arXiv subjects

Bei Zeng

Publications and source records attributed to Bei Zeng.

At least 55 records · Page 3Linked to original sources

arXiv2021

Observing geometry of quantum states in a three-level system

In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the quantum state space to the Euclidean space via measurements of observables on the system. Despite the great success of this method in studying two-level quantum systems (qubits) with the celebrated Bloch sphere representation, there is always the difficulty to reveal the geometry of multi-dimensional quantum systems. Here we report the first experiment measuring the geometry of such projections beyond the qubit. Specifically, we observe the joint numerical ranges (JNRs) of a triple of observables in a three-level photonic system, providing complete classification of the JNRs. We further show that the geometry of different classes reveal ground-state degeneracies of a Hamiltonian as a linear combination of the observables, which is related to quantum phases in the thermodynamic limit. Our results offer a versatile geometric approach for exploring the properties of higher-dimensional quantum systems.

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arXiv2020

Simulating Noisy Quantum Circuits with Matrix Product Density Operators

Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in 1D with Matrix Product Density Operators (MPDO), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on Matrix Product States (MPS) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well. Compared with the method of Matrix Product Operators (MPO), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation). Consequently, in case of weak system noise, the resource cost of MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation. In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an `easy' classical simulation. Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy. With truncated inner dimension to a maximum value $κ$ and bond dimension to a maximum value $χ$, the cost of our simulation scales as $\sim NDκ^3χ^3$, for an $N$-qubit circuit with depth $D$.

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arXiv2020

Phase Analysis on the Error Scaling of Entangled Qubits in a 53-Qubit System

We have studied carefully the behaviors of entangled qubits on the IBM Rochester with various connectivities and under a "noisy" environment. A phase trajectory analysis based on our measurements of the GHZ-like states is performed. Our results point to an important fact that entangled qubits are "protected" against environmental noise by a scaling property that impacts only the weighting of their amplitudes. The reproducibility of most measurements has been confirmed within a reasonably short gate operation time. But there still are a few combinations of qubits that show significant entanglement evolution in the form of transitions between quantum states. The phase trajectory of an entangled evolution, and the impact of the sudden death of GHZ-like states and the revival of newly excited states are analyzed in details. All observed trajectories of entangled qubits arise under the influences of the newly excited states in a "noisy" intermediate-scale quantum (NISQ) computer.

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arXiv2020

Determining system Hamiltonian from eigenstate measurements without correlation functions

Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate $|ψ\rangle$ require information of nonlocal correlation functions. In this work, we develop an algorithm to determine local Hamiltonians from only local measurements on $|ψ\rangle$, by reformulating the task as an unconstrained optimization problem of certain target function of Hamiltonian parameters, with only polynomial number of parameters in terms of system size. We also develop a machine learning-based-method to solve the first-order gradient used in the algorithm. Our method is tested numerically for randomly generated local Hamiltonians and returns promising reconstruction in the desired accuracy. Our result shed light on the fundamental question on how a single eigenstate can encode the full system Hamiltonian, indicating a somewhat surprising answer that only local measurements are enough without additional assumptions, for generic cases.

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arXiv2020

Upper bounds for relative entropy of entanglement based on active learning

Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its clear geometric meaning, easy compatibility with different system sizes, and various applications in many other related quantity calculations. Lower bounds of $E_R$ were previously found based on distance to the set of positive partial transpose states. We propose a method to calculate upper bounds of $E_R$ based on active learning, a subfield in machine learning, to generate an approximation of the set of separable states. We apply our method to calculate $E_R$ for composite systems of various sizes, and compare with the previous known lower bounds, obtaining promising results. Our method adds a reliable tool for entanglement measure calculation and deepens our understanding for the structure of separable states.

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arXiv2020

Testing a Quantum Error-Correcting Code on Various Platforms

Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high fidelity. Here we propose a simple quantum error-correcting code for the detected amplitude damping channel. The code requires only two qubits. We implement the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system. For all of these systems, the error correction advantage appears when the damping rate exceeds some threshold. We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.

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arXiv2019

Higher Rank Matricial Ranges and Hybrid Quantum Error Correction

We introduce and initiate the study of a family of higher rank matricial ranges, taking motivation from hybrid classical and quantum error correction coding theory and its operator algebra framework. In particular, for a noisy quantum channel, a hybrid quantum error correcting code exists if and only if a distinguished special case of the joint higher rank matricial range of the error operators of the channel is non-empty. We establish bounds on Hilbert space dimension in terms of properties of a tuple of operators that guarantee a matricial range is non-empty, and hence additionally guarantee the existence of hybrid codes for a given quantum channel. We also discuss when hybrid codes can have advantages over quantum codes and present a number of examples.

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arXiv2019

Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model

The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here we demonstrate a first step towards simulation of the SYK model on a nuclear-spin-chain simulator. We observed the fermion paring instability of the non-Fermi liquid state and the chaotic-nonchaotic transition at simulated temperatures, as was predicted by previous theories. As the realization of the SYK model in practice, our experiment opens a new avenue towards investigating the key features of non-Fermi liquid states, as well as the quantum chaotic systems and the AdS/CFT duality.

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arXiv2019

Measuring Holographic Entanglement Entropy on a Quantum Simulator

Quantum simulation promises to have wide applications in many fields where problems are hard to model with classical computers. Various quantum devices of different platforms have been built to tackle the problems in, say, quantum chemistry, condensed matter physics, and high-energy physics. Here, we report an experiment towards the simulation of quantum gravity by simulating the holographic entanglement entropy. On a six-qubit nuclear magnetic resonance quantum simulator, we demonstrate a key result of Anti-de Sitter/conformal field theory(\adscft) correspondence---the Ryu-Takayanagi formula is demonstrated by measuring the relevant entanglement entropies on the perfect tensor state. The fidelity of our experimentally prepared the six-qubit state is 85.0\% via full state tomography and reaches 93.7\% if the signal-decay due to decoherence is taken into account. Our experiment serves as the basic module of simulating more complex tensor network states that exploring \adscft correspondence. As the initial experimental attempt to study \adscft via quantum information processing, our work opens up new avenues exploring quantum gravity phenomena on quantum simulators.

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arXiv2019

Local-measurement-based quantum state tomography via neural networks

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.

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arXiv2018

Experimental Implementation of Efficient Quantum Pseudorandomness on a 12-spin System

Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing these objects in realistic physical systems can be a challenging task. In this work, we study quantum pseudorandomness generation on a 12-spin nuclear magnetic resonance system. The experimental process is based on the recently proposed design Hamiltonian approach, which has the merit of being significantly more efficient than previous protocols. By applying random refocusing sequences to the experimental system we create a design Hamiltonian the dynamics of which quickly forms unitary designs. We then use multiple-quantum techniques to measure spreading of quantum coherences over system's degrees of freedom, and so to probe the growth of quantum pseudorandomness. The measured multiple-quantum coherence spectra indicate that substantial quantum pseudorandomness have been achieved.

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arXiv2018

Minimum Entangling Power is Close to Its Maximum

Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the 'weakest' one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the 'weakest' entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state.

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arXiv2018

Local density matrices of many-body states in the constant weight subspaces

Let $V=\bigotimes_{k=1}^{N} V_{k}$ be the $N$ spin-$j$ Hilbert space with $d=2j+1$-dimensional single particle space. We fix an orthonormal basis $\{|m_i\rangle\}$ for each $V_{k}$, with weight $m_i\in \{-j,\ldots j\}$. Let $V_{(w)}$ be the subspace of $V$ with a constant weight $w$, with an orthonormal basis $\{|m_1,\ldots,m_N\rangle\}$ subject to $\sum_k m_k=w$. We show that the combinatorial properties of the constant weight condition imposes strong constraints on the reduced density matrices for any vector $|ψ\rangle$ in the constant weight subspace, which limits the possible entanglement structures of $|ψ\rangle$. Our results find applications in the overlapping quantum marginal problems, quantum error-correcting codes, and the spin-network structures in quantum gravity.

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arXiv2018

16-qubit IBM universal quantum computer can be fully entangled

Entanglement is an important evidence that a quantum device can potentially solve problems intractable for classical computers. In this paper, we prepare connected graph states involving 8 to 16 qubits on ibmqx5, a 16-qubit superconducting quantum processor accessible via IBM cloud,using low-depth circuits. We demonstrate that the prepared state is fully entangled, i.e. the state is inseparable with respect to any fixed partition.

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arXiv2018

Symmetric vs. bosonic extension for bipartite states

A bipartite state $ρ^{AB}$ has a $k$-symmetric extension if there exists a $k+1$-partite state $ρ^{AB_1B_2\ldots B_k}$ with marginals $ρ^{AB_i}=ρ^{AB}, \forall i$. The $k$-symmetric extension is called bosonic if $ρ^{AB_1B_2\ldots B_k}$ is supported on the symmetric subspace of $B_1B_2\ldots B_k$. Understanding the structure of symmetric/bosonic extension has various applications in the theory of quantum entanglement, quantum key distribution and the quantum marginal problem. In particular, bosonic extension gives a tighter bound for the quantum marginal problem based on seperability. In general, it is known that a $ρ^{AB}$ admitting symmetric extension may not have bosonic extension. In this work, we show that when the dimension of the subsystem $B$ is $2$ (i.e. a qubit), $ρ^{AB}$ admits a $k$-symmetric extension if and only if it has a $k$-bosonic extension. Our result has an immediate application to the quantum marginal problem and indicates a special structure for qubit systems based on group representation theory.

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arXiv2018

Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems

This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.

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arXiv2018

Quantum State Tomography for Generic Pure States

We show that a generic $N$-qudit pure quantum state is uniquely determined by only $2$ of its $\lceil\frac{N+1}{2}\rceil$-particle reduced density matrices. Therefore we give a method to uniquely determine a generic $N$-qudit pure state of dimension $D=d^N$ with $O(D)$ local measurements, which is an improvement comparing with the previous known approach using $O(D\log^2 D)$ or $O(D\log D)$ measurements.

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arXiv2017

Quantum Spacetime on a Quantum Simulator

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.

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