arXiv subjects

Christian Z. Pratt

Publications and source records attributed to Christian Z. Pratt.

4 recordsLinked to original sources

arXiv2026

Extreme-Scale Ising Machines with Cluster Mean-Field Theory

Scaling analog and digital Ising machines to larger problems requires overcoming finite device capacity and the cost of communication between devices. We present cluster mean-field theory (CMFT), a framework that partitions a large interaction graph into clusters sized to fit available hardware. Each cluster performs local updates independently, while interactions across cluster boundaries enter through periodically updated effective biases computed from boundary-spin averages. To reduce the error introduced by fixed cluster boundaries, we introduce dynamic partitioning, which cycles through multiple partitions so that interactions approximated by mean fields at one stage can act through instantaneous spins at another. On three-dimensional spin glasses and planted Pegasus instances, dynamic CMFT exhibits power-law decay of residual energy over sweep budgets. This shows that solution quality continues to improve with computational effort despite the mean-field approximation. An automated graph partitioner combined with a weighted recovery ratio provides a practical heuristic for selecting partition combinations on graphs without natural cut directions. We demonstrate CMFT on four GPUs with approximately four million p-bits, reaching comparable energy densities up to 15 times faster than a single-GPU implementation of the full graph. By coupling locally evolving clusters through programmable effective biases, CMFT provides a route to extreme-scale Ising machines on both analog and digital hardware.

cond-mat.dis-nn↗

arXiv2026

Metastable Dynamical Computing with Energy Landscapes: A Primer

Smartphones, laptops, and data centers are CMOS-based technologies that ushered our world into the information age of the 21st century. Despite their advantages for scalable computing, their implementations come with surprisingly large energetic costs. This challenge has revitalized scientific and engineering interest in energy-efficient information-processing designs. One current paradigm -- dynamical computing -- controls the location and shape of minima in potential energy landscapes that are connected to a thermal environment. The landscape supports distinguishable metastable energy minima that serve as a system's mesoscopic memory states. Information is represented by microstate distributions. Dynamically manipulating the memory states then corresponds to information processing. This framing provides a natural description of the associated thermodynamic transformations and required resources. Appealing to bifurcation theory, a computational protocol in the metastable regime can be analyzed by tracking the evolution of fixed points in the state space. We illustrate the paradigm's capabilities by performing 1-bit and 2-bit computations with double-well and quadruple-well potentials, respectively. These illustrate how dynamical computing can serve as a basis for designing universal logic gates and investigating their out-of-equilibrium thermodynamic performance.

cond-mat.stat-mech↗

arXiv2024

Extracting Equations of Motion from Superconducting Circuits

Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principle circuit design, though, leads to prohibitive algebraic complications when deriving the effective equations of motion -- complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically-grounded constraints. This leads to efficient, practical circuit prototyping and access to scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by the quantum flux parametron (QFP). We then show how inductively coupling two QFPs produces a device that is capable of executing 2-bit computations via its composite potential energy landscape. More generally, the synthesis methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.

cond-mat.stat-mech↗

arXiv2024

Controlled Erasure as a Building Block for Universal Thermodynamically-Robust Superconducting Computing

Reducing the energy inefficiency of conventional CMOS-based computing devices -- which rely on logically irreversible gates to process information -- remains both a fundamental engineering challenge and a practical social challenge of increasing importance. We extend an alternative computing paradigm that manipulates microstate distributions to store information in the metastable minima determined by an effective potential energy landscape. These minima serve as mesoscopic memories that are manipulated by a dynamic landscape to perform information processing. Central to our results is the control erase (CE) protocol that controls the landscape's metastable minima to determine whether information is preserved or erased. Importantly, successive protocol executions can implement a NAND gate -- a logically-irreversible universal logic gate. We show how to practically implement this in a device created by two inductively-coupled superconducting quantum interference devices (SQUIDs). We identify circuit parameter ranges that give rise to effective CEs and establish the device's robustness against logical errors. These SQUID-based logical devices are capable of operating above GHz frequencies and at the $k_\text{B} T$ energy scale. Due to this, optimized devices and associated protocols provide a universal-computation substrate that is both computationally fast and energy efficient.

cond-mat.supr-con↗