Energetic cost of Hamiltonian quantum gates

2021/02/12 by Sebastian Deffner
Computer Science · Mathematics · Physics and Astronomy · #Dissipative system #Hamiltonian (control theory) #Law #Mathematical optimization #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum error correction #Quantum information #Quantum mechanics #Quantum-Dot Cellular Automata #Qubit #Statistical physics #Unitary state #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1209/0295-5075/134/40002

published as EPL 134, 40002 (2021) · 7 pages, 1 figure; corrected very unfortunate typo in the derivation

arxiv created 2021/02/12 · openalex publication_date 2021/05/01 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Abstract Landauer's principle laid the main foundation for the development of modern thermodynamics of information. However, in its original inception the principle relies on semiformal arguments and dissipative dynamics. Hence, if and how Landauer's principle applies to unitary quantum computing is less than obvious. Here, we prove an inequality bounding the change of Shannon information encoded in the logical quantum states by quantifying the energetic cost of Hamiltonian gate operations. The utility of this bound is demonstrated by outlining how it can be applied to identify energetically optimal quantum gates in theory and experiment. The analysis is concluded by discussing the energetic cost of quantum error correcting codes with non-interacting qubits, such as Shor's code.

Citations

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