arXiv subjects

Yong-Xin Yao

Publications and source records attributed to Yong-Xin Yao.

At least 37 records · Page 2Linked to original sources

arXiv2024

Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning

Quantum computing technology has the potential to revolutionize the simulation of materials and molecules in the near future. A primary challenge in achieving near-term quantum advantage is effectively mitigating the noise effects inherent in current quantum processing units (QPUs). This challenge is also decisive in the context of quantum-classical hybrid schemes employing variational quantum eigensolvers (VQEs) that have attracted significant interest in recent years. In this work, we present a novel method that employs parametric Gaussian process regression (GPR) within an active learning framework to mitigate noise in quantum computations, focusing on VQEs. Our approach, grounded in probabilistic machine learning, exploits a custom prior based on the VQE ansatz to capture the underlying correlations between VQE outputs for different variational parameters, thereby enhancing both accuracy and efficiency. We demonstrate the effectiveness of our method on a 2-site Anderson impurity model and a 8-site Heisenberg model, using the IBM open-source quantum computing framework, Qiskit, showcasing substantial improvements in the accuracy of VQE outputs while reducing the number of direct QPU energy evaluations. This work contributes to the ongoing efforts in quantum error mitigation and optimization, bringing us a step closer to realizing the potential of quantum computing in quantum matter simulations.

quant-ph↗

arXiv2023

Adaptive variational ground state preparation for spin-1 models on qubit-based architectures

We apply the adaptive variational quantum imaginary time evolution (AVQITE) method to prepare ground states of one-dimensional spin $S=1$ models. We compare different spin-to-qubit encodings (standard binary, Gray, unary, and multiplet) with regard to the performance and quantum resource cost of the algorithm. Using statevector simulations we study two well-known spin-1 models: the Blume-Capel model of transverse-field Ising spins with single-ion anisotropy, and the XXZ model with single-ion anisotropy. We consider system sizes of up to $20$ qubits, which corresponds to spin-$1$ chains up to length $10$. We determine the dependence of the number of CNOT gates in the AVQITE state preparation circuit on the encoding, the initial state, and the choice of operator pool in the adaptive method. Independent on the choice of encoding, we find that the CNOT gate count scales cubically with the number of spins for the Blume-Capel model and quartically for the anistropic XXZ model. However, the multiplet and Gray encodings present smaller prefactors in the scaling relations. These results provide useful insights for the implementation of AVQITE on quantum hardware.

quant-ph↗

arXiv2023

Ab-initio Simulations of Coherent Phonon-Induced Pumping of Carriers in Zirconium Pentatelluride

Laser-driven coherent phonons can act as modulated strain fields and modify the adiabatic ground state topology of quantum materials. Here we use time-dependent first-principles and effective model calculations to simulate the effect of the coherent phonon induced by strong terahertz electric field on electronic carriers in the topological insulator ZrTe$_5$. We show that a coherent $A_\text{1g}$ Raman mode modulation can effectively pump carriers across the band gap, even though the phonon energy is about an order of magnitude smaller than the equilibrium band gap. We reveal the microscopic mechanism of this effect which occurs via Landau-Zener-Stückelberg tunneling of Bloch electrons in a narrow region in the Brillouin zone center where the transient energy gap closes when the system switches from strong to weak topological insulator. The quantum dynamics simulation results are in excellent agreement with recent pump-probe experiments in ZrTe$_5$ at low temperature.

cond-mat.mtrl-sci↗

arXiv2023

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

quant-ph↗

arXiv2023

Benchmarks and results of the two-band Hubbard model from the Gutzwiller conjugate gradient minimization theory

Ground-state properties, such as energies and double occupancies, of a one-dimensional two-band Hubbard model are calculated using a first principles Gutzwiller conjugate gradient minimization theory. The favorable agreement with the results from the density matrix renormalization group theory demonstrates the accuracy of our method. A rotationally invariant approach is further incorporated into the method to greatly reduce the computational complexity with a speedup of 300 times. Moreover, we investigate the Mott transition between a metal and a Mott insulator by evaluating the charge gap. With greatly reduced computational effort, our method reproduces the phase diagram in reasonable agreement with the density matrix renormalization group theory.

cond-mat.str-el↗

arXiv2022

Architectures for Multinode Superconducting Quantum Computers

Many proposals to scale quantum technology rely on modular or distributed designs where individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, a limiting factor of these machines will be internode gates, which may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require a range of techniques, including improvements in entanglement generation, the use of entanglement distillation, and optimized software and compilers, and it remains unclear how improvements to these components interact to affect overall system performance, what performance from each is required, or even how to quantify the performance of each. In this paper, we employ a `co-design' inspired approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. In the case of superconducting MNQCs with microwave-to-optical links, we uncover a tradeoff between entanglement generation and distillation that threatens to degrade performance. We show how to navigate this tradeoff, lay out how compilers should optimize between local and internode gates, and discuss when noisy quantum links have an advantage over purely classical links. Using these results, we introduce a roadmap for the realization of early MNQCs which illustrates potential improvements to the hardware and software of MNQCs and outlines criteria for evaluating the landscape, from progress in entanglement generation and quantum memory to dedicated algorithms such as distributed quantum phase estimation. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.

quant-ph↗

arXiv2022

Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models

Hybrid quantum-classical embedding methods for correlated materials simulations provide a path towards potential quantum advantage. However, the required quantum resources arising from the multi-band nature of $d$ and $f$ electron materials remain largely unexplored. Here we compare the performance of different variational quantum eigensolvers in ground state preparation for interacting multi-orbital embedding impurity models, which is the computationally most demanding step in quantum embedding theories. Focusing on adaptive algorithms and models with 8 spin-orbitals, we show that state preparation with fidelities better than $99.9\%$ can be achieved using about $2^{14}$ shots per measurement circuit. When including gate noise, we observe that parameter optimizations can still be performed if the two-qubit gate error lies below $10^{-3}$, which is slightly smaller than current hardware levels. Finally, we measure the ground state energy on IBM and Quantinuum hardware using a converged adaptive ansatz and obtain a relative error of $0.7\%$.

quant-ph↗

arXiv2021

Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation

An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H$_4$, H$_2$O and BeH$_2$ molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is demonstrated through a set of AVQITE calculations of quantum spin models. Finally, it is shown that quantum Lanczos calculations can also be naturally performed alongside AVQITE without additional quantum resource costs.

physics.chem-ph↗

arXiv2021

Adaptive Variational Quantum Dynamics Simulations

We propose a general-purpose, self-adaptive approach to construct variational wavefunction ansätze for highly accurate quantum dynamics simulations based on McLachlan's variational principle. The key idea is to dynamically expand the variational ansatz along the time-evolution path such that the ``McLachlan distance'', which is a measure of the simulation accuracy, remains below a set threshold. We apply this adaptive variational quantum dynamics simulation (AVQDS) approach to the integrable Lieb-Schultz-Mattis spin chain and the nonintegrable mixed-field Ising model, where it captures both finite-rate and sudden post-quench dynamics with high fidelity. The AVQDS quantum circuits that prepare the time-evolved state are much shallower than those obtained from first-order Trotterization and contain up to two orders of magnitude fewer CNOT gate operations. We envision that a wide range of dynamical simulations of quantum many-body systems on near-term quantum computing devices will be made possible through the AVQDS framework.

quant-ph↗

arXiv2021

Electronic Properties of Single-Layer CoO$_2$/Au(111)

We report direct measurements via angle-resolved photoemission spectroscopy (ARPES) of the electronic dispersion of single-layer CoO$_2$. The Fermi contour consists of a large hole pocket centered at the $\overlineΓ$ point. To interpret the ARPES results, we use density functional theory (DFT) in combination with the multi-orbital Gutzwiller Approximation (DFT+GA), basing our calculations on crystalline structure parameters derived from x-ray photoelectron diffraction and low-energy electron diffraction. Our calculations are in good agreement with the measured dispersion. We conclude that the material is a moderately correlated metal. We also discuss substrate effects, and the influence of hydroxylation on the CoO$_2$ single-layer electronic structure.

cond-mat.mtrl-sci↗

arXiv2020

Spatial decomposition of magnetic anisotropy in magnets: application for doped Fe16N2

We propose a scheme of decomposition of the total relativistic energy in solids to intra- and interatomic contributions. The method is based on a variation of the speed of light from its value in relativistic theory to infinity (a non-relativistic limit). As an illustration of the method, we tested such decomposition in the case of a spin-orbit interaction variation for decomposition of the magnetic anisotropy energy (MAE) in CoPt. We further studied the α''-Fe16N2 magnet doped by Bi, Sb, Co and Pt atoms. It has been found that the addition of Pt atoms can enhance the MAE by as large as five times while Bi and Sb substitutions double the total MAE. Using the proposed technique we demonstrate the spatial distribution of these enhancements. Our studies also suggest that Sb, Pt and Co substitutions could be synthesized by experiments.

cond-mat.mtrl-sci↗

arXiv2020

Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning

A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we design a computational framework combining quantum-embedding (QE) methods with machine learning. This allows us to bypass altogether the most computationally-expensive components of QE algorithms, making their overall cost comparable to bare Density Functional Theory (DFT). We perform benchmark calculations of a series of actinide systems, where our method describes accurately the correlation effects, reducing by orders of magnitude the computational cost. We argue that, by producing a larger-scale set of training data, it will be possible to apply our method to systems with arbitrary stoichiometries and crystal structures, paving the way to virtually infinite applications in condensed matter physics, chemistry and materials science.

cond-mat.str-el↗

arXiv2020

Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all subterms for each excitation operator, a single-term representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit. With these strategies, VQE calculations on a noiseless quantum simulator achieve energies within a few meVs of those obtained with the full UCCSD ansatz for $\mathrm{H}_4$ square, $\mathrm{H}_4$ chain and $\mathrm{H}_6$ hexagon molecules; while the number of controlled-NOT (CNOT) gates, a measure of the quantum-circuit depth, is reduced by a factor of as large as 35. Furthermore, we introduced an efficient "score" parameter to rank the excitation operators, so that the operators causing larger energy reduction can be applied first. Using $\mathrm{H}_4$ square and $\mathrm{H}_4$ chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational ansatz.

quant-ph↗

arXiv2020

Ground state properties of one-dimensional and two-dimensional Hubbard model from Gutzwiller conjugate gradient minimization theory

We introduce Gutzwiller conjugate gradient minimization (GCGM) theory, an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. GCGM uses the Gutzwiller wave function but does not use the commonly adopted Gutzwiller approximation (GA), which is a major source of inaccuracy. Instead, the theory uses an approximation that is based on the occupation probability of the on-site configurations, rather than approximations that decouple the site-site correlations as used in the GA. We test the theory in the one-dimensional and two-dimensional Hubbard models at various electron densities and find that GCGM reproduces energies and double occupancies in reasonable agreement with benchmark data at a very small computational cost.

cond-mat.str-el↗

arXiv2018

Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model

We present detailed benchmark ground-state calculations of the one- and two-dimensional Hubbard model utilizing the cluster extensions of the rotationally invariant slave-boson (RISB) mean-field theory and the density matrix embedding theory (DMET). Our analysis shows that the overall accuracy and the performance of these two methods are very similar. Furthermore, we propose a unified computational framework that allows us to implement both of these techniques on the same footing. This provides us with a new line of interpretation and paves the ways for developing systematically new generalizations of these complementary approaches.

cond-mat.str-el↗

arXiv2018

Uncovering the Origin of Divergence in the CsM(CrO$_4$)$_2$ (M = La, Pr, Nd, Sm, Eu; Am) Family through Examination of the Chemical Bonding in a Molecular Cluster and by Band Structure Analysis

A series of f-block chromates, CsM(CrO$_4$)$_2$ (M = La, Pr, Nd, Sm, Eu; Am), were prepared revealing notable differences between the AmIII derivatives and their lanthanide analogs. While all compounds form similar layered structures, the americium compound exhibits polymorphism and adopts both a structure isomorphous with the early lanthanides as well as one that possesses lower symmetry. Both polymorphs are dark red and possess band gaps that are smaller than the LnIII compounds. In order to probe the origin of these differences, the electronic structure of $α$-CsSm(CrO$_4$)$_2$, $α$-CsEu(CrO$_4$)$_2$ and $α$-CsAm(CrO$_4$)$_2$ were studied using both a molecular cluster approach featuring hybrid density functional theory and QTAIM analysis, and by the periodic LDA+GA and LDA+DMFT methods. Notably, the covalent contributions to bonding by the f orbitals was found to be more than twice as large in the AmIII chromate than in the SmIII and EuIII compounds, and even larger in magnitude than the Am-5f spin-orbit splitting in this system. Our analysis indicates also that the Am-O covalency in $α$-CsAm(CrO$_4$)$_2$ is driven by the degeneracy of the 5f and 2p orbitals, and not by orbital overlap.

cond-mat.str-el↗

arXiv2018

Critical role of electronic correlations in determining crystal structure of transition metal compounds

The choice that a solid system "makes" when adopting a crystal structure (stable or metastable) is ultimately governed by the interactions between electrons forming chemical bonds. By analyzing 6 prototypical binary transition-metal compounds we demonstrate here that the orbitally-selective strong $d$-electron correlations influence dramatically the behavior of the energy as a function of the spatial arrangements of the atoms. Remarkably, we find that the main qualitative features of this complex behavior can be traced back to simple electrostatics, i.e., to the fact that the strong $d$-electron correlations influence substantially the charge transfer mechanism, which, in turn, controls the electrostatic interactions. This result advances our understanding of the influence of strong correlations on the crystal structure, opens a new avenue for extending structure prediction methodologies to strongly correlated materials, and paves the way for predicting and studying metastability and polymorphism in these systems.

cond-mat.str-el↗

arXiv2015

Gutzwiller Renormalization Group

We develop a variational scheme called "Gutzwiller renormalization group" (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method can exploit the low-entanglement property of the ground state in combination with the framework of the Gutzwiller wavefunction, and suggests that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and indicate that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.

cond-mat.str-el↗