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Abstract:

Abstract Erasure is fundamental for information processing. It is also key in connecting information theory and thermodynamics, as it is a logically irreversible task. We provide a new angle on this connection, noting that there may be an additional cost to erasure, that is not captured by standard results such as Landauer’s principle. To make this point we use a model of irreversibility based on constructor theory—a recently proposed generalization of the quantum theory of computation. The model uses a machine called the ‘quantum homogenizer’, which has the ability to approximately realise the transformation of a qubit from any state to any other state and remain approximately unchanged, through overall entirely unitary interactions. We argue that when performing erasure via quantum homogenization there is an additional cost to performing the erasure step of the Szilard’s engine, because it is more difficult to reliably produce pure states in a cycle than to produce maximally mixed states. We also discuss the implications of this result for the cost of erasure in more general terms.

Abstract:

Abstract Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the 1 + 1 dimensional λ ϕ 4 quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational quantum circuit (quantum neural network) analogs of the Jordan–Lee–Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the Lehmann—Symanzik—Zimmermann reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the ‘spectral crowding’ problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.