Entanglement Barrier and its Symmetry Resolution: Theory and Experimental Observation

Rath, Aniket; Vitale, Vittorio; Murciano, Sara; Votto, Matteo; Dubail, Jérôme; Kueng, Richard; Branciard, Cyril; Calabrese, Pasquale; Vermersch, Benoît

doi:10.1103/prxquantum.4.010318

Cited by 44 publications

(23 citation statements)

References 116 publications

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“…As shown in Table S4, such an attempt for a simple QCMPS (Figure S4) is not successful. Therefore, the capability of QCMPS to generate exponentially large tensors on a quantum computer does lead to a practical advantage over classical computers, which makes it possible to simulate systems requiring a bond dimension that goes beyond the capability of classical algorithms such as in the time-dependent simulations 88 with the entanglement barrier effect.…”

Section: Numerical Resultsmentioning

confidence: 99%

Quantum Circuit Matrix Product State Ansatz for Large-Scale Simulations of Molecules

Fan,

Liu,

et al. 2023

J. Chem. Theory Comput.

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As demonstrated in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is determined by the size of the matrices or, in other words, the bond dimension, which unfortunately may be required to be very large in quantum chemistry simulations. In this study, we propose to calculate the ground state energies of molecular systems by variationally optimizing quantum circuit MPS (QCMPS) with a relatively small number of qubits. It is demonstrated that with carefully chosen circuit structure and orbital localization scheme, QCMPS can reach a similar accuracy as that achieved in DMRG with an exponentially large bond dimension. QCMPS simulation of a linear hydrogen molecular chain with 50 orbitals can reach the chemical accuracy using only 6 qubits at a moderate circuit depth. These results suggest that QCMPS is a promising wave function ansatz in the variational quantum eigensolver algorithm for molecular systems.

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Section: Numerical Resultsmentioning

confidence: 99%

Quantum Circuit Matrix Product State Ansatz for Large-Scale Simulations of Molecules

Fan,

Liu,

et al. 2023

J. Chem. Theory Comput.

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“…it is complex, and wonder if the symmetry-resolved entropy is positive-definite as well. Of course, the entanglement entropy is not the only entanglement measure that can be resolved in symmetry sectors, for example the negativity, which can be employed to study entanglement in disjoint subsystems [64,71], or the operator entanglement [34]. One can also consider to carry out a similar analysis for them.…”

Section: Discussionmentioning

confidence: 99%

“…Recent experiments with cold atoms and ion traps have shown that some properties of many-body quantum systems can be understood by analyzing the entanglement in the symmetry sectors of the theory [30][31][32][33][34]. The basic tool to investigate how entanglement distributes among symmetry sectors is the symmetry-resolved entanglement entropy [35][36][37], which provides a finer measure of the entanglement content in extended systems that is not accessible from the total entanglement entropy.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-resolved entanglement in critical non-Hermitian systems

Fossati¹,

Ares²,

Calabrese³

2023

Preprint

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“…Remarkably, the symmetry resolved entanglement has been recently experimentally accessed in trapped-ion setups [86][87][88].…”

Section: J Stat Mech (2023) 073102mentioning

confidence: 99%

Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

2023

Self Cite

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We consider the ground state of two species of one-dimensional critical free theories coupled together via a conformal interface. They have an internal U(1) global symmetry and we investigate the quantum fluctuations of the total charge on one side of the interface, giving analytical predictions for the full counting statistics, the charged moments of the reduced density matrix and the symmetry resolved Rényi entropies. Our approach is based on the relation between the geometry with the defect and the homogeneous one, and it provides a way to characterize the spectral properties of the correlation functions restricted to one of the two species. Our analytical predictions are tested numerically, finding a perfect agreement.

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Entanglement Barrier and its Symmetry Resolution: Theory and Experimental Observation

Cited by 44 publications

References 116 publications

Quantum Circuit Matrix Product State Ansatz for Large-Scale Simulations of Molecules

Quantum Circuit Matrix Product State Ansatz for Large-Scale Simulations of Molecules

Symmetry-resolved entanglement in critical non-Hermitian systems

Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

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