Quantum Landauer erasure with a molecular nanomagnet

Abstract

The erasure of a bit of information is an irreversible operation whose minimal entropy production of k B ln 2 is set by the Landauer limit 1 . This limit has been verified in a variety of classical systems, including particles in traps 2,3 and nanomagnets 4 . Here, we extend it to the quantum realm by using a crystal of molecular nanomagnets as a quantum spin memory and showing that its erasure is still governed by the Landauer principle. In contrast to classical systems, maximal energy efficiency is achieved while preserving fast operation owing to its high-speed spin dynamics. The performance of our spin register in terms of energy-time cost is orders of magnitude better than existing memory devices to date. The result shows that thermodynamics sets a limit on the energy cost of certain quantum operations and illustrates a way to enhance classical computations by using a quantum system.While a computation performed with an ideal binary logic gate (for example, NOT) has no lower energy dissipation limit [5][6][7] , one carried out in a memory device does. The reason is that in the former the bit is merely displaced isentropically in the space of states, whereas in the latter the minimal operation, called Landauer erasure, entails resetting the memory irrespective of its initial state. Let us see how this erasure applies to a classical N-bit register (Fig. 1a, left) and how the Landauer limit comes about. In the first stage, each bit of the register, in a definite state '0' or '1' , is allowed to explore the two binary states by lowering the potential barrier and through the action of temperature fluctuations. This doubling of the phase space is accompanied by an entropy production Δ S = k B ln 2 per bit, where k B is the Boltzmann constant. In the second stage, a work W ≥ TΔ S is required to reduce the register's entropy and phase space to their initial values 8 . The limit W = TΔ S is reached only if this reduction is carried out reversibly. This can be achieved when using a frictionless system in a quasi-static fashion (that is, at timescales slower than its relaxation time τ rel ), so that unwanted memory and hysteresis effects are avoided. For this reason, slow (fast) operation-with respect to the system-dependent τ rel -is generally associated with a lower (higher) dissipation.This complementarity between work and time suggests considering the product Wτ rel -rather than either of the two-as the figure of merit assessing the energy-time cost of a computation. On one hand, driven by the demand for speed, effort has been put into pursuing fast-switching storage devices. This has successfully produced stateof-the-art systems with picosecond timescales, although operating far (≳ 10 6 ) above the reversible limit [9][10][11][12] . On the other hand, reducing W down to the Landauer limit, at the expense of slow operation, has been beautifully demonstrated using small particles in traps 2,3 or single-domain nanomagnets 4 as envisioned by Landauer and Bennett 1,8 . All of the mentioned systems are large enough to ...

Nonequilibrium quantum bounds to Landauer's principle: Tightness and effectiveness

“…Hence, in these regions neither bound is any more informative than Clausius' law, Eq. (8). Notice that a lower environmental temperature reduces the size of these regions significantly, and we remark for β 10 we find β Q > 0 (since the environment is essentially in its ground state) and one bound is always positive.…”

“…(2) as the "entropic bound". The growing interest in exploring the thermodynamics of quantum systems [3] has led to a closer examination of Landauer's principle and the dissipated heat [6][7][8][9][10][11][12][13][14][18][19][20][21]. Recently, a different approach to bounding β Q was proposed in Ref.…”

“…Indeed, such disordered forms of energy are a potential source of inefficiency in emerging quantum technologies. Thus recently, several studies have explored lower bounds on the dissipated heat in a variety of systems, including the experimental tests of Landauer's principle [5][6][7][8], examining the validity of Landauer's bound for a fully quantum setting [4], its behavior in open quantum systems [9,10], schemes to minimize the dissipated heat [11], and a rigorous tightening of Landauer's bound [12]. While Landauer's principle is rooted in the use of information-theoretic entropies [1,2,12], recent studies have shown that other approaches that do not necessarily invoke any information theoretic tools but rather rely on the dynamics of the system, can be used to derive a "nonequilibrium thermodynamic" lower bound on the dissipated heat [13,14].…”

Quantum hardware simulating four-dimensional inelastic neutron scattering

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Finite-size spin systems could constitute key elements in future spintronics devices [1][2][3][4][5], longlasting nano-scale memories [6] or scalable and noise-resilient quantum computing platforms [7][8][9]. They are also natural test-beds for investigating peculiar quantum phenomena [10]. Inelastic Neutron Scattering is the technique of choice to model these systems.

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Dissipation During the Gating Cycle of the Bacterial Mechanosensitive Ion Channel Approaches the Landauer’s Limit

“…Recently, however, it was demonstrated that carefully built artificial systems can actually operate very close to the Landauer's bound. This was achieved with several types of systems: a single colloidal particle in an optical 14,15 or feedback [16][17][18] traps, nanomagnetic bits [19][20][21] , superconducting flux bit 22 and even quantum systems 23,24 . Based on these results, it is natural to ask whether there are any biological memory erasing processes that operate close to the Landauer's limit.…”