arXiv subjects

Robert N. Schwartz

Publications and source records attributed to Robert N. Schwartz.

5 recordsLinked to original sources

arXiv2023

Quantum Gates Between Mesoscopic Spin Ensembles

Quantum algorithmics with single spins poses serious technological challenges such as precision fabrication, rapid decoherence, atomic-scale addressing and readout. To circumvent atomic-scale challenges, we examine the case of fully polarized mesoscopic spin ensembles (spin-coherent states) whose total angular momenta states map to qudit submanifolds. We show that in the limit where the size of the ensembles is small compared to their separation, it is possible to treat them as qubits with an effective coupling strength that scales with the number of spins. If the spins within each ensemble are decoupled (e.g., via control fields, spinning or diffusional averaging or materials engineering), one- and two-qubit gate operations can be implemented with high fidelities.

cond-mat.mes-hall↗

arXiv2022

Quantum Control of Spin Qubits Using Nanomagnets

Single-qubit gates are essential components of a universal quantum computer. Without selective addressing of individual qubits, scalable implementation of quantum algorithms is not possible. When the qubits are discrete points or regions on a lattice, the selective addressing of magnetic spin qubits at the nanoscale remains a challenge due to the difficulty of localizing and confining a classical divergence-free field to a small volume of space. Herein we propose a new technique for addressing spin qubits using voltage-control of nanoscale magnetism, exemplified by the use of voltage control of magnetic anisotropy (VCMA). We show that by tuning the frequency of the nanomagnet's electric field drive to the Larmor frequency of the spins confined to a nanoscale volume, and by modulating the phase of the drive, single-qubit quantum gates with fidelities approaching those for fault-tolerant quantum computing can be implemented. Such single-qubit gate operations have the advantage of remarkable energy efficiency, requiring only tens of femto-Joules per gate operation, and lossless, purely magnetic field control (no E-field over the target volume). Their physical realization is also straightforward using existing foundry manufacturing techniques.

cond-mat.mes-hall↗

arXiv2020

Criticality or Supersymmetry Breaking ?

In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power-spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently developed approximation-free supersymmetric theory of stochastic differential equations, or stochastics, (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti-)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation)annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.

q-bio.NC↗

arXiv2017

A neuronal dynamics study on a neuromorphic chip

Neuronal firing activities have attracted a lot of attention since a large population of spatiotemporal patterns in the brain is the basis for adaptive behavior and can also reveal the signs for various neurological disorders including Alzheimer's, schizophrenia, epilepsy and others. Here, we study the dynamics of a simple neuronal network using different sets of settings on a neuromorphic chip. We observed three different types of collective neuronal firing activities, which agree with the clinical data taken from the brain. We constructed a brain phase diagram and showed that within the weak noise region, the brain is operating in an expected noise-induced phase (N-phase) rather than at a so-called self-organized critical boundary. The significance of this study is twofold: first, the deviation of neuronal activities from the normal brain could be symptomatic of diseases of the central nervous system, thus paving the way for new diagnostics and treatments; second, the normal brain states in the N-phase are optimal for computation and information processing. The latter may provide a way to establish powerful new computing paradigm using collective behavior of networks of spiking neurons.

q-bio.NC↗

arXiv2016

Topological supersymmetry breaking: Definition and stochastic generalization of chaos and the limit of applicability of statistics

The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not "thermalized", i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.

math-ph↗