  The erasure of a bit of information encoded in a physical system is an
irreversible operation bound to dissipate an amount of energy $Q = k_\text{B}
T\ln 2$. As a result, work $W \geq Q$ has to be applied to the physical system
to restore the erased information content. This limit, called Landauer limit,
sets a minimal energy dissipation inherent to any classical computation. In the
pursuit of the fastest and most efficient means of computation, the ultimate
challenge is to produce a memory device executing an operation as close to this
limit in the shortest time possible. Here, we use a crystal of molecular
nanomagnets as a spin-memory device and measure the work needed to carry out a
storage operation. Exploiting a form of quantum annealing, we border the
Landauer limit while preserving fast operation. Owing to the tunable and fast
dynamics of this process, the performance of our device in terms of energy-time
cost is orders of magnitude better than existing memory devices to date. This
result suggests a way to enhance classical computations by using quantum
processes.
