Energetic cost of Hamiltonian quantum gates

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.

7 pages, 1 figure; corrected very unfortunate typo in the derivation

References in corpus (12)

• Charge insensitive qubit design derived from the Cooper pair box
• Suppressing Charge Noise Decoherence in Superconducting Charge Qubits
• Correcting Quantum Errors with Entanglement
• Quantum Decoherence
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• High-precision test of Landauer's principle in a feedback trap
• Experimental demonstration of a graph state quantum error-correction code
• Quantum annealing correction for random Ising problems
• Quantum speed limits and the maximal rate of information production
• Optimal control of a qubit in an optical cavity
• Thermodynamic control -- an old paradigm with new applications
• Information-thermodynamics link revisited

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• Optimal charging of a superconducting quantum battery
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• Energetics of a Single Qubit Gate
• Topological Speed Limit
• The role of quantum coherence in energy fluctuations
• Counterdiabatic control in the impulse regime
• The Impact of Imperfect Timekeeping on Quantum Control
• Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy
• Bounding the Minimum Time of a Quantum Measurement
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• The resource cost of large scale quantum computing
• Optimal solutions to quantum annealing using two independent control functions
• Classical dissipative cost of quantum control