Entanglement Hamiltonian tomography in quantum simulation

Kokail, Christian; Bijnen, Rick van; Elben, Andreas; Vermersch, Benoît; Zoller, P.

doi:10.1038/s41567-021-01260-w

Cited by 84 publications

(74 citation statements)

References 56 publications

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“…For instance, it can be used to detect and characterize topological order and quantum phase transitions, as well as to determine whether a system obeys an area law and thus can be efficiently simulated classically [12,15,16,20,26,29,31,43,52]. Thus, Entanglement spectroscopy is an especially useful tool for analyzing outcomes of quantum simulation of many-body systems [28,30,33]. It may be similarly useful in characterizing the performance of NISQ devices.…”

Section: Introductionmentioning

confidence: 99%

Qubit-efficient entanglement spectroscopy using qubit resets

Yirka

Subaşı

2021

Quantum

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One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n-th power of the density operator of a quantum system, Tr(ρn), (related to the Rényi entropy of order n) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n, are variants of previous algorithms with width proportional to n, an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating Tr(ρn) for larger n than possible with previous algorithms.

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Section: Introductionmentioning

confidence: 99%

Qubit-efficient entanglement spectroscopy using qubit resets

Yirka

Subaşı

2021

Quantum

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“…The real-space plaquette order structure, as well as the presence of topological defects and corner-like states, could be revealed using a quantum gas microscope with single-site resolution [101][102][103]. The non-trivial topological properties could be accessed by measuring the entanglement spectrum, which can be achieved in an efficient manner using near-term quantum simulators [104,105]. Although here we focus on ultracold molecules, we notice that similar physics could be also simulated using magnetic atoms [106], where spin models with dipolar interactions have already been realized experimentally [107,108], or trapped ions [55][56][57][58].…”

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confidence: 99%

Higher-order topological quantum paramagnets

González-Cuadra

2021

Preprint

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“…Further insights could also be obtained by realizing these phases experimentally with synthetic quantum systems. In particular, protocols have been developed theoretically to characterize non-trivial topological properties of such systems, including the analysis of currents [57][58][59][60][61], randomized measurements [62][63][64], and interferometry [65][66][67][68].…”

Section: Discussionmentioning

confidence: 99%

Characterizing fractional topological phases of lattice bosons near the first Mott lobe

Boesl,

Dilip,

Pollmann

et al. 2021

Preprint

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The Bose-Hubbard model subjected to an effective magnetic field hosts a plethora of phases with different topological orders when tuning the chemical potential. Using the density matrix renormalization group method, we identify several gapped phases near the first Mott lobe at strong interactions. By a particle-hole symmetry, they are connected to a variety of quantum Hall states stabilized at low fillings. We characterize phases of both particle and hole type and identify signatures compatible with Laughlin, Moore-Read, and Bosonic Integer Quantum Hall states by calculating the quantized Hall conductance and by extracting the topological entanglement entropy. Furthermore, we analyze the entanglement spectrum of a Laughlin state of bosonic particles and holes for a range of interaction strengths. These results further corroborate the existence of topological states at high fillings, close to the first Mott lobe, as hole analogues of the respective low-filling states.

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Entanglement Hamiltonian tomography in quantum simulation

Cited by 84 publications

References 56 publications

Qubit-efficient entanglement spectroscopy using qubit resets

Qubit-efficient entanglement spectroscopy using qubit resets

Higher-order topological quantum paramagnets

Characterizing fractional topological phases of lattice bosons near the first Mott lobe

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