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A Universal Ecumenical Proof System for Reversible and Quantum Computation

Gustav Olaf Yunus Laitinen-Fredriksson Lundström-Imanov

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.7170772

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A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic-force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase-breaking (i.e., quantum-phase-coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.
Conventional computing has many sources of heat dissipation, but one of these--the Landauer limit--poses a fundamental lower bound of 1 bit of entropy per bit erased. 'Reversible Computing' avoids this source of dissipation, but is dissipationless computation possible? In this paper, a general proof is given for open quantum systems showing that a computer thermally coupled to its environment will necessarily dissipate entropy (and hence heat). Specifically, a lower bound is obtained that corresponds to the adiabatic regime, in which the amount of entropy dissipated per computational operation is proportional to the rate of computation.