Publications

Order by: publication date number of citations

• Improved Hilbert space exploration algorithms for finite temperature calculations

  Albertus J. J. M. de Klerk, Jean-Sébastien Caux

  SciPost Phys. Core 6, 039 (2023) · published 23 May 2023 | Toggle abstract · pdf

  Computing correlation functions in strongly-interacting quantum systems is one of the most important challenges of modern condensed matter theory, due to their importance in the description of many physical observables. Simultaneously, this challenge is one of the most difficult to address, due to the inapplicability of traditional perturbative methods or the few-body limitations of numerical approaches. For special cases, where the model is integrable, methods based on the Bethe Ansatz have succeeded in computing the spectrum and given us analytical expressions for the matrix elements of physically important operators. However, leveraging these results to compute correlation functions generally requires the numerical evaluation of summations over eigenstates. To perform these summations efficiently, Hilbert space exploration algorithms have been developed which has resulted most notably in the ABACUS library. While this performs quite well for correlations on ground states or low-entropy states, the case of high entropy states (most importantly at finite temperatures or after a quantum quench) is more difficult, and leaves room for improvement. In this work, we develop a new Hilbert space exploration algorithm for the Lieb-Liniger model, specially tailored to optimize the computational order on finite-entropy states for correlations of density-related operators.

  1 citation

• Collective Monte Carlo updates through tensor network renormalization

  Miguel Frías-Pérez, Michael Mariën, David Pérez García, Mari Carmen Bañuls, Sofyan Iblisdir

  SciPost Phys. 14, 123 (2023) · published 22 May 2023 | Toggle abstract · pdf

  We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present benchmark computations for a wide variety of instances of the two-dimensional Ising model, including ferromagnetic, antiferromagnetic, (fully) frustrated and Edwards-Anderson spin glass instances, and we show that, with modest computational effort, our Markov chain achieves sizeable acceptance rates, even in the vicinity of critical points. In each of the situations we have considered, the Markov chain compares well with other Monte Carlo schemes such as the Metropolis or Wolff's algorithm: equilibration times appear to be reduced by a factor that varies between $40$ and $2000$, depending on the model and the observable being monitored. We also present an extension to three spatial dimensions, and demonstrate that it exhibits fast equilibration for finite ferro- and antiferromagnetic instances. Additionally, and although it is originally designed for a square lattice of finite degrees of freedom with open boundary conditions, the proposed scheme can be used as such, or with slight modifications, to study triangular lattices, systems with continuous degrees of freedom, matrix models, a confined gas of hard spheres, or to deal with arbitrary boundary conditions.

  2 citations

• Quantum-inspired tempering for ground state approximation using artificial neural networks

  Tameem Albash, Conor Smith, Quinn Campbell, Andrew D. Baczewski

  SciPost Phys. 14, 121 (2023) · published 19 May 2023 | Toggle abstract · pdf

  A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem's small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.

• Quantum annealing for neural network optimization problems: A new approach via tensor network simulations

  Guglielmo Lami, Pietro Torta, Giuseppe E. Santoro, Mario Collura

  SciPost Phys. 14, 117 (2023) · published 17 May 2023 | Toggle abstract · pdf

  Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

  1 citation

• On classical and hybrid shadows of quantum states

  Saumya Shivam, Curt W. von Keyserlingk, Shivaji L. Sondhi

  SciPost Phys. 14, 094 (2023) · published 4 May 2023 | Toggle abstract · pdf

  Classical shadows are a computationally efficient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by performing repeated random measurements. In this note we offer some comments on this approach. We note that the resources needed to form classical shadows with bounded relative error depend strongly on the target state. We then comment on the advantages and limitations of using classical shadows to simulate many-body dynamics. In addition, we introduce the notion of a hybrid shadow, constructed from measurements on a part of the system instead of the entirety, which provides a framework to gain more insight into the nature of shadow states as one reduces the size of the subsystem measured, and a potential alternative to compressing quantum states.

  3 citations

• Nonlocal correlations in noisy multiqubit systems simulated using matrix product operators

  Haggai Landa, Grégoire Misguich

  SciPost Phys. Core 6, 037 (2023) · published 1 May 2023 | Toggle abstract · pdf

  We introduce an open-source solver for the Lindblad master equation, based on matrix product states and matrix product operators. Using this solver we study the dynamics of tens of interacting qubits with different connectivities, focusing on a problem where an edge qubit is being continuously driven on resonance, which is a fundamental operation in quantum devices. Because of the driving, induced excitations propagate through the qubits until the system reaches a steady state due to the incoherent terms. We find that with alternating-frequency qubits whose interactions with their off-resonant neighbors appear weak, the tunneling excitations lead to large correlations between distant qubits in the system. Some two-qubit correlation functions are found to increase as a function of distance in the system (in contrast to the typical decay with distance), peaking on the two edge qubits farthest apart from each other.

  5 citations

• Spatial separation of spin currents in transition metal dichalcogenides

  Antonio L. R. Manesco, Artem Pulkin

  SciPost Phys. Core 6, 036 (2023) · published 1 May 2023 | Toggle abstract · pdf

  We theoretically predict spatial separation of spin-polarized ballistic currents in transition metal dichalcogenides (TMDs) due to trigonal warping. We quantify the effect in terms of spin polarization of charge carrier currents in a prototypical 3-terminal ballistic device where spin-up and spin-down charge carriers are collected by different leads. We show that the magnitude of the current spin polarization depends strongly on the charge carrier energy and the direction with respect to crystallographic orientations in the device. We study the (negative) effect of lattice imperfections and disorder on the observed spin polarization. Our investigation provides an avenue towards observing spin discrimination in a defect-free time reversal-invariant material.

• Simulating thermal density operators with cluster expansions and tensor networks

  Bram Vanhecke, David Devoogdt, Frank Verstraete, Laurens Vanderstraeten

  SciPost Phys. 14, 085 (2023) · published 26 April 2023 | Toggle abstract · pdf

  We provide an efficient approximation for the exponential of a local operator in quantum spin systems using tensor-network representations of a cluster expansion. We benchmark this cluster tensor network operator (cluster TNO) for one-dimensional systems, and show that the approximation works well for large real- or imaginary-time steps. We use this formalism for representing the thermal density operator of a two-dimensional quantum spin system at a certain temperature as a single cluster TNO, which we can then contract by standard contraction methods for two-dimensional tensor networks. We apply this approach to the thermal phase transition of the transverse-field Ising model on the square lattice, and we find through a scaling analysis that the cluster-TNO approximation gives rise to a continuous phase transition in the correct universality class; by increasing the order of the cluster expansion we find good values of the critical point up to surprisingly low temperatures.

  4 citations

• Unifying semiclassics and quantum perturbation theory at nonlinear order

  Daniel Kaplan, Tobias Holder, Binghai Yan

  SciPost Phys. 14, 082 (2023) · published 25 April 2023 | Toggle abstract · pdf

  Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo's formula for resonances at finite frequency. However, a precise connection between both approaches has not been established. Focusing on the second order nonlinear response, here we show how the semiclassical limit can be recovered from perturbation theory in the velocity gauge, provided that finite quasiparticle lifetimes are taken into account. We find that matrix elements related to the band geometry combine in this limit to produce the semiclassical nonlinear conductivity. We demonstrate the power of the new formalism by deriving a quantum contribution to the nonlinear conductivity which is of order $\tau^{-1}$ in the relaxation time $\tau$, which is principally inaccessible within the Boltzmann approach. We outline which steps can be generalized to higher orders in the applied perturbation, and comment about potential experimental signatures of our results.

  10 citations

• Temperature dependence of quasiparticle interference in $d$-wave superconductors

  Harun Al Rashid, Garima Goyal, Alireza Akbari, Dheeraj Kumar Singh

  SciPost Phys. Core 6, 033 (2023) · published 24 April 2023 | Toggle abstract · pdf

  We investigate the temperature dependence of quasiparticle interference in the high $T_c$-cuprates using an exact-diagonalization + Monte-Carlo based scheme to simulate the $d$-wave superconducting order parameter. The quasiparticle interference patterns have features largely resulting from the scattering vectors of the octet model at lower temperature. Our findings suggest that the features of quasiparticle interference in the pseudogap region of the phase diagram are also dominated by the set of scattering vectors belonging to the octet model because of the persisting antinodal gap beyond the superconducting transition $T_c$. However, beyond a temperature when the antinodal gap becomes very small, a set of scattering vectors different from those belonging to the octet model are responsible for the quasiparticle interference patterns. With a rise in temperature, the patterns are increasingly broadened.

  1 citation