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 ...