Machine Learning Topological Phases with a Solid-State Quantum Simulator

Lian, Wenqian; Wang, Shengtao; Lu, Sirui; Huang, Yuanyuan; Wang, Fei; Yuan, Xinxing; Zhang, Wengang; Ouyang, Xiaolong; Wang, Xin; Huang, Xue-Lin; He, Lenian; Chang, Xiuying; Deng, Dong-Ling; Duan, Luming

doi:10.1103/physrevlett.122.210503

Cited by 72 publications

(47 citation statements)

References 43 publications

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“…In this appendix, we will present how to measure a quantum state in the qutrit system through quantum state tomography [40,57]. The density matrix can be written in terms of eight real parameters as…”

Section: Appendix C: Quantum State Tomographymentioning

confidence: 99%

“…Quantum simulators have been proven to be powerful platforms to experimentally study novel topological phases. During the past decade, there have been great advances in simulating various topological phases via different quantum simulators including cold atom systems [34][35][36][37][38], solid-state spin systems [39][40][41][42][43] and superconducting circuits [44][45][46][47]. Trapped ions provide an alternative flexible platform to perform quantum simulations due to its state-of-the-art technologies to control and measure [48,49], enabling us to use it to simulate exotic topological phases and directly probe their intriguing topological properties through measurements with high precision.…”

Section: Introductionmentioning

confidence: 99%

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Observation of topological Euler insulators with a trapped-ion quantum simulator

Zhao¹,

Yang²,

Jiang³

et al. 2022

Preprint

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Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and higher-order topology. However, as a minimum model of fragile topology, the twodimensional topological Euler insulator consisting of three bands remains a significant challenge to be implemented in experiments. Here, we experimentally realize a three-band Hamiltonian to simulate a topological Euler insulator with a trapped-ion quantum simulator. Through quantum state tomography, we successfully evaluate the Euler class, Wilson loop flow and entanglement spectra to show the topological properties of the Hamiltonian. We also measure the Berry phases of the lowest energy band, illustrating the existence of four crossing points protected by the Euler class. The flexibility of the trapped-ion quantum simulator further allows us to probe dynamical topological features including skyrmion-antiskyrmion pairs and Hopf links in momentum-time space from quench dynamics. Our results show the advantage of quantum simulation technologies for studying exotic topological phases and open a new avenue for investigating fragile topological phases in experiments.

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Section: Appendix C: Quantum State Tomographymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observation of topological Euler insulators with a trapped-ion quantum simulator

Zhao¹,

Yang²,

Jiang³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The proposed ML scheme answers an important question regarding the application of ML to topological phases: how much data is required to reliably distinguish topological phases? Various ML strategies have been suggested to address this issue, including the concept of quantum loop topography [20,21], and using either the wave function [22][23][24], Hamiltonian [25][26][27][28], electron density [29], system parameters [30,31], transfer matrix [32], or density matrix [33] as the input data. Here, we present a simple ML scheme based on input data comprising at most D + 1 real numbers in D dimensions applicable to different symmetry classes and weakly interacting systems.…”

Section: Introductionmentioning

confidence: 99%

A supervised learning algorithm for interacting topological insulators based on local curvature

Molignini

Zegarra

Nieuwenburg³

et al. 2021

SciPost Phys.

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Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the curvature function diverges and changes sign at certain high symmetry points in the Brillouin zone. These generic properties suggest the introduction of a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. { We apply this scheme to a variety of interacting topological insulators in different dimensions and symmetry classes. We demonstrate that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases with very little numerical effort.} Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality in the examples studied.

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“…On the other hand, machine learning (ML) is designed to discover hidden data correlations, and it is widely used in classification problems [23]. It has been recently introduced in quantum information tasks to mitigate crosstalks in multi-qubit readout [24], to enhance quantum metrology [25,26], to identify quantum phases of matter and phase transitions [27][28][29], to identify entanglement [30][31][32], and even to determine existence of quantum advantage [33], to name a few. In particular, ML shows success in efficient interpretation of quantum state tomography (QST), by being robust to partial QST and state-preparation-and-measurement (SPAM) errors [32,[34][35][36].…”

mentioning

confidence: 99%

Repetitive readout enhanced by machine learning

Liu

Chen

Liu

et al. 2020

Mach. Learn.: Sci. Technol.

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Single-shot readout is a key component for scalable quantum information processing. However, many solid-state qubits with favorable properties lack the single-shot readout capability. One solution is to use the repetitive quantum-non-demolition readout technique, where the qubit is correlated with an ancilla, which is subsequently read out. The readout fidelity is therefore limited by the back-action on the qubit from the measurement. Traditionally, a threshold method is taken, where only the total photon count is used to discriminate qubit state, discarding all the information of the back-action hidden in the time trace of repetitive readout measurement. Here we show by using machine learning (ML), one obtains higher readout fidelity by taking advantage of the time trace data. ML is able to identify when back-action happened, and correctly read out the original state. Since the information is already recorded (but usually discarded), this improvement in fidelity does not consume additional experimental time, and could be directly applied to preparation-by-measurement and quantum metrology applications involving repetitive readout. IntroductionSingle-shot readout is a key component for scalable quantum information processing [1, 2], for its close connection to state initialization and fault-tolerant quantum error correction [3]. Indeed, it is one of the main deciding factors in the selection of potential qubits. Single-shot readout has been achieved in various physical qubit systems, ranging from neutral atoms [4][5][6], to trapped ions [7], superconducting qubit [8], and solid-state defect centers [9][10][11][12][13][14][15][16]. There are however situations where a candidate qubit has favorable coherence properties, but does not naturally come with single-shot readout capabilities. Examples include Al + ions [17,18] and roomtemperature nitrogen-vacancy (NV) centers in diamond [12][13][14][15][16], where a closed optical cycle for readout is either lacking, or experimentally challenging. A solution to this problem is through repetitive quantum-nondemolition (QND) measurements [18].In the repetitive QND protocol, a controlled-NOT (CNOT) gate is applied to correlate the qubit state to an ancilla, which is subsequently read out ( figure 1(a)). If the readout operator commutes with the qubit's intrinsic Hamiltonian, in other words, if the readout is QND, one can repeat the above process multiple times to increase signal-to-noise ratio, until the desired fidelity is reached.This protocol is also known as the repetitive readout technique widely adopted in NV research at roomtemperature, where the nuclear spin state (here the 14 N or a 13 C) is repetitively read out with the help of the NV electronic spin [12,19]. In its implementations so far, the spin state was determined by comparing the total photon number collected through all the repetitive readouts with a previously established threshold ( figure 1(b)). The detected photon count numbers are thus divided into two classes, referred to as bright (dark) state of the...

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Machine Learning Topological Phases with a Solid-State Quantum Simulator

Cited by 72 publications

References 43 publications

Observation of topological Euler insulators with a trapped-ion quantum simulator

Observation of topological Euler insulators with a trapped-ion quantum simulator

A supervised learning algorithm for interacting topological insulators based on local curvature

Repetitive readout enhanced by machine learning

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