QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

Weinberg, Phillip; Bukov, Marin

doi:10.21468/scipostphys.7.2.020

Cited by 298 publications

(149 citation statements)

References 112 publications

(161 reference statements)

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“…DS acknowledges support from the FWO as post-doctoral fellow of the Research Foundation -Flanders and CMTV. We used QuSpin for simulating the dynamics of the qubit systems [89,90]. The authors are pleased to acknowledge that the computational work reported on in this paper was performed on the Shared Computing Cluster which is administered by Boston University's Research Computing Services.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Reinforcement Learning in Different Phases of Quantum Control

Bukov¹,

Day²,

Sels³

et al. 2018

Phys. Rev. X

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335

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The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet, preparing states quickly and with high fidelity remains a formidable challenge. In this work we implement cutting-edge Reinforcement Learning (RL) techniques and show that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in non-integrable many-body quantum systems of interacting qubits. RL methods learn about the underlying physical system solely through a single scalar reward (the fidelity of the resulting state) calculated from numerical simulations of the physical system. We further show that quantum state manipulation, viewed as an optimization problem, exhibits a spinglass-like phase transition in the space of protocols as a function of the protocol duration. Our RL-aided approach helps identify variational protocols with nearly optimal fidelity, even in the glassy phase, where optimal state manipulation is exponentially hard. This study highlights the potential usefulness of RL for applications in out-of-equilibrium quantum physics. S = {s = (t, h x (t))}, A = {a = δh x }, R = {r ∈ [0, 1]}.

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Section: Acknowledgmentsmentioning

confidence: 99%

Reinforcement Learning in Different Phases of Quantum Control

Bukov¹,

Day²,

Sels³

et al. 2018

Phys. Rev. X

Self Cite

392

335

View full text Add to dashboard Cite

show abstract

“…NSF PHY-1748958. We used QuSpin for simulating the dynamics of the spin systems [89,90]. The authors are pleased to acknowledge that the computational work reported on in this paper was performed on the Shared Computing Cluster which is administered by Boston University's Research Computing Services.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Geometric Speed Limit of Accessible Many-Body State Preparation

2019

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We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol duration is bounded from below by the geodesic length set by the quantum geometric tensor. The conjecture implies a geometric lower bound for the quantum speed limit (QSL). We prove the conjecture for arbitrary, sufficiently slow protocols using adiabatic perturbation theory and show that the bound is saturated by geodesic protocols, which keep the energy variance constant along the trajectory. Our conjecture implies that any optimal unit-fidelity protocol, even those that drive the system far from equilibrium, are fundamentally constrained by the quantum geometry of adiabatic evolution. When the control space includes all possible couplings, spanning the full Hilbert space, we recover the well-known Mandelstam-Tamm bound. However, using only accessible local controls to anneal in complex models such as glasses or to target individual excited states in quantum chaotic systems, the geometric bound for the quantum speed limit can be exponentially large in the system size due to a diverging geodesic length. We validate our conjecture both analytically by constructing counter-diabatic and fast-forward protocols for a three-level system, and numerically in nonintegrable spin chains and a nonlocal SYK model. arXiv:1804.05399v2 [quant-ph]

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“…Acknowledgements.-It is a pleasure to thank Ehud Altman, Jorge Hirsch, Laimei Nie, and Daniel Parker for helpful discussions. Some of the quantum calculations have been performed using the QuSpin package [55,56] Appendix A: Saddle-dominated scrambling in Dicke model In this appendix, we show that saddle-dominated scrambling also takes place in the Dicke model [42,58]. Originally, it was conceived to describe N two-level atoms coupled to a single optical cavity mode.…”

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confidence: 99%

Does Scrambling Equal Chaos?

2020

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Focusing on semiclassical systems, we show that the parametrically long exponential growth of outof-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in an integrable model. We derive a lower bound on the OTOC Lyapunov exponent which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e. for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.

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QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

Cited by 298 publications

References 112 publications

Reinforcement Learning in Different Phases of Quantum Control

Reinforcement Learning in Different Phases of Quantum Control

Geometric Speed Limit of Accessible Many-Body State Preparation

Does Scrambling Equal Chaos?

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