds to a logically irreversible operation and for this reason it must be accompanied by the corresponding heat dissipation. This shows the validity of Landauer's principle even in quantum Szilard engines without Maxwell's demon.
This paper explores the possibility of extending the existing model of a single-particle Quantum Szilard Engine to take advantage of some features of quantum information for driving typical mechanical systems. It focuses on devices that output mechanical work, extracting energy from a single thermal reservoir at the cost of increasing the entropy of a qubit; the reverse process is also considered. In this alternative, several engines may share the information carried by the same qubit, although its interception will prove completely worthless for any illegitimate user. To this end, multi-partite quantum entanglement is employed. Besides, some changes in the cycle of the standard single-particle Quantum Szilard Engine are described, which lend more flexibility to meeting additional requirements in typical mechanical systems. The modifications allow having qubit input and output states of adjustable entropy. This feature enables the possibility of chaining the qubit between engines so that its output state from one can be used as an input state for another. Finally, another tweak is presented that allows for tuning the average output force of the engine.
Abstract A reinvention of the classical Maxwel demon was proposed by Szilard around the time quantum mechanics was developed. His model continues to attract great interest, especially quantum versions of it. A quantum formulation of the Szilard engine is introduced and investigated here. It is made to operate through specified cycles in such a way that all thermodynamic quantities which pertain to the system can be evaluated exactly in closed form along each sequence of steps through a cycle. It is shown that as a result of the structure of the model, it is possible to calculate and compare various thermodynamic quantities as the engine proceeds around a well defined specific cycle.