In this talk, I will present the meta-VQE, an algorithm capable to learn the ground state energy profile of a parametrized Hamiltonian. By training the meta-VQE with a few data points, it delivers an initial circuit parametrization that can be used to compute the ground state energy of any parametrization of the Hamiltonian within a certain trust region. We test this algorithm with a XXZ spin chain, an electronic H4 Hamiltonian and a single-transmon quantum simulation. In all cases, the meta-VQE is able to learn the shape of the energy functional and, in some cases, resulted in improved accuracy in comparison to individual VQE optimization. The meta-VQE algorithm introduces both a gain in efficiency for parametrized Hamiltonians, in terms of the number of optimizations, and a good starting point for the quantum circuit parameters for individual optimizations. The proposed algorithm can be readily mixed with other improvements in the field of variational algorithms to shorten the distance between the current state-of-the-art and applications with quantum advantage.

PRX Quantum 2, 020329 (2021) (preprint: https://arxiv.org/abs/2009.13545)

Although Evolutionary Algorithms (EAs) have made big progress over the past few decades, researches are increasingly faced with the difficulty of choosing an appropriate algorithm capable to solve their optimisation problem in an efficient manner. Furthermore, the complexity of most real-world optimisation problems, including high dimensionality and computational expensiveness, together with big data makes new challenges for EAs. To achieve significant improvement of performance, EAs are inspired from Quantum Physics and Quantum Computing (QC) for their application on classical computers. We discuss, how quantum-inspired approach can provide a boost to EAs, enabling them to reduce the number of calls of evaluation functions and consequently, to efficiently tackle complex problems on the classical computers. On the other hand, we explore how EAs can help to overcome current limitations of Noisy Intermediate-Scale Quantum (NISQ) technologies. QC and EAs together has a great potential for development of Quantum Computational Intelligence.

Computationally intractable tasks are often encountered in physics and optimization. Such tasks often comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints. This may yield, in general, to difficult and non-convex optimization tasks. A number of standard methods are used to tackle such problems: variational approaches focus on parameterizing a subclass of solutions within the feasible set; in contrast, relaxation techniques have been proposed to approximate it from outside, thus complementing the variational approach by providing ultimate bounds to the global optimal solution. In this work, we propose a novel approach combining the power of relaxation techniques with deep reinforcement learning in order to find the best possible bounds within a limited computational budget. We illustrate the viability of the method in the context of finding the ground state energy of many-body quantum systems, a paradigmatic problem in quantum physics. We benchmark our approach against other classical optimization algorithms such as breadth-first search or Monte-Carlo, and we characterize the effect of transfer learning. We find the latter may be indicative of phase transitions, with a completely autonomous approach. Finally, we provide tools to generalize the approach to other common applications in the field of quantum information processing.

Many combinatorial optimization problems relevant to computer science, computational biology, and physics can be tackled with simulated annealing, which is a powerful framework for optimizing the properties of complex systems through the lens of statistical mechanics. However, simulated annealing and its quantum counterpart, simulated quantum annealing, are traditionally implemented via Markov chain Monte Carlo, often displaying slow convergence to optimal solutions for challenging optimization problems. We show a combination of the variational principle in classical and quantum physics with recurrent neural networks (RNNs), whose dynamics are naturally devoid of slow Markov chains, to emulate annealing in its classical and quantum formulations, for the purpose of solving optimization problems. We find that our variational implementation of classical annealing is not only superior to its quantum analog in terms of speed of convergence and accuracy of solutions but also outperforms traditional simulated annealing and simulated quantum annealing on prototypical spin glass models in the asymptotic limit. These results advocate for the use of our variational implementation of classical annealing as a competitive algorithm to tackle real-world optimization problems.

arXiv preprint: https://arxiv.org/pdf/2101.10154.pdf

Tensor network methods are an efficient classical numerical approach that is becoming a powerful tool to support quantum simulators and computers development, providing benchmarking, verification, and insights into the quantum computation and simulation results. We review some of their latest achievements in quantum computation and simulation benchmarking and their application as a novel route to perform machine learning tasks. As an exemplary application, we apply them to events classification of the LHCb experiment and show how quantum information concepts can be used to improve and explain the classification performance.

I will present a family of experimentally friendly protocols to benchmark quantum devices. In our protocols, we analyze the bitstrings accumulated from randomized measurements to estimate the key physical properties characterizing a quantum device: purity, state fidelities, entanglement criteria, etc. The estimations are made in a state agnostic way, and are robust against measurement errors. I will also show how to boost the efficiency of our protocols using importance sampling, and machine learning based regression methods.

Excitement about the promise of quantum computers is tempered by the reality that the hardware remains exceptionally fragile and error-prone, forming a bottleneck in the development of novel applications. In this talk I will introduce the concept and experimental implementation of robust quantum control, providing a pathway to maximizing hardware performance in near term systems, and forming a complement to quantum error correction in future systems. I will present the first demonstration of Deep Reinforcement Learning (DRL) to autonomously design a Universal gateset showing superior performance to calibrated default gates. DRL-designed two-qubit cross-resonance gates exhibit ~2.5X improvements relative to standard gates, and obviate the need for additional compensating signals designed to mitigate crosstalk. We demonstrate drift-robust two-qubit gate performance at the level of ~99.5% fidelity (near T1 limits) up to 25 days from gate design with no recalibration, while default gates require recalibration every 12-24 hours. These experiments reveal a pathway to autonomously designing error-robust quantum logic at scale across complex systems with unknown couplings and Hamiltonian terms.

The current methodology of designing control pulses for superconducting circuits often results in an absurd situation: simplified analytic models which fail to predict gate fidelities to high accuracy, and calibrated pulse shapes which achieve good fidelities, but have no corresponding model. Moreover, for a large number of qubits the QPU calibration is long and difficult, and determining a detailed error budget is nearly impossible. But without an error budget we have no insight into what is limiting QPU performance and how to improve it. To rectify the situation, we are implementing a novel procedure of Combined Calibration and Characterization (C3): An iterative combination of open-loop control optimization, model-free reinforcement learning of controls and iterative model learning from experimental data, utilizing a high-performance TensorFlow simulator. C3 will allow for a rapid, and largely automated bring-up process of QPUs. The result is a high-fidelity model, commensurate high-fidelity gates and a detailed error budget. Further, these serve as the basis for additional machine-learning capabilities such as adversarial system characterization and automated experiment design, to further accelerate the process of gaining insight into the behavior of our systems. C3 software is made available as an open-source project at q-optimize.org.

At the intersection of machine learning and noisy intermediate-scale quantum computing lies optimization problems traditionally associated with quantum optimal control theory.

In this presentation, I discuss striking results from applying reinforcement learning using AlphaZero as well as supervised learning using a landscape metamodel. These demonstrate that black box quantum dynamics can be efficiently classically learned and used to steer the quantum optimizer well beyond standard local hill climbing.

In this talk I show how we use Gaussian Process Regression (GPR) in our daily research. As examples I discuss (i) the extraction of geometry parameters of a molecular dimer and (ii) the optimization of laser parameters for a Rydberg quantum simulator [1]. I conclude with comments on the determination of excitonic wavefunctions from near field spectroscopy [2].

[1] C.D.B. Bentley, A. Eisfeld; J. Phys. B 51, 205003 (2018)
[2] F. Zheng, X. Gao, A. Eisfeld; Phys. Rev. Lett. 123, 163202 (2019)

Weakly-bound complexes are appealing as model systems for ultrafast-dynamics studies of bimolecular chemical reactions. Unraveling the dynamical basis of such molecular and chemical processes requires an accurate quantum mechanical description of these systems. However, this is very challenging due to the large-amplitude character of the motions, resulting in potential-energy surfaces with complicated shapes, e.g., many minima and connecting saddle points. The exponential scaling of the computational burden with the number of degrees of freedom, i.e., size of the molecular system, renders the computational costs of existing variational methods unaffordable for clusters composed of more than two moieties.

Here, we present our recent application of machine-learning algorithms for simulating the dynamics of the weakly-bound pyrrole-water dimer. In particular, we present a new active-learning algorithm designed for the construction of multi-dimensional ab initio potential energy surfaces using a minimum number of electronic structure calculations [1]. Furthermore, we present our ongoing efforts to construct a reliable and computationally efficient nonlinear variational framework to simultaneously compute several eigenfunctions of linear Hamiltonians acting on infinite-dimensional Hilbert spaces.

[1] Y. Saleh, V. Sanjay, A. Iske, A. Yachmenev, and J. Küpper, J. Chem. Phys., submitted (2021); arXiv:2104.00708 [physics].

The design of new quantum experiments and hardware can be demanding for humans. To overcome this challenge, scientists begin to employ computational and artificial intelligence-powered design methods to discover new quantum experiments with particular desired functionalities [1]. Numerous computer-designed experiments have been implemented in laboratories, allowing for the observation of quantum phenomena that before have only been studied on paper.

At this point, one important question arises: Do we understand the solutions discovered by computers? Can we learn something new? This is crucial, because — after all — scientific understanding is an essential aim of Physics. We take inspiration from the Philosophy of Science [2], and describe an algorithm that can solve previously open design questions in quantum optics, and simultaneously extract the conceptual cores of solutions. Human scientists can then understand and generalize these conceptual cores [3]. This result indicates that computers can take a new role in physics and act as a (re)source of inspiration for new scientific concepts and understanding.

[1] Krenn, Erhard, Zeilinger, Computer-inspired quantum experiments. Nature Reviews Physics, 2(11), 649-661 (2020).
[2] De Regt, Understanding scientific understanding. Oxford University Press (2017).
[3] Krenn, Kottmann, Tischler, Aspuru-Guzik, Conceptual understanding through efficient inverse-design of quantum optical experiments. arXiv:2005.06443.

In this work, we develop a variational quantum algorithm to solve partial differential equations (PDE’s) using a space-efficient variational ansatz that merges structured quantum circuits for coarse-graining with Fourier-based interpolation. We implement variational circuits to represent symmetrical smooth functions as the ansatz and combine them with classical optimizers that differ on the gradient calculation: no gradient, numerical gradient and analytic gradient. We apply this method to the computation of the ground state of the one-dimensional quantum harmonic oscillator and the transmon qubit. In idealized quantum computers, we show that the harmonic oscillator can be solved with an infidelity of order 10^{−5} with 3 qubits and the transmon qubit with an error of order 10^{−4} with 4 qubits. We find that these fidelities can be approached in real noisy quantum computers, either directly or through error mitigation techniques. However, we also find that the precision in the estimate of the eigenvalues is still sub-par with other classical methods, suggesting the need for better strategies in the optimization and the evaluation of the cost function itself.

Modern quantum simulators can prepare a wide variety of quantum states, but extraction of relevant observables from this “quantum data” is often challenging.

We tackle this problem by developing a quantum state tomography scheme for open quantum systems, which relies on approximating the target POVM (positive operator valued measurement) distribution in the variational manifold represented by a convolutional neural network. We show an excellent representability of typical ground- and steady states within the network, often requiring only a polynomial scaling of the number of variational parameters. This compressed representation allows us to achieve RMS (root mean square) errors of experimentally interesting observables that are up to an order of magnitude smaller than what is obtainable via standard methods for identical sample sizes.

Many of the most relevant observables of matter depend explicitly on atomistic and electronic details, rendering a first principles approach to computational materials design mandatory. Alas, even when using high-performance computers, brute force high-throughput screening of material candidates is beyond any capacity for all but the simplest systems and properties due to the combinatorial nature of compound space, i.e. all the possible combinations of compositional and structural degrees of freedom. Consequently, efficient exploration algorithms exploit implicit redundancies and correlations. I will discuss recently developed statistical learning based approaches for interpolating quantum mechanical observables throughout compound space. Numerical results indicate promising performance in terms of efficiency, accuracy, scalability and transferability.

Coauthors: Richard Li, Rosa Di Felice, Remo Rohs, Daniel Lidar

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. We studied the ability of a quantum machine learning approach to classify and rank binding affinities. Using simplified data sets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding.

The results were compared to state-of-the-art classical approaches for the same simplified data sets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. We retrieve biologically relevant information. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems.

One of the most significant challenges in the field of topological matter is the determination of global topological invariants from local measurements. Solving this problem will enable significant advances in the physics of topological materials. It could pave the way to determine the Chern number in two-dimensional chiral superconductors. We investigate the utilization of supervised machine learning to determine Chern numbers based on the local density of states measurements.

We develop a variational approach to simulating the dynamics of open quantum many-body systems using deep autoregressive neural networks. The parameters of a compressed representation of a mixed quantum state are adapted dynamically according to the Lindblad master equation by employing a time-dependent variational principle. We illustrate our approach by solving the dissipative quantum Heisenberg model in one and two dimensions for up to 40 spins and by applying it to the simulation of confinement dynamics in the presence of dissipation.

We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a significant improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to next generation of variational problems with many physical degrees of freedom.

arXiv: https://arxiv.org/abs/2103.16161

Molecules can be modeled on computers by solving the Schrödinger equation for the electrons. Multi-reference theories are a subclass of such quantum chemistry methods for some particularly challenging types of problems. Having been established in traditional computational chemistry for a long time, multi-reference methods have also received significant interest in the quantum computing scene: the system is partitioned into an active space, which could be solved on a prospective quantum computer, and the remainder that would be treated on a classical computer. Difficulties in the application of multi-reference methods include the high computational demand, and the need to select an active space.

In ongoing work at HQS, we are employing a machine learning method to create models of potential energy surfaces for molecules. Energies and gradients from quantum chemical multi-reference calculations (on classical computers) are taken as the input for the machine learning procedure. The goal is to create representations of the potential energy surface for specific molecules. Ultimately, such models can be used to calculate the dynamics of the respective molecules faster and more easily than by direct application of the quantum chemical methods.

In recent years Machine Learning has made strong progress based on the application of deep neural networks and corresponding training methods. This is also true in the field of sensors and sensor solutions for industrial automation. In this contribution, application examples from factory automation and logistics automation will be shown. The context of digitization and Industry 4.0 will be discussed briefly together with the aspect of “inference at the edge”. An outlook into possible connections with Quantum Technology will be given from an industrial point of view.

Given the current limitations of the quantum hardware, a promising class of quantum algorithms is the one of the heuristic algorithms, which combine classical and quantum computers in order to find the optimal solution of a problem. All the projects that involve working with graphs or that require a subroutine of combinatorial optimization could highly benefit in terms of speedup from these heuristic algorithms. A well-known example of this class of algorithms is the quantum approximate optimization algorithm (QAOA) whose hybrid quantum-classical nature combines the parametrized evolution of a quantum state with a classical optimization routine. Typically, the optimization of the gate parameters in the quantum circuit is performed via simple search strategies or gradient-based methods. In this talk we will explore different optimization methods and compare their performance and success probability.

In this talk, I will focus on how NISQ device algorithm. Start with a basic review of the NISQ QML algorithm and explain our method of supervised quantum machine learning that predicts the excited-state properties of molecules only from their ground state wavefunction. Our method reduced the computational cost for calculating the excited states.

Predicting excited states from ground state wavefunction by supervised quantum machine learning – IOP Science