arXiv subjects

Joshua Job

Publications and source records attributed to Joshua Job.

12 recordsLinked to original sources

arXiv2024

Quantifying fault tolerant simulation of strongly correlated systems using the Fermi-Hubbard model

Understanding the physics of strongly correlated materials is one of the grand challenge problems for physics today. A large class of scientifically interesting materials, from high-$T_c$ superconductors to spin liquids, involve medium to strong correlations, and building a holistic understanding of these materials is critical. Doing so is hindered by the competition between the kinetic energy and Coulomb repulsion, which renders both analytic and numerical methods unsatisfactory for describing interacting materials. Fault-tolerant quantum computers have been proposed as a path forward to overcome these difficulties, but this potential capability has not yet been fully assessed. Here, using the multi-orbital Fermi-Hubbard model as a representative model and a source of scalable problem specifications, we estimate the resource costs needed to use fault-tolerant quantum computers for obtaining experimentally relevant quantities such as correlation function estimation. We find that advances in quantum algorithms and hardware will be needed in order to reduce quantum resources and feasibly address utility-scale problem instances.

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arXiv2024

The Cost of Entanglement Renormalization on a Fault-Tolerant Quantum Computer

We perform a detailed resource estimate for the prospect of using deep entanglement renormalization ansatz (DMERA) on a fault-tolerant quantum computer, focusing on the regime in which the target system is large. For probing a relatively large system size ($64\times 64$), we observe up to an order of magnitude reduction in the number of qubits, compared to the approaches based on quantum phase estimation (QPE). We discuss two complementary strategies to measure the energy. The first approach is based on a random sampling of the local terms of the Hamiltonian, requiring $\mathcal{O}(1/\epsilon^2)$ invocations of quantum circuits, each of which have depth of at most $\mathcal{O}(\log N)$, where $\epsilon$ is the relative precision in the energy and $N$ is the system size. The second approach is based on a coherent estimation of the expectation value of observables averaged over space, which achieves the Heisenberg scaling while incurring only a logarithmic cost in the system size. For estimating the energy per site of $\epsilon$, $\mathcal{O}\left(\frac{\log N}{\epsilon} \right)$ $T$ gates and $\mathcal{O}\left(\log N \right)$ qubits suffice. The constant factor of the leading contribution is shown to be determined by the depth of the DMERA circuit, the gates used in the ansatz, and the periodicity of the circuit. We also derive tight bounds on the variance of the energy gradient, assuming the gates are random Pauli rotations.

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arXiv2023

Efficient, direct compilation of SU(N) operations into SNAP & Displacement gates

We present a function which connects the parameter of a previously published short sequence of selective number-dependent arbitrary phase (SNAP) and displacement gates acting on a qudit encoded into the Fock states of a superconducting cavity, $V_k(\alpha)=D(\alpha)R_\pi(k)D(-2\alpha)R_\pi(k)D(\alpha)$ to the angle of the Givens rotation $G(\theta)$ on levels $|k\rangle,|k+1\rangle$ that sequence approximates, namely $\alpha=\Phi(\theta) = \frac{\theta}{4\sqrt{k+1}}$. Previous publications left the determination of an appropriate $\alpha$ to numerical optimization at compile time. The map $\Phi$ gives us the ability to compile directly any $d$-dimensional unitary into a sequence of SNAP and displacement gates in $O(d^3)$ complex floating point operations with low constant prefactor, avoiding the need for numerical optimization. Numerical studies demonstrate that the infidelity of the generated gate sequence $V_k$ per Givens rotation $G$ scales as approximately $O(\theta^6)$. We find numerically that the error on compiled circuits can be made arbitrarily small by breaking each rotation into $m$ $\theta/m$ rotations, with the full $d\times d$ unitary infidelity scaling as approximately $O(m^{-4})$. This represents a significant reduction in the computational effort to compile qudit unitaries either to SNAP and displacement gates or to generate them via direct low-level pulse optimization via optimal control.

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arXiv2021

Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model

Quantum spin systems may offer the first opportunities for beyond-classical quantum computations of scientific interest. While general quantum simulation algorithms likely require error-corrected qubits, there may be applications of scientific interest prior to the practical implementation of quantum error correction. The variational quantum eigensolver (VQE) is a promising approach to finding energy eigenvalues on noisy quantum computers. Lattice models are of broad interest for use on near-term quantum hardware due to the sparsity of the number of Hamiltonian terms and the possibility of matching the lattice geometry to the hardware geometry. Here, we consider the Kitaev spin model on a hardware-native square-octagon qubit connectivity map, and examine the possibility of efficiently probing its rich phase diagram with VQE approaches. By benchmarking different choices of variational Ansatz states and classical optimizers, we illustrate the advantage of a mixed optimization approach using the Hamiltonian variational Ansatz (HVA) and the potential of probing the system's phase diagram using VQE. We further demonstrate the implementation of HVA circuits on Rigetti's Aspen-9 chip with error mitigation.

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arXiv2020

Systematic comparison of deep belief network training using quantum annealing vs. classical techniques

In this work we revisit and expand on a 2015 study that used a D-Wave quantum annealer as a sampling engine to assist in the training of a Deep Neural Network. The original 2015 results were reproduced using more recent D-Wave hardware. We systematically compare this quantum-assisted training method to a wider range of classical techniques, including: Contrastive Divergence with a different choice of optimizer; Contrastive Divergence with an increased number of steps (CD-k); and Simulated Annealing (SA). We find that quantum-assisted training still outperforms the CD with Gibbs sampling-based techniques; however, SA is able to match the performance of quantum-assisted training trivially using a quench-like schedule with a single sweep at high temperature followed by one at the target temperature.

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arXiv2019

Restricted Boltzmann Machines for galaxy morphology classification with a quantum annealer

We present the application of Restricted Boltzmann Machines (RBMs) to the task of astronomical image classification using a quantum annealer built by D-Wave Systems. Morphological analysis of galaxies provides critical information for studying their formation and evolution across cosmic time scales. We compress galaxy images using principal component analysis to fit a representation on the quantum hardware. Then, we train RBMs with discriminative and generative algorithms, including contrastive divergence and hybrid generative-discriminative approaches, to classify different galaxy morphologies. The methods we compare include Quantum Annealing (QA), Markov Chain Monte Carlo (MCMC) Gibbs Sampling, and Simulated Annealing (SA) as well as machine learning algorithms like gradient boosted decision trees. We find that RBMs implemented on D-Wave hardware perform well, and that they show some classification performance advantages on small datasets, but they don't offer a broadly strategic advantage for this task. During this exploration, we analyzed the steps required for Boltzmann sampling with the D-Wave 2000Q, including a study of temperature estimation, and examined the impact of qubit noise by comparing and contrasting the original D-Wave 2000Q to the lower-noise version recently made available. While these analyses ultimately had minimal impact on the performance of the RBMs, we include them for reference.

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arXiv2019

Charged particle tracking with quantum annealing-inspired optimization

At the High Luminosity Large Hadron Collider (HL-LHC), traditional track reconstruction techniques that are critical for analysis are expected to face challenges due to scaling with track density. Quantum annealing has shown promise in its ability to solve combinatorial optimization problems amidst an ongoing effort to establish evidence of a quantum speedup. As a step towards exploiting such potential speedup, we investigate a track reconstruction approach by adapting the existing geometric Denby-Peterson (Hopfield) network method to the quantum annealing framework and to HL-LHC conditions. Furthermore, we develop additional techniques to embed the problem onto existing and near-term quantum annealing hardware. Results using simulated annealing and quantum annealing with the D-Wave 2X system on the TrackML dataset are presented, demonstrating the successful application of a quantum annealing-inspired algorithm to the track reconstruction challenge. We find that combinatorial optimization problems can effectively reconstruct tracks, suggesting possible applications for fast hardware-specific implementations at the LHC while leaving open the possibility of a quantum speedup for tracking.

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arXiv2019

Quantum adiabatic machine learning with zooming

Recent work has shown that quantum annealing for machine learning, referred to as QAML, can perform comparably to state-of-the-art machine learning methods with a specific application to Higgs boson classification. We propose QAML-Z, a novel algorithm that iteratively zooms in on a region of the energy surface by mapping the problem to a continuous space and sequentially applying quantum annealing to an augmented set of weak classifiers. Results on a programmable quantum annealer show that QAML-Z matches classical deep neural network performance at small training set sizes and reduces the performance margin between QAML and classical deep neural networks by almost 50% at large training set sizes, as measured by area under the ROC curve. The significant improvement of quantum annealing algorithms for machine learning and the use of a discrete quantum algorithm on a continuous optimization problem both opens a new class of problems that can be solved by quantum annealers and suggests the approach in performance of near-term quantum machine learning towards classical benchmarks.

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arXiv2017

Test-driving 1000 qubits

Quantum computing is no longer a nascent field. Programmable quantum annealing devices with more that 1000 qubits are commercially available. How does one know that a putative quantum annealing device is indeed quantum? How should one go about benchmarking its performance and compare it to classical algorithms? How can its performance be improved by error correction? In this contribution to the focus collection on "What would you do with 1000 qubits?", we review the work we and others have done in this area, since the first D-Wave quantum annealer with 108 qubits was made available to us. Some of the lessons we have learned will be useful when other quantum computing platforms reach a similar scale, and practitioners will attempt to demonstrate quantum speedup.

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arXiv2015

Teleportation-based Fault-tolerant Quantum Computation in Multi-qubit Large Block Codes

A major goal for fault-tolerant quantum computation (FTQC) is to reduce the overhead needed for error correction. One approach is to use block codes that encode multiple qubits, which can achieve significantly higher rates for the same code distance than single-qubit code blocks or topological codes. We present a scheme for universal quantum computation using multi-qubit Calderbank-Shor-Steane (CSS) block codes, where codes admitting different transversal gates are used to achieve universality, and logical teleportation is used to move qubits between code blocks. All circuits for both computation and error correction are transversal. We also argue that single shot fault-tolerant error correction can be done in Steane syndrome extraction. Then, we present estimates of information lifetime for a few possible codes, which suggests that highly nontrivial quantum computations can be achieved at reasonable error rates, using codes that require significantly less than 100 physical qubits per logical qubit.

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arXiv2015

Probing for quantum speedup in spin glass problems with planted solutions

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.

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arXiv2014

Defining and detecting quantum speedup

The development of small-scale digital and analog quantum devices raises the question of how to fairly assess and compare the computational power of classical and quantum devices, and of how to detect quantum speedup. Here we show how to define and measure quantum speedup in various scenarios, and how to avoid pitfalls that might mask or fake quantum speedup. We illustrate our discussion with data from a randomized benchmark test on a D-Wave Two device with up to 503 qubits. Comparing the performance of the device on random spin glass instances with limited precision to simulated classical and quantum annealers, we find no evidence of quantum speedup when the entire data set is considered, and obtain inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results for one particular benchmark do not rule out the possibility of speedup for other classes of problems and illustrate that quantum speedup is elusive and can depend on the question posed.

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