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arXiv:1311.7612 · Physical Review Letters

Guaranteed Energy-Efficient Bit Reset in Finite Time

Cormac Browne, Andrew J. P. Garner, Oscar Dahlsten, Vlatko Vedral

Published Sep 4, 2014• 31 citations
arXivHTMLPDF

Abstract

Landauer's principle states that it costs at least kBTln2 of work to reset one bit in the presence of a heat bath at temperature T. The bound of kBTln2 is achieved in the unphysical infinite-time limit. Here we ask what is possible if one is restricted to finite-time protocols. We prove analytically that it is possible to reset a bit with a work cost close to kBTln2 in a finite time. We construct an explicit protocol that achieves this, which involves thermalizing and changing the system's Hamiltonian so as to avoid quantum coherences. Using concepts and techniques pertaining to single-shot statistical mechanics, we furthermore prove that the heat dissipated is exponentially close to the minimal amount possible not just on average, but guaranteed with high confidence in every run. Moreover, we exploit the protocol to design a quantum heat engine that works near the Carnot efficiency in finite time.

DOI
10.1103/physrevlett.113.100603

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Landauer's principle states that it costs at least kBTln2 of work to reset one bit in the presence of a heat bath at temperature T. The bound of kBTln2 is achieved in the unphysical infinite-time limit. Here we ask what is possible if one is restricted to finite-time protocols. We prove analytically that it is possible to reset a bit with a work cost close to kBTln2 in a finite time. We construct an explicit protocol that achieves this, which involves thermalizing and changing the system's Hamiltonian so as to avoid quantum coherences. Using concepts and techniques pertaining to single-shot statistical mechanics, we furthermore prove that the heat dissipated is exponentially close to the minimal amount possible not just on average, but guaranteed with high confidence in every run. Moreover, we exploit the protocol to design a quantum heat engine that works near the Carnot efficiency in finite time.
Landauer’s principle states that it costs at least kBT ln 2 of work to reset one bit in the presence of a heat bath at temperature T. The bound of kBT ln 2 is achieved in the unphysical infinite-time limit. Here we consider two different finite-time protocols - one with discretised time and the second in the continuous limit. We prove analytically that the discrete time protocol enables one to reset a bit with a work cost close to kBT ln 2 in a finite time. We construct an explicit protocol that achieves this, which involves thermalising and changing the system’s Hamiltonian so as to avoid quantum coherences. Using concepts and techniques pertaining to single-shot statistical mechanics, we furthermore prove that the heat dissipated is exponentially close to the minimal amount possible not just on average, but guaranteed with high confidence in every run. Moreover we exploit the protocol to design a quantum heat engine that works near the Carnot efficiency in finite time. We further contrast this to a continuous time version of the protocol which is substantially less energy sufficient. We also consider the fluctuations in the work cost, and calculate how their magnitude is suppressed by a factor depending on the length of the protocol. We demonstrate with an experiment how molecules are a natural test-bed for probing fundamental quantum thermodynamics. Single-molecule spectroscopy has undergone transformative change in the past decade with the advent of techniques permitting individual molecules to be distinguished and probed. By considering the time-resolved emission spectrum of organic molecules as arising from quantum jumps between states, we demonstrate that the quantum Jarzynski equality is satisfied in this set-up. This relates the heat dissipated into the environment to the free energy difference between the initial and final state. We demonstrate also how utilizing the quantum Jarzynski equality allows for the detection of energy shifts within a molecule, beyond the relative shift.
The thermodynamic cost of resetting an arbitrary initial state to a particular desired state is lower bounded by Landauer's bound. However, here we demonstrate that this lower bound is necessarily unachievable for every initial state (except possibly the single minimally dissipative input) for any reliable reset mechanism. Since local heating threatens rapid decoherence, this issue is of substantial importance beyond mere energy efficiency. For the case of qubit reset, we find the minimally dissipative state analytically for any reliable reset protocol, in terms of the entropy-flow vector introduced here. This allows us to verify a recent theorem about initial-state dependence of entropy production for any finite-time transformation, as it pertains to quantum state preparation.
Landauer's principle shows that the minimum energy cost to reset a classical bit in a bath with temperature T is k_{B}Tln2 in the infinite time. However, the task to reset the bit in finite time has posted a new challenge, especially for quantum bit (qubit) where both the operation time and controllability are limited. We design a shortcut-to-isothermal scheme to reset a qubit in finite time τ with limited controllability. The energy cost is minimized with the optimal control scheme with and without bound. This optimal control scheme can provide a reference to realize qubit reset with minimum energy cost for the limited time.
The standard Landauer bound W≥kBTln2 sets the fundamental thermodynamic cost for information erasure under ideal conditions: weak system-bath coupling, quasistatic operation, and equilibrium reservoirs. However, realistic quantum error correction (QEC) operates in a profoundly different regime-finite-time syndrome extraction, strong coupling to cryogenic environments, and non-equilibrium dynamics. Here, we develop a unified thermodynamic framework for fault-tolerant quantum computing that incorporates corrections beyond the ideal Landauer limit. We derive a generalized bound on the heat dissipation per QEC cycle: Qmin≥kBTln2+kBTΔISB+ℏτ, and scaling this result to large-scale quantum computers, we find that the total heat load grows polynomially with code distance but remains in the nanowatt range for million-qubit systems-well within the cooling power of modern dilution refrigerators. Applying our model to superconducting qubit architectures, we show that while strong coupling can add up to ∼20% to the ideal cost, finite-time effects contribute approximately 0.55% at 100 ns and 5.5% at 10 ns reset operations. Our results establish that the true thermodynamic cost of fault tolerance, while exceeding the naive Landauer estimate, does not pose a fundamental obstacle to scalability; the dominant engineering challenges lie in the heat load of control electronics and wiring, not in the fundamental dissipation of qubit reset.
Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this Letter, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.