#36: August 21st – 27th

📰News:

📽Videos:

👨‍💻Developers:

Amazon Braket v1.8.0

 Features
  • Calculate arbitrary observables when shots=0
Bug Fixes and Other Changes
  • Remove immutable default args

📗Papers:


Quantum Alphatron

Patrick Rebentrost,Miklos Santha,Siyi YangAug 27 2021 quant-ph arXiv:2108.11670v1

Many machine learning algorithms optimize a loss function with stochastic gradient descent and use kernel methods to extend linear learning tasks to non-linear learning tasks. Both ideas have been discussed in the context of quantum computing, especially for near-term quantum computing with variational methods and the use of the Hilbert space to encode features of data. In this work, we discuss a quantum algorithm with provable learning guarantee in the fault-tolerant quantum computing model. In a well-defined learning model, this quantum algorithm is able to provide a polynomial speedup for a large range of parameters of the underlying concept class. We discuss two types of speedups, one for evaluating the kernel matrix and one for evaluating the gradient in the stochastic gradient descent procedure. Our work contributes to the study of quantum learning with kernels and noise.

Quantum adaptive agents with efficient long-term memories

Thomas J. Elliott,Mile Gu,Andrew J. P. Garner,Jayne ThompsonAug 25 2021 quant-phcond-mat.stat-mechcs.AIcs.ITmath.IT arXiv:2108.10876v1

Central to the success of adaptive systems is their ability to interpret signals from their environment and respond accordingly — they act as agents interacting with their surroundings. Such agents typically perform better when able to execute increasingly complex strategies. This comes with a cost: the more information the agent must recall from its past experiences, the more memory it will need. Here we investigate the power of agents capable of quantum information processing. We uncover the most general form a quantum agent need adopt to maximise memory compression advantages, and provide a systematic means of encoding their memory states. We show these encodings can exhibit extremely favourable scaling advantages relative to memory-minimal classical agents when information must be retained about events increasingly far into the past.

A variational quantum algorithm for the Feynman-Kac formula

Hedayat Alghassi,Amol Deshmukh,Noelle Ibrahim,Nicolas Robles,Stefan Woerner,Christa ZoufalAug 25 2021 quant-ph arXiv:2108.10846v1

We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the correspondence between the Feynman-Kac partial differential equation (PDE) and the Wick-rotated Schrödinger equation for this purpose. The results for a (2+1)(2+1) dimensional Feynman-Kac system, obtained through the variational quantum algorithm are then compared against classical ODE solvers and Monte Carlo simulation. We see a remarkable agreement between the classical methods and the quantum variational method for an illustrative example on six qubits. In the non-trivial case of PDEs which are preserving probability distributions — rather than preserving the ℓ2ℓ2-norm — we introduce a proxy norm which is efficient in keeping the solution approximately normalized throughout the evolution. The algorithmic complexity and costs associated to this methodology, in particular for the extraction of properties of the solution, are investigated. Future research topics in the areas of quantitative finance and other types of PDEs are also discussed.

New Trends in Quantum Machine Learning

Lorenzo Buffoni,Filippo CarusoAug 24 2021 quant-phcond-mat.dis-nncs.LGstat.ML arXiv:2108.09664v1

Here we will give a perspective on new possible interplays between Machine Learning and Quantum Physics, including also practical cases and applications. We will explore the ways in which machine learning could benefit from new quantum technologies and algorithms to find new ways to speed up their computations by breakthroughs in physical hardware, as well as to improve existing models or devise new learning schemes in the quantum domain. Moreover, there are lots of experiments in quantum physics that do generate incredible amounts of data and machine learning would be a great tool to analyze those and make predictions, or even control the experiment itself. On top of that, data visualization techniques and other schemes borrowed from machine learning can be of great use to theoreticians to have better intuition on the structure of complex manifolds or to make predictions on theoretical models. This new research field, named as Quantum Machine Learning, is very rapidly growing since it is expected to provide huge advantages over its classical counterpart and deeper investigations are timely needed since they can be already tested on the already commercially available quantum machines.

Grover search revisited; application to image pattern matching

Hiroyuki Tezuka,Kouhei Nakaji,Takahiko Satoh,Naoki YamamotoAug 25 2021 quant-ph arXiv:2108.10854v1

The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there have been no proposal to realize the original motivating application of the algorithm, i.e., the database search or more broadly the pattern matching in a practical setting, mainly due to the technical difficulty in efficiently implementing the data loading and amplitude amplification processes. In this paper, we propose a quantum algorithm that approximately executes the entire Grover database search or pattern matching algorithm. The key idea is to use the recently proposed approximate amplitude encoding method on a shallow quantum circuit, together with the easily implementable inversion-test operation for realizing the projected quantum state having similarity to the query data, followed by the amplitude amplification independent to the target index. We provide a thorough demonstration of the algorithm in the problem of image pattern matching.

Training a discrete variational autoencoder for generative chemistry and drug design on a quantum annealer

A.I. Gircha,A.S. Boev,K. Avchaciov,P.O. Fedichev,A.K. FedorovAug 27 2021 quant-phcs.LGq-bio.BMq-bio.QM arXiv:2108.11644v1

Deep generative chemistry models emerge as powerful tools to expedite drug discovery. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome with hybrid architectures combining quantum computers with deep classical networks. We built a compact discrete variational autoencoder (DVAE) with a Restricted Boltzmann Machine (RBM) of reduced size in its latent layer. The size of the proposed model was small enough to fit on a state-of-the-art D-Wave quantum annealer and allowed training on a subset of the ChEMBL dataset of biologically active compounds. Finally, we generated 42904290 novel chemical structures with medicinal chemistry and synthetic accessibility properties in the ranges typical for molecules from ChEMBL. The experimental results point towards the feasibility of using already existing quantum annealing devices for drug discovery problems, which opens the way to building quantum generative models for practically relevant applications.

Variational quantum eigensolver techniques for simulating carbon monoxide oxidation

M.D. Sapova,A.K. FedorovAug 26 2021 physics.chem-phquant-ph arXiv:2108.11167v1

A family of Variational Quantum Eigensolver (VQE) methods is designed to maximize the resource of existing noisy intermediate-scale quantum (NISQ) devices. However, VQE approaches encounter various difficulties in simulating molecules of industrially relevant sizes, among which the choice of the ansatz for the molecular wavefunction plays a crucial role. In this work, we push forward the capabilities of adaptive variational algorithms (ADAPT-VQE) by demonstrating that the measurement overhead can be significantly reduced via adding multiple operators at each step while keeping the ansatz compact. Within the proposed approach, we simulate a set of molecules, O22, CO, and CO22, participating in the carbon monoxide oxidation processes using the statevector simulator and compare our findings with the results obtained using VQE-UCCSD and classical methods. Based on these results, we estimate the energy characteristics of the chemical reaction. Our results pave the way to the use of variational approaches for solving practically relevant chemical problems.

Quantum kernels with squeezed-state encoding for machine learning

Long Hin Li,Dan-Bo Zhang,Z. D. WangAug 26 2021 quant-ph arXiv:2108.11114v1

Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is closely related to kernel methods, where the exponentially large Hilbert space turns to be a feature space more expressive than classical ones. In this paper, we generalize quantum kernel methods by encoding data into continuous-variable quantum states, which can benefit from the infinite-dimensional Hilbert space of continuous variables. Specially, we propose squeezed-state encoding, in which data is encoded as either in the amplitude or the phase. The kernels can be calculated on a quantum computer and then are combined with classical machine learning, e.g. support vector machine, for training and predicting tasks. Their comparisons with other classical kernels are also addressed. Lastly, we discuss physical implementations of squeezed-state encoding for machine learning in quantum platforms such as trapped ions.

Unraveling correlated materials’ properties with noisy quantum computers: Natural-orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach

Pauline Besserve,Thomas AyralAug 25 2021 quant-phcond-mat.str-el arXiv:2108.10780v1

We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy that uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve the embedded model. While previous approaches were limited to purely local, one-impurity embedded models, requiring at most four qubits and relatively shallow circuits, we solve a two-impurity model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This iterative scheme, dubbed Natural Orbitalization (NOization), gradually transforms the single-particle basis to the approximate Natural-Orbital basis, in which the ground state can be minimally expressed, at the cost of measuring the one-particle reduced density-matrix of the embedded problem. We show that this transformation tends to make the variational optimization of existing (but too deep) ansatz circuits faster and more accurate, and we propose an ansatz, the Multi-Reference Excitation Preserving (MREP) ansatz, that achieves great expressivity without requiring a prohibitive gate count. The one-impurity version of the ansatz has only one parameter, making the ground state preparation a trivial step, which supports the optimal character of our approach. Within a Rotationally Invariant Slave Boson embedding scheme that requires a minimal number of bath sites and does not require computing the full Green’s function, the NOization combined with the MREP ansatz allow us to compute accurate, space-resolved quasiparticle weights and static self-energies for the Hubbard model even in the presence of noise levels representative of current NISQ processors. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.

Quantum Artificial Intelligence for the Science of Climate Change

Manmeet Singh,Chirag Dhara,Adarsh Kumar,Sukhpal Singh Gill,Steve UhligAug 25 2021 cs.AIphysics.ao-phquant-ph arXiv:2108.10855v1

Climate change has become one of the biggest global problems increasingly compromising the Earth’s habitability. Recent developments such as the extraordinary heat waves in California & Canada, and the devastating floods in Germany point to the role of climate change in the ever-increasing frequency of extreme weather. Numerical modelling of the weather and climate have seen tremendous improvements in the last five decades, yet stringent limitations remain to be overcome. Spatially and temporally localized forecasting is the need of the hour for effective adaptation measures towards minimizing the loss of life and property. Artificial Intelligence-based methods are demonstrating promising results in improving predictions, but are still limited by the availability of requisite hardware and software required to process the vast deluge of data at a scale of the planet Earth. Quantum computing is an emerging paradigm that has found potential applicability in several fields. In this opinion piece, we argue that new developments in Artificial Intelligence algorithms designed for quantum computers – also known as Quantum Artificial Intelligence (QAI) – may provide the key breakthroughs necessary to furthering the science of climate change. The resultant improvements in weather and climate forecasts are expected to cascade to numerous societal benefits.

Categories: Week-in-QML

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