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Nonequilibrium thermodynamics of erasure with superconducting flux logic
Olli-Pentti Saira,
1, 2,
Matthew H. Matheny,
1
Raj Katti,
1
Warren Fon,
1
Gregory
Wimsatt,
3
James P. Crutchfield,
3
Siyuan Han,
4
and Michael L. Roukes
1,
1
Condensed Matter Physics and Kavli Nanoscience Institute,
California Institute of Technology, Pasadena, CA 91125
2
Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973
3
Complexity Sciences Center and Physics Department,
University of California at Davis, One Shields Avenue, Davis, CA 95616
4
Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045
(Dated: October 1, 2019)
We implement a thermal-fluctuation driven logical bit reset on a superconducting flux logic cell.
We show that the logical state of the system can be continuously monitored with only a small
perturbation to the thermally activated dynamics at 500 mK. We use the trajectory information to
derive a single-shot estimate of the work performed on the system per logical cycle. We acquire a
sample of 10
5
erasure trajectories per protocol, and show that the work histograms agree with both
microscopic theory and global fluctuation theorems. The results demonstrate how to design and
diagnose complex, high-speed, and thermodynamically efficient computing using superconducting
technology.
Information storage and processing are vital in coordi-
nating modern society. A considerable fraction (10%) of
the global electrical power output is spent on operating
and cooling the required computing infrastructure [1].
On scales large and small, reduction and mitigation of
the processor waste heat is critically important to high-
performance computing. Two complementary strategies
for developing an optimal computing platform [2] suggest
themselves. The first improves the speed and energy-
efficiency of the hardware platforms through engineering
advances, and the second, a scientific endeavor, identi-
fies and pursues the fundamental physical limits of com-
puting machines. The latter originates most directly in
the works of Landauer [3], who argued from a micro-
scopic perspective that logically irreversible operations
have an irreducible energy cost. This limit is approached,
though, only when the clock rate of the computation
is low enough to allow nearly-adiabatic physical evolu-
tion [4–9]. Most generally, physically-embedded comput-
ing requires a trade-off between between efficiency and
speed, amongst other factors [10].
A key advance to efficient nonadiabatic computing ap-
peared with the fluctuation theorems (FTs) that exactly
describe the thermodynamics of small systems – sys-
tems that are necessarily driven out of equilibrium by
external controls during information processing [11, 12].
Experimental tests of FTs have been performed in a
variety of microscopic systems [13–19] – systems natu-
rally amendable to performing Landauer-efficient com-
putation. However, a large discrepancy exists between
the speed and complexity of the thermodynamically-
optimal systems, on one hand, and application-relevant
but inefficient traditional processors, on the other. As a
Corresponding authors: osaira@bnl.gov (present address),
roukes@caltech.edu
consequence, the experimental challenges of operating a
Landauer-efficient processor so that its logical functional-
ity and thermodynamic performance are measurable typ-
ically preclude complexity beyond one-bit logic. Here, we
perform a now-classic Landauer bit erasure experiment
on a new hardware platform that promises to obviate
many such limitations – superconducting flux logic [20].
It is interesting to note that recent implementations of
heat engines based on weakly anharmonic superconduct-
ing resonators [21, 22] rely on altogether different opera-
tion principles compared to our device which exhibits a
strong nonlinearity due to flux quantization.
Exploiting the intrinsic advantages of superconduct-
ing flux circuits, our device not only allows for a faithful
implementation of the idealized picture put forth by Lan-
dauer, but provides a number of practical and theoretical
advantages. The magnetic fluxes threading the supercon-
ducing loops, though describing macroscopic phenomena,
are true microscopic coordinates in the sense that other
electronic degrees of freedom are frozen through conden-
sation to a quantum-mechanical ground state. Static
controls cause no dissipation on the device, as the mag-
netic fields are sourced with superconducting leads. The
intrinsic clock speed of the system, the plasma frequency,
is high (
ω
p
/
2
π
10
10
Hz). Industrial-scale fabrica-
tion
en masse
and coupling of a large number of flux
logic cells is possible [23, 24]. Owing to these features,
high-performance processors implementing complex log-
ical functions have been realized with superconducting
architectures [25–27].
For studying the fundamental
physics of computing, it is interesting to note that dy-
namics dominated either by classical or quantum effects
can be accessed within this class of devices by a simple
change of component values, external bias conditions, or
temperature [28]. Finally, it is straightforward to engi-
neer the dissipation acting on the remaining dynamical
coordinates. Intrinsic dissipation in superconducting cir-
cuits has been found to be very low at frequencies up
arXiv:1909.13828v1 [cond-mat.mes-hall] 30 Sep 2019