Quantum algorithm for the Laughlin wave function

Latorre, José I.; Picó, V.; Riera, Arnau

doi:10.1103/physreva.81.060309

Cited by 5 publications

(4 citation statements)

References 24 publications

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“…In Ref. [112], a quantum circuit that creates the Laughlin state (Eq. 58) for an arbitrary number of particles (qudits) n in the case of filling fraction one is presented.…”

Section: 1 })mentioning

confidence: 99%

A short review on entanglement in quantum spin systems

Latorre¹,

Riera²

2009

J. Phys. A: Math. Theor.

210

202

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We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.

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“…In Ref. [112], a quantum circuit that creates the Laughlin state (Eq. 58) for an arbitrary number of particles (qudits) n in the case of filling fraction one is presented.…”

Section: 1 })mentioning

confidence: 99%

A short review on entanglement in quantum spin systems

Latorre¹,

Riera²

2009

J. Phys. A: Math. Theor.

210

202

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show abstract

“…Different approaches to quantum simulation include the exact simulation of the dynamics of a strongly correlated systems by unitary gates [83], or the the creation of interesting strongly correlated states which are ground states of interesting Hamiltonians [84].…”

Section: Introductionmentioning

confidence: 99%

Dirac equation for cold atoms in artificial curved spacetimes

et al. 2011

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We argue that the Fermi-Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields, is exactly equivalent to the gauge theory Hamiltonian describing Dirac fermions in the lattice. We show that it is possible to couple the Dirac fermions to an "artificial" gravitational field, i.e. to consider the Dirac physics in a curved spacetime. We identify the special class of spacetime metrics that admit a simple realization in terms of a Fermi-Hubbard model subjected to an artificial SU (2) field, corresponding to position dependent hopping matrices. As an example, we discuss in more detail the physics of the 2+1D Rindler metric, its possible experimental realization and detection.

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“…As an example of an ansatz which can be validated by VQU, we examine a proposal by Latorre et al [70] for a family of quantum circuits that can generate Laughlin wave functions, which are conjectured to be groundstates of the fractional quantum Hall effect [71,72]. In this work they construct an ansatz for a system of n qudits that can generate the Laughlin states |Ψ n L (written in terms of single particle angular momentum eigenstates) with a filling fraction of one.…”

Section: Appendix C: Ansatz Validationmentioning

confidence: 99%

Variational quantum unsampling on a quantum photonic processor

et al. 2020

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Quantum algorithms for Noisy Intermediate-Scale Quantum (NISQ) machines have recently emerged as new promising routes towards demonstrating near-term quantum advantage (or supremacy) over classical systems. In these systems samples are typically drawn from probability distributions which -under plausible complexity-theoretic conjectures -cannot be efficiently generated classically. Rather than first define a physical system and then determine computational features of the output state, we ask the converse question: given direct access to the quantum state, what features of the generating system can we efficiently learn? In this work we introduce the Variational Quantum Unsampling (VQU) protocol, a nonlinear quantum neural network approach for verification and inference of near-term quantum circuits outputs. In our approach one can variationally train a quantum operation to unravel the action of an unknown unitary on a known input state; essentially learning the inverse of the black-box quantum dynamics. While the principle of our approach is platform independent, its implementation will depend on the unique architecture of a specific quantum processor. Here, we experimentally demonstrate the VQU protocol on a quantum photonic processor. Alongside quantum verification, our protocol has broad applications; including optimal quantum measurement and tomography, quantum sensing and imaging, and ansatz validation.

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Quantum algorithm for the Laughlin wave function

Cited by 5 publications

References 24 publications

A short review on entanglement in quantum spin systems

A short review on entanglement in quantum spin systems

Dirac equation for cold atoms in artificial curved spacetimes

Variational quantum unsampling on a quantum photonic processor

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