Related papers: Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits

Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits

URL: http://arxiv.org/abs/2405.06021v1
Date: Thu, 9 May 2024 18:00:05 GMT
Title: Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
Authors: Kai Klocke, Joel E. Moore, Michael Buchhold,
Abstract summary: We introduce a hybrid, non-reciprocal setup featuring a quantum circuit. The circuit is represented by a Majorana quantum chain controlled by a classical $N$-state Potts chain.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here we introduce a hybrid, non-reciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical $N$-state Potts chain undergoing pair-flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an $N$-colored loop model. It yields an equivalent description of the circuit by an $SU(N)$-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an $N$-component height field. For $N=2$, we find a diffusive growth of the half-chain entanglement towards a stationary profile $S(L)\sim L^{1/2}$ for $L$ sites. For $N\ge3$, the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth towards $S(L)\sim L^{0.57}$. This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in non-reciprocal hybrid circuit architectures.

Related papers

Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
arXiv Detail & Related papers (2024-11-06T22:51:27Z)
Hybrid Quantum-Classical Scheduling for Accelerating Neural Network Training with Newton's Gradient Descent [37.59299233291882]
We propose Q-Newton, a hybrid quantum-classical scheduler for accelerating neural network training with Newton's GD. Q-Newton utilizes a streamlined scheduling module that coordinates between quantum and classical linear solvers. Our evaluation showcases the potential for Q-Newton to significantly reduce the total training time compared to commonly used quantum machines.
arXiv Detail & Related papers (2024-04-30T23:55:03Z)
Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning [2.2301710048942103]
We analyze the trainability and controllability of variational quantum circuits (VQCs) We first design and prove the feasibility of new data loaders, performing quantum amplitude encoding of $binomnk$-dimensional vectors. Lastly, we analyze the trainability of Hamming weight preserving circuits, and show that the variance of the $binomnk$ of the subspace is bounded according to the $binomnk$ of the subspace.
arXiv Detail & Related papers (2023-09-27T10:11:07Z)
Spin-$S$ $\mathrm{U}(1)$ Quantum Link Models with Dynamical Matter on a Quantum Simulator [3.1192594881563127]
We present a bosonic mapping for the representation of gauge and electric fields with effective spin-$S$ operators. We then propose an experimental scheme for the realization of a large-scale spin-$1$ $mathrmU(1)$ QLM using spinless bosons in an optical superlattice.
arXiv Detail & Related papers (2023-05-10T18:00:01Z)
Observing super-quantum correlations across the exceptional point in a single, two-level trapped ion [48.7576911714538]
In two-level quantum systems - qubits - unitary dynamics theoretically limit these quantum correlations to $2qrt2$ or 1.5 respectively. Here, using a dissipative, trapped $40$Ca$+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics.
arXiv Detail & Related papers (2023-04-24T19:44:41Z)
Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
arXiv Detail & Related papers (2022-11-26T15:04:11Z)
Quantum Spin Puddles and Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics [0.0]
We show how a simple parameter sweep can dynamically project a family of initial product states into the constrained space. We analytically and numerically show that this method efficiently prepares a spin liquid in finite-sized regions. Our work opens up a new avenue in the study of non-equilibrium physics.
arXiv Detail & Related papers (2022-11-02T18:00:01Z)
Non-commutative phase-space Lotka-Volterra dynamics: the quantum analogue [0.0]
The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics (QM) The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales. The generality of the framework developed here extends the boundaries of the understanding of quantum-like effects on competitive microscopical bio-systems.
arXiv Detail & Related papers (2022-06-14T11:23:04Z)
Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z)
Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z)
Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions [0.0]
We study the quantum dynamics of many-body systems, in the presence of dissipation, under Kibble-Zurek protocols. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation.
arXiv Detail & Related papers (2020-03-17T10:01:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.