arXiv subjects

Ryan Levy

Publications and source records attributed to Ryan Levy.

16 recordsLinked to original sources

arXiv2026

Compiling the 2D Fermi-Hubbard ground-state energy estimation algorithm for active volume quantum architectures

As quantum computing enters the early fault-tolerant era, circuit compilation choices will increasingly depend on details of the underlying architecture rather than solely optimizing for generic proxies such as non-Clifford count. We present an active-volume-aware compilation of the ground-state energy estimation algorithm for the two-dimensional Fermi-Hubbard model using quantum phase estimation and Trotterized time evolution. The proposed compilation reduces the active volume across $L\times L$ square lattices with $L=4$ to $20$, achieving up to a $3.9\times$ reduction over prior work optimized for non-Clifford cost. As a by-product of these compilation improvements, the resulting circuits also achieve state-of-the-art Toffoli counts, with a ~$2\times$ reduction for the $L=20$ case. Lastly, the active volume architecture and recent execution scheduling advances provide a means of translating these reduction trends into runtime. This demonstrates the increasing importance of architecture-aware compilation for practical early fault-tolerant quantum computing.

quant-ph↗

arXiv2026

AutoHF: a general Hartree-Fock solver utilizing direct energy minimization with automatic differentiation

We present autohf, a general, easy-to-use mean-field solver for quantum many-fermion Hamiltonians. It allows the user to bypass the process of deciphering the mean-field form for each many-body Hamiltonian $H$ and thus avoid setting up a tailored program for each $H$. Rather, autohf finds the optimal Slater determinant $|\Psi\rangle$, written in terms of orbital coefficients and subject to symmetry constraints, by directly minimizing the variational energy $\langle H \rangle$. By embracing this variational approach, autohf makes use of the growing power of automatic differentiation and optimization tools developed by the machine learning community.

cond-mat.str-el↗

arXiv2025

Magic of the Well: assessing quantum resources of fluid dynamics data

We investigate the quantum resource requirements of a dataset generated from simulations of two-dimensional, periodic, incompressible shear flow, aimed at training machine learning models. By measuring entanglement and non-stabilizerness on MPS-encoded functions, we estimate the computational complexity encountered by a stabilizer or a tensor network solver applied to Computational Fluid Dynamics (CFD) simulations across different flow regimes. Our analysis reveals that, under specific initial conditions, the shear width identifies a transition between resource-efficient and resource-intensive regimes for non-trivial evolution. Furthermore, we find that the two resources qualitatively track each other in time, and that the mesh resolution along with the sign structure play a crucial role in determining the resource content of the encoded state. These findings offer useful guidelines for the development of scalable, quantum-inspired approaches to fluid dynamics.

quant-ph↗

arXiv2025

Searching for superconductivity in doped triangular lattice Kitaev magnets

Motivated by exploring correlated metals with frustrating bond-dependent exchange interactions, we study hole and electron doped Kitaev Mott insulators on the triangular lattice. Using homogeneous parton mean field theory, we find that the stripe antiferromagnetic (AFM) order for Kitaev coupling $K>0$ and the ferromagnetic (FM) order for $K<0$, both vanish at sufficiently large doping, beyond which we find regimes with chiral $d\pm i d$ singlet pairing and $p\pm ip$ triplet pairing respectively. Our tensor network computations however reveal that the superconducting correlations are strongly suppressed; while FM order stubbornly persists for the doped $K<0$ model, the doped $K>0$ model features emergent spin-charge modulated stripe orders. At higher hole doping for $K > 0$, where AFM order is more strongly suppressed than for the electron doped case, incorporating a sufficiently strong nearest-neighbor attraction yields evidence for singlet $d$-wave superconductivity with Luttinger parameter $K_{\rm sc} < 1$. Our work sets the stage for a broader exploration of doping effects in triangular lattice magnets such as NaRuO$_2$ which feature bond-dependent exchange interactions.

cond-mat.str-el↗

arXiv2024

Compressing multivariate functions with tree tensor networks

Tensor networks are a compressed format for multi-dimensional data. One dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum functions by ``quantizing'' the inputs into discrete binary digits. Here we demonstrate the power of more general tree tensor networks (TTNs) for this purpose. We provide direct constructions of a number of elementary functions as generic tree tensor networks and interpolative constructions for more complicated functions via a generalization of the tensor cross interpolation algorithm. For a range of multi-dimensional functions we show how more structured tree tensor networks offer a significantly more efficient ansatz than the commonly used tensor train. Finally, we demonstrate how the methods introduced in this work can be used to realize a TTN-based solver for multi-dimensional, non-linear Fredholm equations.

quant-ph↗

arXiv2024

Ground state phases of the two-dimension electron gas with a unified variational approach

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different ansatze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs = 37 +/- 1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.

cond-mat.str-el↗

arXiv2023

Automatic Order Detection and Restoration Through Systematically Improvable Variational Wave Functions

Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte Carlo and modern variational optimization techniques including automatic differentiation. The resulting ansatz, consisting of several slices of optimized projectors, is highly expressive and systematically improvable. We benchmark this form on the two-dimensional Hubbard model, using both cylindrical and large, fully periodic supercells. The computed ground-state energies are competitive with the best variational results. Moreover, the optimized wave functions predict the correct ground-state order with near full symmetry restoration (i.e. translation invariance) despite initial states with incorrect orders. The ansatz can become a tool for local order prediction, leading to a new paradigm for variational studies of bulk systems. It can also be viewed as an approach to produce accurate and systematically improvable wave functions in a convenient form of non-orthogonal Slater determinants (e.g., for quantum chemistry) at polynomial computational cost.

cond-mat.str-el↗

arXiv2022

Towards solving the Fermi-Hubbard model via tailored quantum annealers

The Fermi-Hubbard model (FHM) on a two dimensional square lattice has long been an important testbed and target for simulating fermionic Hamiltonians on quantum hardware. We present an alternative for quantum simulation of FHMs based on an adiabatic protocol that could be an attractive target for next generations of quantum annealers. Our results rely on a recently introduced low-weight encoding that allows the FHM to be expressed in terms of Pauli operators with locality of at most three. We theoretically and numerically determine promising quantum annealing setups for both interacting 2D spinless and spinful systems, that enable to reach near the ground state solution with high fidelity for systems as big as $6\times 6$ (spinless) and $4\times 3$ (spinful). Moreover, we demonstrate the scaling properties of the minimal gap and analyze robustness of the protocol against control noise. Additionally, we identify and discuss basic experimental requirements to construct near term annealing hardware tailored to simulate these problems. Finally, we perform a detailed resource estimation for the introduced adiabatic protocol, and discuss pros and cons of this approach relative to gate-based approaches for near-term platforms.

quant-ph↗

arXiv2021

Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers

Quantum process tomography is a powerful tool for understanding quantum channels and characterizing properties of quantum devices. Inspired by recent advances using classical shadows in quantum state tomography [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020).], we have developed ShadowQPT, a classical shadow method for quantum process tomography. We introduce two related formulations with and without ancilla qubits. ShadowQPT stochastically reconstructs the Choi matrix of the device allowing for an a-posteri classical evaluation of the device on arbitrary inputs with respect to arbitrary outputs. Using shadows we then show how to compute overlaps, generate all $k$-weight reduced processes, and perform reconstruction via Hamiltonian learning. These latter two tasks are efficient for large systems as the number of quantum measurements needed scales only logarithmically with the number of qubits. A number of additional approximations and improvements are developed including the use of a pair-factorized Clifford shadow and a series of post-processing techniques which significantly enhance the accuracy for recovering the quantum channel. We have implemented ShadowQPT using both Pauli and Clifford measurements on the IonQ trapped ion quantum computer for quantum processes up to $n=4$ qubits and achieved good performance.

quant-ph↗

arXiv2021

Entanglement Entropy Transitions with Random Tensor Networks

Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network proposed to have an entanglement entropy transition first considered by Vasseur et al.[Phys. Rev. B 100, 134203 (2019)]. We find that by varying the bond dimension of the tensors in the network we can observe a transition between an area and volume phase with a logarithmic critical point around $D\approx 2$. We further characterize the critical behavior measuring a critical exponent using entanglement entropy and the tripartite quantum mutual information, observe a crossover from a `nearly pure' to entangled area law phase using the the distributions of the entanglement entropy and find a cubic decay of the pairwise mutual information at the transition. We further consider the dependence of these observables for different R\'enyi entropy. This work helps further validate and characterize random tensor networks as a paradigmatic examples of an entanglement transition.

cond-mat.stat-mech↗

arXiv2020

Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions

The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter physics systems. However, its efficient parallel implementation is challenging due to limited concurrency, large memory footprint, and tensor sparsity. We mitigate these problems by implementing two new parallel approaches that handle block sparsity arising in DMRG, via Cyclops, a distributed memory tensor contraction library. We benchmark their performance on two physical systems using the Blue Waters and Stampede2 supercomputers. Our DMRG performance is improved by up to 5.9X in runtime and 99X in processing rate over ITensor, at roughly comparable computational resource use. This enables higher accuracy calculations via larger tensors for quantum state approximation. We demonstrate that despite having limited concurrency, DMRG is weakly scalable with the use of efficient parallel tensor contraction mechanisms.

cs.DC↗

arXiv2020

Topology and the one-dimensional Kondo-Heisenberg model

The Kondo-Heinsberg chain is an interesting model of a strongly correlated system which has a broad superconducting state with pair-density wave (PDW) order. Some of us have recently proposed that this PDW state is a symmetry-protected topological (SPT) state, and the gapped spin sector of the model supports Majorana zero modes. In this work, we reexamine this problem using a combination of numeric and analytic methods. In extensive density matrix renormalization group calculations, we find no evidence of a topological ground state degeneracy or the previously proposed Majorana zero modes in the PDW phase of this model. This result motivated us to reexamine the original arguments for the existence of the Majorana zero modes. A careful analysis of the effective continuum field theory of the model shows that the Hilbert space of the spin sector of the theory does not contain any single Majorana fermion excitations. This analysis shows that the PDW state of the doped 1D Kondo-Heisenberg model is not an SPT with Majorana zero modes.

cond-mat.str-el↗

arXiv2019

Mitigating the Sign Problem Through Basis Rotations

Quantum Monte Carlo simulations of quantum many body systems are plagued by the Fermion sign problem. The computational complexity of simulating Fermions scales exponentially in the projection time $\beta$ and system size. The sign problem is basis dependent and an improved basis, for fixed errors, lead to exponentially quicker simulations. We show how to use sign-free quantum Monte Carlo simulations to optimize over the choice of basis on large two-dimensional systems. We numerically illustrate these techniques decreasing the `badness' of the sign problem by optimizing over single-particle basis rotations on one and two-dimensional Hubbard systems. We find a generic rotation which improves the average sign of the Hubbard model for a wide range of $U$ and densities for $L \times 4$ systems. In one example improvement, the average sign (and hence simulation cost at fixed accuracy) for the $16\times 4$ Hubbard model at $U/t=4$ and $n=0.75$ increases by $\exp\left[8.64(6)\beta\right]$. For typical projection times of $\beta\gtrapprox 100$, this accelerates such simulation by many orders of magnitude.

cond-mat.str-el↗

arXiv2019

Magnetic Susceptibility and Simulated Neutron Signal in the 2D Hubbard Model

We compute dynamic spin susceptibilities in the two-dimensional Hubbard model using the method of Dual Fermions and provide comparison to lattice Monte Carlo and cluster dynamical mean field theory. We examine the energy dispersion identified by peaks in ${\rm Im}\chi(\omega,q)$ which define spin modes and compare the exchange scale and magnon dispersion to neutron experiments on the parent La$_2$CuO$_4$ cuprate. We present the evolution of the spin excitations as a function of Hubbard interaction strengths and doping and explore the particle-hole asymmetry of the spin excitations. We also study the correlation lengths and the spin excitation dispersion peak structure and find a `Y'-shaped dispersion similar to neutron results on doped HgBa$_2$CuO$_{4+\delta}$.

cond-mat.str-el↗

arXiv2018

Updated Core Libraries of the ALPS Project

The open source ALPS (Algorithms and Libraries for Physics Simulations) project provides a collection of physics libraries and applications, with a focus on simulations of lattice models and strongly correlated electron systems. The libraries provide a convenient set of well-documented and reusable components for developing condensed matter physics simulation codes, and the applications strive to make commonly used and proven computational algorithms available to a non-expert community. In this paper we present an update of the core ALPS libraries. We present in particular new Monte Carlo libraries and new Green's function libraries.

physics.comp-ph↗

arXiv2016

Implementation of the Maximum Entropy Method for Analytic Continuation

We present $\texttt{Maxent}$, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to the real axis. The code works for imaginary time and Matsubara frequency data and implements the 'Legendre' representation of finite temperature Green's functions. It implements a variety of kernels, default models, and grids for continuing bosonic, fermionic, anomalous, and other data. Our implementation is licensed under GPLv2 and extensively documented. This paper shows the use of the programs in detail.

physics.comp-ph↗