Sirui Lu - Research Overview

My arXiv keywords cloud 

My research mainly focuses on theoretical quantum information science. Currently, I am especially interested in the following topics:

  • Many-body physics, tensor network, and topological phases.

  • Quantum algorithms on near-term devices: quantum machine learning and quantum approximate optimization algorithms (QAOA).

  • Quantum error correction and fault tolerance.

  • Quantum simulation on AMO platforms.

  • Quantum complexity, quantum information theory and more.

(Updated July 9, 2019).

Many-body physics, tensor network, and topological phases

We derived neural network representations for many quantum many-body states, such as (generalized) stabilizer states, and topological ordered states. We expect our exact representation results will inspire future numerical studies for larger system sizes.

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Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines.
Sirui Lu, Xun Gao, L.-M. Duan.
Phys. Rev. B, 99, 155136, arXiv:quant-ph/1810.02352
Abstract: Representation by neural networks, in particular by restricted Boltzmann machines (RBM), has provided a powerful computational tool to solve quantum many-body problems. An important open question is how to characterize which class of quantum states can be efficiently represented with RBMs. Here, we show that RBMs can efficiently represent a wide class of many-body entangled states with rich exotic topological orders. This includes: (1) ground states of double semion and twisted quantum double models with intrinsic topological orders; (2) states of the AKLT model and two-dimensional CZX model with symmetry protected topological orders; (3) states of Haah code model with fracton topological order; (4) (generalized) stabilizer states and hypergraph states that are important for quantum information protocols. One twisted quantum double model state considered here harbors non-abelian anyon excitations. Our result shows that it is possible to study a variety of quantum models with exotic topological orders and rich physics using the RBM computational toolbox.

Quantum algorithms on near-term devices

Two candidates for noisy intermediate quantum technologies are quantum machine learning algorithms and quantum approximate optimization algorithm (QAOA). For QML, I did a numerical simulation for a generative quantum machine learning model and proposed a variational learning algorithm. For QAOA, the two most important open questions are its circuit depth scaling of intermediate depth and its diabatic mechanism. I address the first question with Murphy Yuezhen Niu and Prof. Isaac Chuang and the second question with Sheng-Tao Wang on diabatic annealing.

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Optimizing QAOA: Success Probability and Runtime Dependence on Circuit Depth.
Murphy Yuezhen Niu, Sirui Lu, Issac L. Chuang
Abstract: The quantum approximate optimization algorithm (QAOA) initially proposed by Farhi et al. is generalizable to a large family of heuristic quantum algorithms, where computation consists of interleaved unitary transformations induced by two mutually non-commuting sets of Hamiltonians. Due to its simplicity, universality, and optimality for many variational problems, QAOA has been considered a useful near-term algorithm for conducting classical optimization and quantum simulation. We answer a long-held open question of how the QAOA perform in regard to its success probability and runtime dependence on the quantum circuit depth in solving a state transfer problem in a one-dimensional spin chain. We provide an analytic proof on the success probability scaling by leveraging the spectral property of the XY Hamiltonian which is supported by the numerical results in optimized QAOA for up to N=20 qubits. We prove the perfect state transfer needs O(N) time using Lieb-Robinson bound and confirm this numerically.

Quantum entanglement

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Separability-entanglement classifier via machine learning
Sirui Lu, Shilin Huang, Keren Li, Jun Li, Jianxin Chen, Dawei Lu, Zhengfeng Ji, Yi Shen, Duanlu Zhou, and Bei Zeng.
Phys. Rev. A, 98:012315, Jul 2018.
Abstract: The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial transpose (PPT) criterion and the k-symmetric extendibility criterion to tackle this problem in practice, none of them enables a general, effective solution to the problem even for small dimensions. Explicitly, separable states form a high-dimensional convex set, which exhibits a vastly complicated structure. In this work, we build a new separability-entanglement classifier underpinned by machine learning techniques. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum entanglement via the machine learning approach.
(published version) (arXiv) (slide) (code)

Quantum simulation on AMO platforms.

I have collaborated with many experimentalists in simulating quantum physics and benchmarking quantum devices on NMR and NV center systems. Collaborations on different experiments platform deepen my understanding of the strength and limitations of different systems. This, in turn, will help me to better work on theories with relevance to state-of-the-art experiments.

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Experimental machine learning of topological phases in a solid-state quantum simulator
W.-Q. Lian∗, S.-T. Wang∗, S.-R. Lu, Y.-Y. Huang, F. Wang, X.-X. Yuan, W.-G. Zhang, X.-L. Ouyang, X. Wang, X.-Z. Huang, L. He, X.-Y. Chang, D.-L. Deng, and L.-M. Duan.
Phys. Rev. Lett. 122, 210503, 2019.
Abstract: The experimental identification of topological phases is an important task in condensed matter physics. Traditionally, this might be accomplished by measuring some exotic properties, such as quantized Hall conductance, that are rooted in the topology of the quantum systems. Here, we report the first proof-of-principle experimental demonstration of a machine learning approach, with a focus on the three-dimensional chiral topological insulators. We show that convolutional neural networks—a class of deep feed-forward artificial neural networks with widespread applications in machine learning—can be trained to successfully identify different chiral topological phases from experimental data generated by a solid-state quantum simulator. Our results explicitly showcase the exceptional power of machine learning in the experimental detection of topological phases, which paves a new way to study rich topological phenomena with the machine learning toolbox.

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Quantum Spacetime on a Quantum Simulator.
Keren Li*, Youning Li*, Muxin Han*, Sirui Lu, Jie Zhou, Dong Ruan, Guilu Long, Yidun Wan, Dawei Lu, Bei Zeng.
(Communications Physics, to appear)], arXiv:quant-ph/1712.08711
Abstract: We experimentally simulate the spin networks—a fundamental description of quantum spacetime at the Planck level. We achieve this by simulating quantum tetrahedra and their interactions. The tensor product of these quantum tetrahedra comprises spin networks. In this initial attempt to study quantum spacetime by quantum information processing, on a four-qubit nuclear magnetic resonance quantum simulator, we simulate the basic module—comprising five quantum tetrahedra—of the interactions of quantum spacetime. By measuring the geometric properties on the corresponding quantum tetrahedra and simulate their interactions, our experiment serves as the basic module that represents the Feynman diagram vertex in the spin-network formulation of quantum spacetime.
My contribution: tensor network simulation of spin networks.

Together with my collaborators in Prof. Bei Zeng’s group, we develope the first NMR cloud quantum computing platform: NMRCloudQ.

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NMRCloudQ: A Quantum Cloud Experience on a Nuclear Magnetic Resonance Quantum Computer
Tao Xin, Shilin Huang, Sirui Lu, Keren Li, Zhihuang Luo, Zhangqi Yin, Jun Li, Dawei Lu, Guilu Long, Bei Zeng.
published in Science Bulletin, 2017, ISSN 2095-9273.
(published version)(arXiv)
Abstract: Cloud-based quantum computing is anticipated to be the most useful and reachable form for public users to experience with the power of quantum. As initial attempts, IBM Q has launched influential cloud services on a superconducting quantum processor in 2016, but no other platforms have followed up yet. Here, we report our new cloud quantum computing service – NMRCloudQ (, where nuclear magnetic resonance, one of the pioneer platforms with mature techniques in experimental quantum computing, plays as the role of implementing computing tasks. Our service provides a comprehensive software environment preconfigured with a list of quantum information processing packages, and aims to be freely accessible to either amateurs that look forward to keeping pace with this quantum era or professionals that are interested in carrying out real quantum computing experiments in person. In our current version, four qubits are already usable within average 99.10% single-qubit gate fidelity and 97.15% two-qubit fidelity via randomized benchmarking tests. Improved control precisions as well as a new seven-qubit processor are also in preparation and will be available later.

We proposed a machine learning based method for the local quantum state tomography, which may be scalable to a large number of qubits.

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Local-measurement-based quantum state tomography via neural networks
Tao Xin*, Sirui Lu*, Ningping Cao*, Galit Anikeeva, Dawei Lu, Jun Li, Guilu Long, Bei Zeng.
(arXiv) (code)
Abstract: Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the reconstruction of the full state thereafter is hard. Here, we present a machine learning method to recover the full quantum state from its local information, where a fully-connected neural network is built to fulfill the task with up to seven qubits. In particular, we test the neural network model with a practical dataset, that in a 4-qubit nuclear magnetic resonance system our method yields global states via the 2-local information with high accuracy. Our work paves the way towards scalable state tomography in large quantum systems.

Quantum error correction and fault-tolerance

In this work, we construct quantum codes that allow transmitting both quantum and classical information with better parameters than hybrid codes obtained from the best-known stabilizer quantum codes. Our code construction is based on the codeword-stabilized code, which is the most general framework for constructing codes beyond stabilizer formalisms. This work elicited my interesting in non-stabilizer codes.

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Codes for simultaneous transmission of quantum and classical information
Markus Grassl, Sirui Lu, and Bei Zeng.
Published in IEEE International Symposium on Information Theory Proceedings (ISIT), 2017, Jul 2018.
(published version) (arXiv) (slides)
Abstract: We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as ‘hybrid codes’. We construct hybrid codes [[n,k:m,d]]_q with length n and distance d, that simultaneously transmit k qudits and m symbols from a classical alphabet of size q. Many good codes such as [[7,1:1,3]]_2, [[9,2:2,3]]_2, [[10,3:2,3]]_2, [[11,4:2,3]]_2, [[11,1:2,4]]_2, [[13,1:4,4]]_2, [[13,1:1,5]]_2, [[14,1:2,5]]_2, [[15,1:3,5]]_2, [[19,9:1,4]]_2, [[20,9:2,4]]_2, [[21,9:3,4]]_2, [[22,9:4,4]]_2 have been found. All these codes have better parameters than hybrid codes obtained from the best known stabilizer quantum codes.

Since then, I became particularly interested in understanding how non-stabilizer codes could attribute to the realization of large-scale quantum computation. Examples abound: non-additive codes with a higher rate, topologically ordered system such as double semion and double Fibonacci, many fault-tolerant techniques involving the code deformation, code-switching, gauge fixing, and “loosely” versions of transversal gates. I am also interested in studying different physics from the quantum error correction perspective — for example, topological order and the black hole.