arXiv subjects

Alejandro Perdomo-Ortiz

Publications and source records attributed to Alejandro Perdomo-Ortiz.

35 records · Page 2Linked to original sources

arXiv2019

Robust Implementation of Generative Modeling with Parametrized Quantum Circuits

Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansatz, a robust and thorough assessment on-hardware of such features has been missing to date. From the optimizer perspective, the primary challenge lies in the solver's stochastic nature, and their significant variance over the random initialization. Therefore, a robust comparison requires that one perform several training curves for each solver before one can reach conclusions about their typical performance. Since each of the training curves requires the execution of thousands of quantum circuits in the quantum computer, such a robust study remained a steep challenge for most hybrid platforms available today. Here, we leverage on Rigetti's Quantum Cloud Services to overcome this implementation barrier, and we study the on-hardware performance of the data-driven quantum circuit learning (DDQCL) for three different state-of-the-art classical solvers, and on two-different circuit ansatze associated to different entangling connectivity graphs for the same task. Additionally, we assess the gains in performance from varying circuit depths. To evaluate the typical performance associated with each of these settings in this benchmark study, we use at least five independent runs of DDQCL towards the generation of quantum generative models capable of capturing the patterns of the canonical Bars and Stripes data set.

quant-ph↗

arXiv2018

Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers

With quantum computing technologies nearing the era of commercialization and quantum supremacy, machine learning (ML) appears as one of the promising "killer" applications. Despite significant effort, there has been a disconnect between most quantum ML proposals, the needs of ML practitioners, and the capabilities of near-term quantum devices to demonstrate quantum enhancement in the near future. In this contribution to the focus collection on "What would you do with 1000 qubits?", we provide concrete examples of intractable ML tasks that could be enhanced with near-term devices. We argue that to reach this target, the focus should be on areas where ML researchers are struggling, such as generative models in unsupervised and semi-supervised learning, instead of the popular and more tractable supervised learning techniques. We also highlight the case of classical datasets with potential quantum-like statistical correlations where quantum models could be more suitable. We focus on hybrid quantum-classical approaches and illustrate some of the key challenges we foresee for near-term implementations. Finally, we introduce the quantum-assisted Helmholtz machine (QAHM), an attempt to use near-term quantum devices to tackle high-dimensional datasets of continuous variables. Instead of using quantum computers to assist deep learning, as previous approaches do, the QAHM uses deep learning to extract a low-dimensional binary representation of data, suitable for relatively small quantum processors which can assist the training of an unsupervised generative model. Although we illustrate this concept on a quantum annealer, other quantum platforms could benefit as well from this hybrid quantum-classical framework.

quant-ph↗

arXiv2018

Quantum-assisted Helmholtz machines: A quantum-classical deep learning framework for industrial datasets in near-term devices

Machine learning has been presented as one of the key applications for near-term quantum technologies, given its high commercial value and wide range of applicability. In this work, we introduce the \textit{quantum-assisted Helmholtz machine:} a hybrid quantum-classical framework with the potential of tackling high-dimensional real-world machine learning datasets on continuous variables. Instead of using quantum computers only to assist deep learning, as previous approaches have suggested, we use deep learning to extract a low-dimensional binary representation of data, suitable for processing on relatively small quantum computers. Then, the quantum hardware and deep learning architecture work together to train an unsupervised generative model. We demonstrate this concept using 1644 quantum bits of a D-Wave 2000Q quantum device to model a sub-sampled version of the MNIST handwritten digit dataset with 16x16 continuous valued pixels. Although we illustrate this concept on a quantum annealer, adaptations to other quantum platforms, such as ion-trap technologies or superconducting gate-model architectures, could be explored within this flexible framework.

quant-ph↗

arXiv2018

Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models

Mainstream machine-learning techniques such as deep learning and probabilistic programming rely heavily on sampling from generally intractable probability distributions. There is increasing interest in the potential advantages of using quantum computing technologies as sampling engines to speed up these tasks or to make them more effective. However, some pressing challenges in state-of-the-art quantum annealers have to be overcome before we can assess their actual performance. The sparse connectivity, resulting from the local interaction between quantum bits in physical hardware implementations, is considered the most severe limitation to the quality of constructing powerful generative unsupervised machine-learning models. Here we use embedding techniques to add redundancy to data sets, allowing us to increase the modeling capacity of quantum annealers. We illustrate our findings by training hardware-embedded graphical models on a binarized data set of handwritten digits and two synthetic data sets in experiments with up to 940 quantum bits. Our model can be trained in quantum hardware without full knowledge of the effective parameters specifying the corresponding quantum Gibbs-like distribution; therefore, this approach avoids the need to infer the effective temperature at each iteration, speeding up learning; it also mitigates the effect of noise in the control parameters, making it robust to deviations from the reference Gibbs distribution. Our approach demonstrates the feasibility of using quantum annealers for implementing generative models, and it provides a suitable framework for benchmarking these quantum technologies on machine-learning-related tasks.

quant-ph↗

arXiv2017

A NASA Perspective on Quantum Computing: Opportunities and Challenges

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so by how much, or how to design quantum algorithms that realize such advantages. Many of the most challenging computational problems arising in the practical world are tackled today by heuristic algorithms that have not been mathematically proven to outperform other approaches but have been shown to be effective empirically. While quantum heuristic algorithms have been proposed, empirical testing becomes possible only as quantum computation hardware is built. The next few years will be exciting as empirical testing of quantum heuristic algorithms becomes more and more feasible. While large-scale universal quantum computers are likely decades away, special-purpose quantum computational hardware has begun to emerge that will become more powerful over time, as well as some small-scale universal quantum computers.

quant-ph↗

arXiv2016

Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics vs quantum approaches

To date, a conclusive detection of quantum speedup remains elusive. Recently, a team by Google Inc.~[V.~S.~Denchev {\em et al}., Phys.~Rev.~X {\bf 6}, 031015 (2016)] proposed a weak-strong cluster model tailored to have tall and narrow energy barriers separating local minima, with the aim to highlight the value of finite-range tunneling. More precisely, results from quantum Monte Carlo simulations, as well as the D-Wave 2X quantum annealer scale considerably better than state-of-the-art simulated annealing simulations. Moreover, the D-Wave 2X quantum annealer is $\sim 10^8$ times faster than simulated annealing on conventional computer hardware for problems with approximately $10^3$ variables. Here, an overview of different sequential, nontailored, as well as specialized tailored algorithms on the Google instances is given. We show that the quantum speedup is limited to sequential approaches and study the typical complexity of the benchmark problems using insights from the study of spin glasses.

quant-ph↗

arXiv2016

Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning

An increase in the efficiency of sampling from Boltzmann distributions would have a significant impact on deep learning and other machine-learning applications. Recently, quantum annealers have been proposed as a potential candidate to speed up this task, but several limitations still bar these state-of-the-art technologies from being used effectively. One of the main limitations is that, while the device may indeed sample from a Boltzmann-like distribution, quantum dynamical arguments suggest it will do so with an {\it instance-dependent} effective temperature, different from its physical temperature. Unless this unknown temperature can be unveiled, it might not be possible to effectively use a quantum annealer for Boltzmann sampling. In this work, we propose a strategy to overcome this challenge with a simple effective-temperature estimation algorithm. We provide a systematic study assessing the impact of the effective temperatures in the learning of a special class of a restricted Boltzmann machine embedded on quantum hardware, which can serve as a building block for deep-learning architectures. We also provide a comparison to $k$-step contrastive divergence (CD-$k$) with $k$ up to 100. Although assuming a suitable fixed effective temperature also allows us to outperform one step contrastive divergence (CD-1), only when using an instance-dependent effective temperature do we find a performance close to that of CD-100 for the case studied here.

quant-ph↗

arXiv2015

Quantum annealing via environment-mediated quantum diffusion

We show that quantum diffusion near the quantum critical point can provide a highly very efficient mechanism of open-system quantum annealing. It is based on the diffusion-mediated recombination of excitations. For an Ising spin chain coupled to a bosonic bath, excitation diffusion in a transverse field sharply slows down as the system moves away from the quantum critical region. This leads to spatial correlations and effective freezing of the excitation density. We find that obtaining an approximate solution via the diffusion-mediated quantum annealing can be faster than via closed-system quantum annealing or Glauber dynamics.

quant-ph↗

arXiv2015

Determination and correction of persistent biases in quantum annealers

Calibration of quantum computing technologies is essential to the effective utilization of their quantum resources. Specifically, the performance of quantum annealers is likely to be significantly impaired by noise in their programmable parameters, effectively misspecification of the computational problem to be solved, often resulting in spurious suboptimal solutions. We developed a strategy to determine and correct persistent, systematic biases between the actual values of the programmable parameters and their user-specified values. We applied the recalibration strategy to two D-Wave Two quantum annealers, one at NASA Ames Research Center in Moffett Field, California, and another at D-Wave Systems in Burnaby, Canada. We show that the recalibration procedure not only reduces the magnitudes of the biases in the programmable parameters but also enhances the performance of the device on a set of random benchmark instances.

quant-ph↗

arXiv2015

A Performance Estimator for Quantum Annealers: Gauge selection and Parameter Setting

With the advent of large-scale quantum annealing devices, several challenges have emerged. For example, it has been shown that the performance of a device can be significantly affected by several degrees of freedom when programming the device; a common example being gauge selection. To date, no experimentally-tested strategy exists to select the best programming specifications. We developed a score function that can be calculated from a number of readouts much smaller than the number of readouts required to find the desired solution. We show how this performance estimator can be used to guide, for example, the selection of the optimal gauges out of a pool of random gauge candidates and how to select the values of parameters for which we have no a priori knowledge of the optimal value. For the latter, we illustrate the concept by applying the score function to set the strength of the parameter intended to enforce the embedding of the logical graph into the hardware architecture, a challenge frequently encountered in the implementation of real-world problem instances. Since the harder the problem instances, the more useful the strategies proposed in this work are, we expect the programming strategies proposed to significantly reduce the time of future benchmark studies and in help finding the solution of hard-to-solve real-world applications implemented in the next generation of quantum annealing devices.

quant-ph↗

arXiv2014

A Quantum Annealing Approach for Fault Detection and Diagnosis of Graph-Based Systems

Diagnosing the minimal set of faults capable of explaining a set of given observations, e.g., from sensor readouts, is a hard combinatorial optimization problem usually tackled with artificial intelligence techniques. We present the mapping of this combinatorial problem to quadratic unconstrained binary optimization (QUBO), and the experimental results of instances embedded onto a quantum annealing device with 509 quantum bits. Besides being the first time a quantum approach has been proposed for problems in the advanced diagnostics community, to the best of our knowledge this work is also the first research utilizing the route Problem $\rightarrow$ QUBO $\rightarrow$ Direct embedding into quantum hardware, where we are able to implement and tackle problem instances with sizes that go beyond previously reported toy-model proof-of-principle quantum annealing implementations; this is a significant leap in the solution of problems via direct-embedding adiabatic quantum optimization. We discuss some of the programmability challenges in the current generation of the quantum device as well as a few possible ways to extend this work to more complex arbitrary network graphs.

quant-ph↗

arXiv2014

Bayesian Network Structure Learning Using Quantum Annealing

We introduce a method for the problem of learning the structure of a Bayesian network using the quantum adiabatic algorithm. We do so by introducing an efficient reformulation of a standard posterior-probability scoring function on graphs as a pseudo-Boolean function, which is equivalent to a system of 2-body Ising spins, as well as suitable penalty terms for enforcing the constraints necessary for the reformulation; our proposed method requires $\mathcal O(n^2)$ qubits for $n$ Bayesian network variables. Furthermore, we prove lower bounds on the necessary weighting of these penalty terms. The logical structure resulting from the mapping has the appealing property that it is instance-independent for a given number of Bayesian network variables, as well as being independent of the number of data cases.

quant-ph↗

arXiv2013

Construction of Energy Functions for Lattice Heteropolymer Models: A Case Study in Constraint Satisfaction Programming and Adiabatic Quantum Optimization

Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as constraint satisfaction problems such as linear programming, maximum satisfiability, and pseudo-boolean optimization. By encoding problems this way, one can leverage substantial insight and powerful solvers from the computer science community which studies constraint programming for diverse applications such as logistics, scheduling, artificial intelligence, and circuit design. We demonstrate how to constrain and embed lattice heteropolymer problems using several strategies. Each strikes a unique balance between number of constraints, complexity of constraints, and number of variables. Finally, we show how to reduce the locality of couplings in these energy functions so they can be realized as Hamiltonians on existing quantum annealing machines. We intend that this review be used as a case study for encoding related combinatorial optimization problems in a form suitable for adiabatic quantum optimization.

quant-ph↗

arXiv2012

Finding low-energy conformations of lattice protein models by quantum annealing

Lattice protein folding models are a cornerstone of computational biophysics. Although these models are a coarse grained representation, they provide useful insight into the energy landscape of natural proteins. Finding low-energy three-dimensional structures is an intractable problem even in the simplest model, the Hydrophobic-Polar (HP) model. Exhaustive search of all possible global minima is limited to sequences in the tens of amino acids. Description of protein-like properties are more accurately described by generalized models, such as the one proposed by Miyazawa and Jernigan (MJ), which explicitly take into account the unique interactions among all 20 amino acids. There is theoretical and experimental evidence of the advantage of solving classical optimization problems using quantum annealing over its classical analogue (simulated annealing). In this report, we present a benchmark implementation of quantum annealing for a biophysical problem (six different experiments up to 81 superconducting quantum bits). Although the cases presented here can be solved in a classical computer, we present the first implementation of lattice protein folding on a quantum device under the Miyazawa-Jernigan model. This paves the way towards studying optimization problems in biophysics and statistical mechanics using quantum devices.

quant-ph↗

arXiv2011

Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2D fluorescence spectroscopy

By applying a phase-modulation fluorescence approach to 2D electronic spectroscopy, we studied the conformation-dependent exciton-coupling of a porphyrin dimer embedded in a phospholipid bilayer membrane. Our measurements specify the relative angle and separation between interacting electronic transition dipole moments, and thus provide a detailed characterization of dimer conformation. Phase-modulation 2D fluorescence spectroscopy (PM-2D FS) produces 2D spectra with distinct optical features, similar to those obtained using 2D photon-echo spectroscopy (2D PE). Specifically, we studied magnesium meso tetraphenylporphyrin dimers, which form in the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. Comparison between experimental and simulated spectra show that while a wide range of dimer conformations can be inferred by either the linear absorption spectrum or the 2D spectrum alone, consideration of both types of spectra constrains the possible structures to a "T-shaped" geometry. These experiments establish the PM-2D FS method as an effective approach to elucidate chromophore dimer conformation.

physics.chem-ph↗

arXiv2011

Envelope molecular-orbital theory of extended systems I. Electronic states of organic quasi-linear nano-heterostructures

A conceptually appealing and computationally economical course-grained molecular-orbital (MO) theory for extended quasi-linear molecular heterostructures is presented. The formalism, which is based on a straightforward adaptation, by including explicitly the vacuum, of the envelope-function approximation widely employed in solid-state physics, leads to a mapping of the three-dimensional single-particle eigenvalue equations into simple one-dimensional hole and electron Schrödinger-like equations with piecewise-constant effective potentials and masses. The eigenfunctions of these equations are envelope MO's in which the short-wavelength oscillations present in the full MO's, associated with the atomistic details of the molecular potential, are smoothed out automatically. The approach is illustrated by calculating the envelope MO's of high-lying occupied and low-lying virtual $π$ states in prototypical nanometric heterostructures constituted by oligomers of polyacetylene and polydiacetylene. Comparison with atomistic electronic-structure calculations reveals that the envelope-MO energies agree very well with the energies of the $π$ MO's and that the envelope MO's describe precisely the long-wavelength variations of the $π$ MO's. This envelope MO theory, which is generalizable to extended systems of any dimensionality, is seen to provide a useful tool for the qualitative interpretation and quantitative prediction of the single-particle quantum states in mesoscopic molecular structures and the design of nanometric molecular devices with tailored energy levels and wavefunctions.

cond-mat.mes-hall↗

arXiv2010

Simulating chemistry using quantum computers

The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.

quant-ph↗