PHYSICAL REVIEW RESEARCH
2
, 013249 (2020)
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
Division of Physics, Mathematics, and Astronomy and Kavli Nanoscience Institute,
California Institute of Technology, Pasadena, California 91125, USA
2
Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA
3
Complexity Sciences Center and Department of Physics, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
4
Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
(Received 30 September 2019; accepted 20 January 2020; published 3 March 2020)
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.
DOI:
10.1103/PhysRevResearch.2.013249
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 proces-
sor waste heat are 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 plat-
forms through engineering advances and the second, a scien-
tific endeavor, identifies and pursues the fundamental physical
limits of computing machines. The latter originates most di-
rectly 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 evolution [
4
–
9
]. Most gen-
erally, physically embedded computing requires a trade-off
between efficiency and speed, among other factors [
10
].
A key advance in efficient nonadiabatic computing
appeared with the fluctuation theorems (FTs) that exactly
describe the thermodynamics of small systems, which 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
] naturally amendable to performing Landauer-
*
Corresponding author: osaira@bnl.gov
†
Corresponding author: roukes@caltech.edu
Published by the American Physical Society under the terms of the
Creative Commons Attribution 4.0 International
license. Further
distribution of this work must maintain attribution to the author(s)
and the published article’s title, journal citation, and DOI.
efficient computation. 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
consequence, the experimental challenges of operating a
Landauer-efficient processor so that its logical functionality
and thermodynamic performance are measurable typically
preclude complexity beyond one-bit logic. Here we perform
a now-classic Landauer bit erasure experiment on a 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 superconducting resonators [
21
,
22
]relyonalto-
gether different operation principles compared to our device,
which exhibits a strong nonlinearity due to flux quantization.
Exploiting the intrinsic advantages of superconducting flux
circuits, our device not only allows for a faithful implemen-
tation of the idealized picture put forth by Landauer, but
provides a number of practical and theoretical advantages.
The magnetic fluxes threading the superconducting loops,
though describing macroscopic phenomena, are true micro-
scopic coordinates in the sense that other electronic degrees
of freedom are frozen through condensation to a quantum-
mechanical ground state. Static controls cause no dissipation
on the device, as the magnetic fields are sourced with super-
conducting leads. The intrinsic clock speed of the system is
set by the frequency of small oscillations around the potential
minimum, i.e., the plasma frequency, which is of the order of
10
10
Hz. Industrial-scale fabrication
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 logical functions have been realized with supercon-
ducting architectures [
25
–
27
]. For studying the fundamental
physics of computing, it is interesting to note that dynam-
ics dominated by either classical or quantum effects can be
2643-1564/2020/2(1)/013249(9)
013249-1
Published by the American Physical Society