arXiv subjects

M. Troyer

Publications and source records attributed to M. Troyer.

At least 19 recordsLinked to original sources

arXiv2022

Propagation of errors and quantitative quantum simulation with quantum advantage

The rapid development in hardware for quantum computing and simulation has led to much interest in problems where these devices can exceed the capabilities of existing classical computers and known methods. Approaching this for problems that go beyond testing the performance of a quantum device is an important step, and quantum simulation of many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum simulators with neutral atoms in optical lattices and trapped ions. Considering the primary sources of error in analogue devices and how they propagate after a quench in studies of the Hubbard or long-range transverse field Ising model, we identify the level of error expected in quantities we extract from experiments. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators. We also identify the hardware requirements to reach the same level of accuracy with future fault-tolerant digital quantum simulation. Verification techniques are already available to test the assumptions we make here, and demonstrating these in experiments will be an important next step.

quant-ph↗

arXiv2020

Towards quantum computing for high-energy excited states in molecular systems: quantum phase estimations of core-level states

This paper explores the utility of the quantum phase estimation (QPE) in calculating high-energy excited states characterized by promotions of electrons occupying inner energy shells. These states have been intensively studied over the last few decades especially in supporting the experimental effort at light sources. Results obtained with the QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is also discussed.

quant-ph↗

arXiv2019

Autonomous tuning and charge state detection of gate defined quantum dots

Defining quantum dots in semiconductor based heterostructures is an essential step in initializing solid-state qubits. With growing device complexity and increasing number of functional devices required for measurements, a manual approach to finding suitable gate voltages to confine electrons electrostatically is impractical. Here, we implement a two-stage device characterization and dot-tuning process which first determines whether devices are functional and then attempts to tune the functional devices to the single or double quantum dot regime. We show that automating well established manual tuning procedures and replacing the experimenter's decisions by supervised machine learning is sufficient to tune double quantum dots in multiple devices without pre-measured input or manual intervention. The quality of measurement results and charge states are assessed by four binary classifiers trained with experimental data, reflecting real device behaviour. We compare and optimize eight models and different data preprocessing techniques for each of the classifiers to achieve reliable autonomous tuning, an essential step towards scalable quantum systems in quantum dot based qubit architectures.

quant-ph↗

arXiv2018

Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena

We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices computed via Density Functional Theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional optical lattices, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks-Girardeau limit and in very deep optical lattices. We also consider a three dimensional optical lattice at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries.

cond-mat.quant-gas↗

arXiv2017

Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass

We study the role of Hamiltonian complexity in the performance of quantum annealers. We consider two general classes of annealing Hamiltonians: stoquastic ones, which can be simulated efficiently using the quantum Monte Carlo algorithm, and nonstoquastic ones, which cannot be treated efficiently. We implement the latter by adding antiferromagnetically coupled two-spin driver terms to the traditionally studied transverse-field Ising model, and compare their performance to that of similar stoquastic Hamiltonians with ferromagnetically coupled additional terms. We focus on a model of long-range Ising spin glass as our problem Hamiltonian and carry out the comparison between the annealers by numerically calculating their success probabilities in solving random instances of the problem Hamiltonian in systems of up to 17 spins. We find that, for a small percentage of mostly harder instances, nonstoquastic Hamiltonians greatly outperform their stoquastic counterparts and their superiority persists as the system size grows. We conjecture that the observed improved performance is closely related to the frustrated nature of nonstoquastic Hamiltonians.

quant-ph↗

arXiv2016

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 systems. The libraries provide a convenient set of well-documented and reusable components for developing condensed matter physics simulation code, and the applications strive to make commonly used and proven computational algorithms available to a non-expert community. In this paper we present an updated and refactored version of the core ALPS libraries geared at the computational physics software development community, rewritten with focus on documentation, ease of installation, and software maintainability.

physics.comp-ph↗

arXiv2016

Hybrid quantum-classical approach to correlated materials

Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.

quant-ph↗

arXiv2016

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP$_2$ (X = Mo, W)

The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe the prediction of a type-II Weyl semimetal phase in the transition metal diphosphides MoP$_2$ and WP$_2$. These materials are characterized by relatively simple band structures with four pairs of type-II Weyl points. Neighboring Weyl points have the same chirality, which makes the predicted topological phase robust with respect to small perturbations of the crystalline lattice. In addition, this peculiar arrangement of the Weyl points results in long topological Fermi arcs, thus making them readily accessible in angle-resolved photoemission spectroscopy.

cond-mat.mes-hall↗

arXiv2016

Training A Quantum Optimizer

We study a variant of the quantum approximate optimization algorithm [ E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with slightly different parametrization and different objective: rather than looking for a state which approximately solves an optimization problem, our goal is to find a quantum algorithm that, given an instance of MAX-2-SAT, will produce a state with high overlap with the optimal state. Using a machine learning approach, we chose a "training set" of instances and optimized the parameters to produce large overlap for the training set. We then tested these optimized parameters on a larger instance set. As a training set, we used a subset of the hard instances studied by E. Crosson, E. Farhi, C. Yen-Yu Lin, H.-H. Lin, and P. Shor (CFLLS) [arXiv:1401.7320]. When tested on the full set, the parameters that we find produce significantly larger overlap than the optimized annealing times of CFLLS. Testing on other random instances from $20$ to $28$ bits continues to show improvement over annealing, with the improvement being most notable on the hardest instances. Further tests on instances of MAX-3-SAT also showed improvement on the hardest instances. This algorithm may be a possible application for near-term quantum computers with limited coherence times.

quant-ph↗

arXiv2015

Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks

Progress in the emergent field of topological superconductivity relies on synthesis of new material combinations, combining superconductivity, low density, and spin-orbit coupling (SOC). For example, theory [1-4] indicates that the interface between a one-dimensional (1D) semiconductor (Sm) with strong SOC and a superconductor (S) hosts Majorana modes with nontrivial topological properties [5-8]. Recently, epitaxial growth of Al on InAs nanowires was shown to yield a high quality S-Sm system with uniformly transparent interfaces [9] and a hard induced gap, indicted by strongly suppressed sub gap tunneling conductance [10]. Here we report the realization of a two-dimensional (2D) InAs/InGaAs heterostructure with epitaxial Al, yielding a planar S-Sm system with structural and transport characteristics as good as the epitaxial wires. The realization of 2D epitaxial S-Sm systems represent a significant advance over wires, allowing extended networks via top-down processing. Among numerous potential applications, this new material system can serve as a platform for complex networks of topological superconductors with gate-controlled Majorana zero modes [1-4]. We demonstrate gateable Josephson junctions and a highly transparent 2D S-Sm interface based on the product of excess current and normal state resistance.

cond-mat.mes-hall↗

arXiv2015

Optimized simulated annealing for Ising spin glasses

We present several efficient implementations of the simulated annealing algorithm for Ising spin glasses on sparse graphs. In particular, we provide a generic code for any choice of couplings, an optimized code for bipartite graphs, and highly optimized implementations using multi-spin coding for graphs with small maximum degree and discrete couplings with a finite range. The latter codes achieve up to 50 spin flips per nanosecond on modern Intel CPUs. We also compare the performance of the codes to that of the special purpose D-Wave devices built for solving such Ising spin glass problems.

cond-mat.dis-nn↗

arXiv2015

Towards Practical Quantum Variational Algorithms

The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state preparation can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state preparation. We test its accuracy and determine the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin-orbitals), and for small molecules. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required number of measurements is astronomically large for quantum chemistry applications to molecules, applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state preparation using short quantum circuits, to prepare trial ground states of models faster than using adiabatic state preparation.

quant-ph↗

arXiv2015

A Bespoke Single-Band Hubbard Model Material

The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the `standard model' of condensed matter physics. The model has been remarkably successful at addressing a range of correlation effects in solids, but beyond one dimension its solution is intractable. Much current research aims, therefore, at finding appropriate approximations to the Hubbard model phase diagram. Here we take the new approach of using ab initio electronic structure methods to design a material whose Hamiltonian is that of the single-band Hubbard model. Solution of the Hubbard model will then be available through measurement of the material's properties. After identifying an appropriate crystal class and several appropriate chemistries, we use density functional theory and dynamical mean-field theory to screen for the desired electronic band structure and metal-insulator transition. We then explore the most promising candidates for structural stability and suitability for doping and propose specific materials for subsequent synthesis. Finally, we identify a regime -- that should manifest in our bespoke material -- in which the single-band Hubbard model on a triangular lattice exhibits exotic d-wave superconductivity.

cond-mat.str-el↗

arXiv2014

Non-local quantum fluctuations and fermionic superfluidity in the imbalanced attractive Hubbard model

We study fermionic superfluidity in strongly anisotropic optical lattices with attractive interactions utilizing the cluster DMFT method, and focusing in particular on the role of non-local quantum fluctuations. We show that non-local quantum fluctuations impact the BCS superfluid transition dramatically. Moreover, we show that exotic superfluid states with delicate order parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase driven by spin population imbalance, can emerge even in the presence of such strong fluctuations.

cond-mat.quant-gas↗

arXiv2014

Improving Quantum Algorithms for Quantum Chemistry

We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Our modification does not require additional ancilla qubits. Then, we demonstrate how many operations can be parallelized, leading to a further linear decrease in the parallel depth of the circuit, at the cost of a small constant factor increase in number of qubits required. Thirdly, we modify the term order in the Trotter-Suzuki decomposition, significantly reducing the error at given Trotter-Suzuki timestep. A final improvement modifies the Hamiltonian to reduce errors introduced by the non-zero Trotter-Suzuki timestep. All of these techniques are validated using numerical simulation and detailed gate counts are given for realistic molecules.

quant-ph↗

arXiv2014

Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: a Quantum Monte Carlo Study

Using continuous-space quantum Monte Carlo methods we investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas under the influence of periodic potentials that describe the effect of a simple-cubic optical lattice. Simulations are performed with balanced and with imbalanced components, including the case of a single impurity immersed in a polarized Fermi sea (repulsive polaron). For an intermediate density below half filling, we locate the transitions between the paramagnetic, and the partially and the fully ferromagnetic phases. As the intensity of the optical lattice increases, the ferromagnetic instability takes place at weaker interactions, indicating a possible route to observe ferromagnetism in experiments performed with ultracold atoms. We compare our findings with previous predictions based on the standard computational method used in material science, namely density functional theory, and with results based on tight-binding models.

cond-mat.quant-gas↗

arXiv2014

A model project for reproducible papers: critical temperature for the Ising model on a square lattice

In this paper we present a simple, yet typical simulation in statistical physics, consisting of large scale Monte Carlo simulations followed by an involved statistical analysis of the results. The purpose is to provide an example publication to explore tools for writing reproducible papers. The simulation estimates the critical temperature where the Ising model on the square lattice becomes magnetic to be Tc /J = 2.26934(6) using a finite size scaling analysis of the crossing points of Binder cumulants. We provide a virtual machine which can be used to reproduce all figures and results.

cs.CE↗

arXiv2013

Critical Temperature of Interacting Bose Gases in Periodic Potentials

The superfluid transition of a repulsive Bose gas in the presence of a sinusoidal potential which represents a simple-cubic optical lattice is investigate using quantum Monte Carlo simulations. At the average filling of one particle per well the critical temperature has a nonmonotonic dependence on the interaction strength, with an initial sharp increase and a rapid suppression at strong interactions in the vicinity of the Mott transition. In an optical lattice the positive shift of the transition is strongly enhanced compared to the homogenous gas. By varying the lattice filling we find a crossover from a regime where the optical lattice has the dominant effect to a regime where interactions dominate and the presence of the lattice potential becomes almost irrelevant.

cond-mat.quant-gas↗