arXiv subjects

Xiao Yuan

Publications and source records attributed to Xiao Yuan.

At least 91 records · Page 5Linked to original sources

arXiv2023

Simulating the Spread of Infection in Networks with Quantum Computers

We propose to use quantum computers to simulate infection spreading in networks. We first show the analogy between the infection distribution and spin-lattice configurations with Ising-type interactions. Then, since the spreading process can be modeled as a classical Markovian process, we show that the spreading process can be simulated using the evolution of a quantum thermal dynamic model with a parameterized Hamiltonian. In particular, we analytically and numerically analyze the evolution behavior of the Hamiltonian, and prove that the evolution simulates a classical Markovian process, which describes the well-known epidemiological stochastic susceptible and infectious (SI) model. A practical method to determine the parameters of the thermal dynamic Hamiltonian from epidemiological inputs is exhibited. As an example, we simulate the infection spreading process of the SARS-Cov-2 variant Omicron in a small-world network.

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arXiv2023

A resource-efficient quantum-classical hybrid algorithm for energy gap evaluation

Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid non-variational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental-friendly. Since our algorithm is non-variational, it is also free from the "barren plateaus" problem. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator.

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arXiv2023

Scaling of entangling-gate errors in large ion crystals

Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for few ions, how to maintain the high fidelity for large scale trapped-ions still remains an open problem.Here, we present an analysis on arbitrary scale ion chain and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases of the Hilbert space dimension. For the motional heating error, We derive a much tighter bound of gate infidelity than previously estimated $O(NΓτ)$, and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals.

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arXiv2023

Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $Θ(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with $d\geqslant2$ non-zero entries, we can reduce the circuit depth to $Θ(\log(nd))$ with $O(nd\log d)$ ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.

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arXiv2023

Quantum Phase Recognition via Quantum Kernel Methods

The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an important class of Quantum Phase Recognition (QPR) problems, which are crucially important in understanding many-particle quantum systems. We prove that, under widely believed complexity theory assumptions, there exists a wide range of QPR problems that cannot be efficiently solved by classical learning algorithms with classical resources. Whereas using a quantum computer, we prove the efficiency and robustness of quantum kernel methods in solving QPR problems through Linear order parameter Observables. We numerically benchmark our algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases. Our results highlight the capability of quantum machine learning in predicting such quantum phase transitions in many-particle systems.

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arXiv2023

A Herculean task: Classical simulation of quantum computers

In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial scale but by pushing the envelope as far as possible through optimal choices of algorithms and hardware the value of the simulator tool is maximized. This work reviews the state-of-the-art numerical simulation methods i.e. the classical algorithms that emulate quantum computer evolution under specific operations. We focus on the mainstream state-vector and tensor-network paradigms while briefly mentioning alternative methods. Moreover we review the diverse applications of simulation across different facets of quantum computer development such as understanding the fundamental difference between quantum and classical computations exploring algorithm design spaces for quantum advantage predicting quantum processor performance at the design stage and characterizing fabricated devices efficiently for fast iterations. This review complements recent surveys on today's tools and implementations here we seek to acquaint the reader with an essential understanding of the theoretical basis of classical simulations detailed discussions on the advantages and limitations of different methods and the demands and challenges arising from practical use cases.

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arXiv2023

Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding

Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules, ab initio simulation of solid-state materials on quantum computers is still in its early stage, mostly owing to the fact that the system size quickly becomes prohibitively large when approaching the thermodynamic limit. In this work, we introduce an orbital-based multi-fragment approach on top of the periodic density matrix embedding theory, resulting in a significantly smaller problem size for the current near-term quantum computer. We demonstrate the accuracy and efficiency of our method compared with the conventional methodologies and experiments on solid-state systems with complex electronic structures. These include spin polarized states of a hydrogen chain (1D-H), the equation of states of a boron nitride layer (h-BN) as well as the magnetic ordering in nickel oxide (NiO), a prototypical strongly correlated solid. Our results suggest that quantum embedding combined with a chemically intuitive fragmentation can greatly advance quantum simulation of realistic materials, thereby paving the way for solving important yet classically hard industrial problems on near-term quantum devices.

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arXiv2023

Overlapped grouping measurement: A unified framework for measuring quantum states

Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as {importance sampling,} observable compatibility, or classical shadows of quantum states, different advanced measurement schemes have been proposed to greatly reduce the large measurement cost. Yet, the underline cost reduction mechanisms seem distinct from each other, and how to systematically find the optimal scheme remains a critical challenge. Here, we address this challenge by proposing a unified framework of quantum measurements, incorporating advanced measurement methods as special cases. Our framework allows us to introduce a general scheme~ -- ~overlapped grouping measurement, which simultaneously exploits the advantages of most existing methods. An intuitive understanding of the scheme is to partition the measurements into overlapped groups with each one consisting of compatible measurements. We provide explicit grouping strategies and numerically verify its performance for different molecular Hamiltonians with up to 16 qubits. Our numerical result shows significant improvements over existing schemes. Our work paves the way for efficient quantum measurement and fast quantum processing with current and near-term quantum devices.

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arXiv2022

Towards a variational Jordan-Lee-Preskill quantum algorithm

Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the 1+1 dimensional $λϕ^4$ quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational quantum circuit (quantum neural network) analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the LSZ reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the "spectral crowding" problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.

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arXiv2022

Unbiased random circuit compiler for time-dependent Hamiltonian simulation

Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$ for product formula-based methods and could be improved to be polylogarithmic with complicated circuit constructions. Here, we develop an unbiased random compiler for TDHS by combining Dyson expansion, an unbiased continuous sampling method for quantum evolution, and leading order rotations, and it is free from algorithmic errors. Our method has the single- and two-qubit gate complexity $O(Λ^2)$ with a constant sampling overhead, where $Λ$ is the time integration of the Hamiltonian strength. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems. In both examples, we observe notable improvements of our method over existing ones. Our work paves the way to efficient realizations of TDHS.

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arXiv2022

Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit

In the noisy-intermediate-scale-quantum era, Variational Quantum Eigensolver (VQE) is a promising method to study ground state properties in quantum chemistry, materials science, and condensed physics. However, general quantum eigensolvers are lack of systematical improvability, and achieve rigorous convergence is generally hard in practice, especially in solving strong-correlated systems. Here, we propose an Orbital Expansion VQE~(OE-VQE) framework to construct an efficient convergence path. The path starts from a highly correlated compact active space and rapidly expands and converges to the ground state, enabling simulating ground states with much shallower quantum circuits. We benchmark the OE-VQE on a series of typical molecules including H$_{6}$-chain, H$_{10}$-ring and N$_2$, and the simulation results show that proposed convergence paths dramatically enhance the performance of general quantum eigensolvers.

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arXiv2022

Perturbative quantum simulation

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to $48$ qubits only using an $8+1$ qubit quantum hardware. We experimentally demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.

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arXiv2022

Power of Quantum Generative Learning

The intrinsic probabilistic nature of quantum mechanics invokes endeavors of designing quantum generative learning models (QGLMs). Despite the empirical achievements, the foundations and the potential advantages of QGLMs remain largely obscure. To narrow this knowledge gap, here we explore the generalization property of QGLMs, the capability to extend the model from learned to unknown data. We consider two prototypical QGLMs, quantum circuit Born machines and quantum generative adversarial networks, and explicitly give their generalization bounds. The result identifies superiorities of QGLMs over classical methods when quantum devices can directly access the target distribution and quantum kernels are employed. We further employ these generalization bounds to exhibit potential advantages in quantum state preparation and Hamiltonian learning. Numerical results of QGLMs in loading Gaussian distribution and estimating ground states of parameterized Hamiltonians accord with the theoretical analysis. Our work opens the avenue for quantitatively understanding the power of quantum generative learning models.

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arXiv2022

Universal quantum algorithmic cooling on a quantum computer

Quantum cooling, a deterministic process that drives any state to the lowest eigenstate, has been widely used from studying ground state properties of chemistry and condensed matter quantum physics, to general optimization problems. However, the cooling procedure is generally non-unitary, hence its realization on a quantum computer either requires deep circuits or assumes specific input states with variational circuits. Here, we propose universal quantum cooling algorithms that overcome these limitations. By utilizing a dual phase representation of decaying functions, we show how to universally and deterministically realize a general cooling procedure with shallow quantum circuits. We demonstrate its applications in cooling an arbitrary input state with known ground state energy, corresponding to satisfactory, linear algebra tasks, and quantum state compiling tasks, and preparing unknown eigenvalues and eigenstates, corresponding to quantum many-body problems. Compared to quantum phase estimation, our method uses only one ancillary qubit and much shallower circuits, showing exponential improvement of the circuit complexity with respect to the final state infidelity. We numerically benchmark the algorithms for the $8$-qubit Heisenberg model and verify its feasibility for accurately finding eigenenergies and obtaining eigenstate measurements. Our work paves the way for efficient and universal quantum algorithmic cooling with near-term as well as universal fault-tolerant quantum devices.

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arXiv2022

Efficient measure for the expressivity of variational quantum algorithms

The superiority of variational quantum algorithms (VQAs) such as quantum neural networks (QNNs) and variational quantum eigen-solvers (VQEs) heavily depends on the expressivity of the employed ansatze. Namely, a simple ansatze is insufficient to capture the optimal solution, while an intricate ansatze leads to the hardness of the trainability. Despite its fundamental importance, an effective strategy of measuring the expressivity of VQAs remains largely unknown. Here, we exploit an advanced tool in statistical learning theory, i.e., covering number, to study the expressivity of VQAs. In particular, we first exhibit how the expressivity of VQAs with an arbitrary ansatze is upper bounded by the number of quantum gates and the measurement observable. We next explore the expressivity of VQAs on near-term quantum chips, where the system noise is considered. We observe an exponential decay of the expressivity with increasing circuit depth. We also utilize the achieved expressivity to analyze the generalization of QNNs and the accuracy of VQE. We numerically verify our theory employing VQAs with different levels of expressivity. Our work opens the avenue for quantitative understanding of the expressivity of VQAs.

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arXiv2022

Experimental investigation of quantum uncertainty relations with classical shadows

The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum uncertainty relations construed with relative entropy of coherence, $l_1$ norm of coherence and coherence of formation. In stead of quantum state tomographic technology, we employ the classical shadow algorithm for the detection of lower bounds in quantum uncertainty relations. With an all optical setup, we prepare a family of quantum states whose purity can be fully controlled. We experimentally explore the tightness of various lower bounds in different reference bases on the prepared states. Our results indicate the tightness of quantum coherence lower bounds dependents on the reference bases as well as the purity of quantum state.

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arXiv2021

Variational algorithms for linear algebra

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices. We show that the solutions of linear systems of equations and matrix-vector multiplications can be translated as the ground states of the constructed Hamiltonians. Based on the variational quantum algorithms, we introduce Hamiltonian morphing together with an adaptive ansatz for efficiently finding the ground state, and show the solution verification. Our algorithms are especially suitable for linear algebra problems with sparse matrices, and have wide applications in machine learning and optimisation problems. The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation. We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations. We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.

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arXiv2021

Experimental quantum state measurement with classical shadows

A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], a thrifty scheme showed how to project the quantum state into classical shadows and simultaneously predict $M$ different functions of a state with only $\mathcal{O}(\log_2 M)$ measurements, independent of the system size and saturating the information-theoretical limit. Here, we experimentally explore the feasibility of the scheme in the realistic scenario with a finite number of measurements and noisy operations. We prepare a four-qubit GHZ state and show how to estimate expectation values of multiple observables and Hamiltonians. We compare the measurement strategies with uniform, biased, and derandomized classical shadows to conventional ones that sequentially measure each state function exploiting either importance sampling or observable grouping. We next demonstrate the estimation of nonlinear functions using classical shadows and analyze the entanglement of the prepared quantum state. Our experiment verifies the efficacy of exploiting (derandomized) classical shadows and sheds light on efficient quantum computing with noisy intermediate-scale quantum hardware.

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