Gigahertz Sub-Landauer Momentum Computing
Kyle J. Ray and James P. Crutchfield
Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616
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ABSTRACT:
We introduce a fast and highly-efficient physically-realizable bit
swap. Employing readily available and scalable Josephson junction
microtechnology, the design implements the recently introduced
paradigm of momentum computing. Its nanosecond speeds and
sub-Landauer thermodynamic efficiency arise from dynamically
storing memory in momentum degrees of freedom. As such, during the
swap, the microstate distribution is never near equilibrium and
the memory-state dynamics fall far outside of stochastic
thermodynamics that assumes detailed-balanced Markovian dynamics.
The device implements a bit-swap operation—a fundamental
operation necessary to build reversible universal computing.
Extensive, physically-calibrated simulations demonstrate that
device performance is robust and that momentum computing can
support thermodynamically-efficient, high-speed, large-scale
general-purpose computing.
Kyle J. Ray and James P. Crutchfield,
“Gigahertz Sub-Landauer Momentum Computing”,
Physical Review Applied 19 (2023) 014049.
doi:10.1103/PhysRevApplied.19.014049.
[pdf]
arxiv.org:2202.07122 [cond-mat.stat-mech].
Selected animations of continuous-time thermodynamically-free bit swap:
See Supplemental Material at [URL will be provided by publisher]
for a suite of animations that showcase the action of the proposed
flux qubit implementation of bit swap on the underlying state space.
Bit swap animations of 1000 trajectories sampled from the
equilibrium distribution of the storage potential from four
different projections. Color encodes the initial informational
state of each trajectory, with red meaning '1' and orange meaning
'0'.
Bit
Swap Animations (MPEG 4)
- Top:
(left) The position space projection shows how the degrees of
freedom react to the potential energy surface as it transitions
between the computational and storage potential parameters,
depicted by the underlying contours. The energy imparted by the
change in potential is manifest in nonequilibrium oscillations of
the conjugate momenta (right). This momentum space projection most
clearly shows the departure and eventual return to equilibrium.
Note that the transition to the storage potential imparts large
oscillations in the ɸdc dimension, because the
double-well (Vstore) and single-well (Vcomp) profiles are
centered about different ɸdc values. However, the bulk of
these oscillations are re-absorbed when the storage potential is
reinstated.
- Bottom:
Marginal phase space projections in both the (left) computational
ɸ and (right) computationally passive ɸdc
dimensions. The left plot shows how the \varphi momenta serves as
a transient memory by allowing the informational states to avoid
crossing in phase space. On the right, we see that the
ɸdc dimension is informationally mute—trajectories
corresponding to both the '0' and '1' informational states lying
on top of eachother in the marginal phase space. The oscillations
in this informationally mute dimension are not necessary for the
computation, but are an inevitable result of the control protocol
when switches between the two potential energy landscapes.
- Both:
The device and protocol simulated for these animations do not
represent a particularly efficient device. Instead, for
illustrations purposes, a device was
selected so that both the swap and the return to equilibrium could
be easily seen at relatively similar timescales. For efficient
devices, the particles end closer to an equilibrium distribution
and the equilibration takes a couple orders of magnitude longer.
Even when simulating this higher dissipation device, the time is
sped up once the swap is accomplished to avoid an overly long
video—an indicator that the dynamics of the swap really must
happen much faster than thermal equilibration.