Quantum random access memory

Quantum algorithms for scientific computing

Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in real world applications. Areas that are likely to have the greatest impact on high performance computing (HPC) include simulation of quantum systems, optimization, and machine learning. We draw our examples from electronic structure calculations and computational fluid dynamics which account for a large fraction of current scientific and engineering use of HPC. Potential challenges include encoding and decoding classical data for quantum devices, and mismatched clock speeds between classical and quantum processors. Even a modest quantum enhancement to current classical techniques would have far-reaching impacts in areas such as weather forecasting, aerospace engineering, and the design of 'green' materials for sustainable development. This requires significant effort from the computational science, engineering and quantum computing communities working together.

Blind Quantum Machine Learning with Quantum Bipartite Correlator

Distributed quantum computing is a promising computational paradigm for performing computations that are beyond the reach of individual quantum devices. Privacy in distributed quantum computing is critical for maintaining confidentiality and protecting the data in the presence of untrusted computing nodes. In this Letter, we introduce novel blind quantum machine learning protocols based on the quantum bipartite correlator algorithm. Our protocols have reduced communication overhead while preserving the privacy of data from untrusted parties. We introduce robust algorithm-specific privacy-preserving mechanisms with low computational overhead that do not require complex cryptographic techniques. We then validate the effectiveness of the proposed protocols through complexity and privacy analysis. Our findings pave the way for advancements in distributed quantum computing, opening up new possibilities for privacy-aware machine learning applications in the era of quantum technologies.

Future Potential of Quantum Computing and Simulations in Biological Science

The review article presents the recent progress in quantum computing and simulation within the field of biological sciences. The article is designed mainly into two portions: quantum computing and quantum simulation. In the first part, significant aspects of quantum computing was illustrated, such as quantum hardware, quantum RAM and big data, modern quantum processors, qubit, superposition effect in quantum computation, quantum interference, quantum entanglement, and quantum logic gates. Simultaneously, in the second part, vital features of the quantum simulation was illustrated, such as the quantum simulator, algorithms used in quantum simulations, and the use of quantum simulation in biological science. Finally, the review provides exceptional views to future researchers about different aspects of quantum simulation in biological science.

Variational quantum algorithm for node embedding

Quantum machine learning has made remarkable progress in many important tasks. However, the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms, making them non-end-to-end. Herein, we propose a quantum algorithm for the node embedding problem that maps a node graph's topological structure to embedding vectors. The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms. With O ( log ( N ) ) qubits to store the information of N nodes, our algorithm will not lose quantum advantage for the subsequent quantum information processing. Moreover, owing to the use of a parameterized quantum circuit with O ( poly ( log ( N ) ) ) depth, the resulting state can serve as an efficient quantum database. In addition, we explored the measurement complexity of the quantum node embedding algorithm, which is the main issue in training parameters, and extended the algorithm to capture high-order neighborhood information between nodes. Finally, we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.

Quantum-parallel vectorized data encodings and computations on trapped-ion and transmon QPUs

Compact data representations in quantum systems are crucial for the development of quantum algorithms for data analysis. In this study, we present two innovative data encoding techniques, known as QCrank and QBArt, which exhibit significant quantum parallelism via uniformly controlled rotation gates. The QCrank method encodes a series of real-valued data as rotations on data qubits, resulting in increased storage capacity. On the other hand, QBArt directly incorporates a binary representation of the data within the computational basis, requiring fewer quantum measurements and enabling well-established arithmetic operations on binary data. We showcase various applications of the proposed encoding methods for various data types. Notably, we demonstrate quantum algorithms for tasks such as DNA pattern matching, Hamming weight computation, complex value conjugation, and the retrieval of a binary image with 384 pixels, all executed on the Quantinuum trapped-ion QPU. Furthermore, we employ several cloud-accessible QPUs, including those from IBMQ and IonQ, to conduct supplementary benchmarking experiments.

On the complexity of quantum link prediction in complex networks

Link prediction methods use patterns in known network data to infer which connections may be missing. Previous work has shown that continuous-time quantum walks can be used to represent path-based link prediction, which we further study here to develop a more optimized quantum algorithm. Using a sampling framework for link prediction, we analyze the query access to the input network required to produce a certain number of prediction samples. Considering both well-known classical path-based algorithms using powers of the adjacency matrix as well as our proposed quantum algorithm for path-based link prediction, we argue that there is a polynomial quantum advantage on the dependence on N, the number of nodes in the network. We further argue that the complexity of our algorithm, although sub-linear in N, is limited by the complexity of performing a quantum simulation of the network's adjacency matrix, which may prove to be an important problem in the development of quantum algorithms for network science in general.

Towards provably efficient quantum algorithms for large-scale machine-learning models

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as [Formula: see text], where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

A universal variational quantum eigensolver for non-Hermitian systems

Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices-Inspired by Schur's triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver-With additional [Formula: see text] quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm's feasibility. We also undertake a comprehensive parametric study to validate VQUE's scalability, generality, and performance in realistic applications.

Implementation and empirical evaluation of a quantum machine learning pipeline for local classification

In the current era, quantum resources are extremely limited, and this makes difficult the usage of quantum machine learning (QML) models. Concerning the supervised tasks, a viable approach is the introduction of a quantum locality technique, which allows the models to focus only on the neighborhood of the considered element. A well-known locality technique is the k-nearest neighbors (k-NN) algorithm, of which several quantum variants have been proposed; nevertheless, they have not been employed yet as a preliminary step of other QML models. Instead, for the classical counterpart, a performance enhancement with respect to the base models has already been proven. In this paper, we propose and evaluate the idea of exploiting a quantum locality technique to reduce the size and improve the performance of QML models. In detail, we provide (i) an implementation in Python of a QML pipeline for local classification and (ii) its extensive empirical evaluation. Regarding the quantum pipeline, it has been developed using Qiskit, and it consists of a quantum k-NN and a quantum binary classifier, both already available in the literature. The results have shown the quantum pipeline's equivalence (in terms of accuracy) to its classical counterpart in the ideal case, the validity of locality's application to the QML realm, but also the strong sensitivity of the chosen quantum k-NN to probability fluctuations and the better performance of classical baseline methods like the random forest.

Error Suppression for Arbitrary-Size Black Box Quantum Operations

Efficient suppression of errors without full error correction is crucial for applications with noisy intermediate-scale quantum devices. Error mitigation allows us to suppress errors in extracting expectation values without the need for any error correction code, but its applications are limited to estimating expectation values, and cannot provide us with high-fidelity quantum operations acting on arbitrary quantum states. To address this challenge, we propose to use error filtration (EF) for gate-based quantum computation, as a practical error suppression scheme without resorting to full quantum error correction. The result is a general-purpose error suppression protocol where the resources required to suppress errors scale independently of the size of the quantum operation, and does not require any logical encoding of the operation. The protocol provides error suppression whenever an error hierarchy is respected-that is, when the ancillary controlled-swap operations are less noisy than the operation to be corrected. We further analyze the application of EF to quantum random access memory, where EF offers hardware-efficient error suppression.

Learning to Learn Variational Quantum Algorithm

Variational quantum algorithms (VQAs) use classical computers as the quantum outer loop optimizer and update the circuit parameters to obtain an approximate ground state. In this article, we present a meta-learning variational quantum algorithm (meta-VQA) by recurrent unit, which uses a technique called "meta-learner." Motivated by the hybrid quantum-classical algorithms, we train classical recurrent units to assist quantum computing, learning to find approximate optima in the parameter landscape. Here, aiming to reduce the sampling number more efficiently, we use the quantum stochastic gradient descent method and introduce the adaptive learning rate. Finally, we deploy on the TensorFlow Quantum processor within approximate quantum optimization for the Ising model and variational quantum eigensolver for molecular hydrogen (H2), lithium hydride (LiH), and helium hydride cation (HeH+). Our algorithm can be expanded to larger system sizes and problem instances, which have higher performance on near-term processors.

Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed 'quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.

Quantum Random Access Memory for Dummies

Quantum Random Access Memory (QRAM) has the potential to revolutionize the area of quantum computing. QRAM uses quantum computing principles to store and modify quantum or classical data efficiently, greatly accelerating a wide range of computer processes. Despite its importance, there is a lack of comprehensive surveys that cover the entire spectrum of QRAM architectures. We fill this gap by providing a comprehensive review of QRAM, emphasizing its significance and viability in existing noisy quantum computers. By drawing comparisons with conventional RAM for ease of understanding, this survey clarifies the fundamental ideas and actions of QRAM. QRAM provides an exponential time advantage compared to its classical counterpart by reading and writing all data at once, which is achieved owing to storage of data in a superposition of states. Overall, we compare six different QRAM technologies in terms of their structure and workings, circuit width and depth, unique qualities, practical implementation, and drawbacks. In general, with the exception of trainable machine learning-based QRAMs, we observe that QRAM has exponential depth/width requirements in terms of the number of qubits/qudits and that most QRAM implementations are practical for superconducting and trapped-ion qubit systems.

A Survey of Universal Quantum von Neumann Architecture

The existence of universal quantum computers has been theoretically well established. However, building up a real quantum computer system not only relies on the theory of universality, but also needs methods to satisfy requirements on other features, such as programmability, modularity, scalability, etc. To this end, here we study the recently proposed model of quantum von Neumann architecture by putting it in a practical and broader setting, namely, the hierarchical design of a computer system. We analyze the structures of quantum CPU and quantum control units and draw their connections with computational advantages. We also point out that a recent demonstration of our model would require less than 20 qubits.

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

Optimal quantum network decongestion strategies

This study clarifies the problem of decongestion in quantum networks, with a specific focus on the crucial task of entanglement distribution. Entangled particles are a valuable resource in quantum networks, as they are used for most quantum protocols. As such, ensuring that nodes in quantum networks are supplied with entanglement efficiently is mandatory. Many times, parts of a quantum network are contested by multiple entanglement resupply processes and the distribution of entanglement becomes a challenge. The most common network intersection topology, the star-shape and it's various generalizations, are analyzed, and effective decongestion strategies, in order to achieve optimal entanglement distribution, are proposed. The analysis is comprehensive and relies on rigorous mathematical calculations which aids in selecting the most appropriate strategy for different scenarios optimally.

A quantum parallel Markov chain Monte Carlo

We propose a novel hybrid quantum computing strategy for parallel MCMC algorithms that generate multiple proposals at each step. This strategy makes the rate-limiting step within parallel MCMC amenable to quantum parallelization by using the Gumbel-max trick to turn the generalized accept-reject step into a discrete optimization problem. When combined with new insights from the parallel MCMC literature, such an approach allows us to embed target density evaluations within a well-known extension of Grover's quantum search algorithm. Letting P d e n o t e t h e n u m b e r o f p r o p o s a l s i n a s i n g l e M C M C i t e r a t i o n , t h e c o m b i n e d s t r a t e g y r e d u c e s t h e n u m b e r o f t a r g e t e v a l u a t i o n s r e q u i r e d f r o m 𝒪 ( P ) t o 𝒪 P 1 / 2 . In the following, we review the rudiments of quantum computing, quantum search and the Gumbel-max trick in order to elucidate their combination for as wide a readership as possible.

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

Noisy Intermediate-Scale Quantum (NISQ) systems and associated programming interfaces make it possible to explore and investigate the design and development of quantum computing techniques for Machine Learning (ML) applications. Among the most recent quantum ML approaches, Quantum Neural Networks (QNN) emerged as an important tool for data analysis. With the QNN advent, higher-level programming interfaces for QNN have been developed. In this paper, we survey the current state-of-the-art high-level programming approaches for QNN development. We discuss target architectures, critical QNN algorithmic components, such as the hybrid workflow of Quantum Annealers and Parametrized Quantum Circuits, QNN architectures, optimizers, gradient calculations, and applications. Finally, we overview the existing programming QNN frameworks, their software architecture, and associated quantum simulators.

Communication-Efficient Quantum Algorithm for Distributed Machine Learning

The growing demands of remote detection and an increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles two traditional machine learning problems, the least-square fitting and softmax regression problems, in the scenario where the dataset is distributed across two parties. Our quantum algorithm finds the model parameters with a communication complexity of O(log_{2}(N)/ε), where N is the number of data points and ε is the bound on parameter errors. Compared to classical and other quantum methods that achieve the same goal, our methods provide a communication advantage in the scaling with data volume. The core of our methods, the quantum bipartite correlator algorithm that estimates the correlation or the Hamming distance of two bit strings distributed across two parties, may be further applied to other information processing tasks.

A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods

Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.

Quantum Computing Approaches for Vector Quantization-Current Perspectives and Developments

In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization.

Variational quantum approximate support vector machine with inference transfer

A kernel-based quantum classifier is the most practical and influential quantum machine learning technique for the hyper-linear classification of complex data. We propose a Variational Quantum Approximate Support Vector Machine (VQASVM) algorithm that demonstrates empirical sub-quadratic run-time complexity with quantum operations feasible even in NISQ computers. We experimented our algorithm with toy example dataset on cloud-based NISQ machines as a proof of concept. We also numerically investigated its performance on the standard Iris flower and MNIST datasets to confirm the practicality and scalability.

Entanglement of Signal Paths via Noisy Superconducting Quantum Devices

Quantum routers will provide for important functionality in emerging quantum networks, and the deployment of quantum routing in real networks will initially be realized on low-complexity (few-qubit) noisy quantum devices. A true working quantum router will represent a new application for quantum entanglement-the coherent superposition of multiple communication paths traversed by the same quantum signal. Most end-user benefits of this application are yet to be discovered, but a few important use-cases are now known. In this work, we investigate the deployment of quantum routing on low-complexity superconducting quantum devices. In such devices, we verify the quantum nature of the routing process as well as the preservation of the routed quantum signal. We also implement quantum random access memory, a key application of quantum routing, on these same devices. Our experiments then embed a five-qubit quantum error-correcting code within the router, outlining the pathway for error-corrected quantum routing. We detail the importance of the qubit-coupling map for a superconducting quantum device that hopes to act as a quantum router, and experimentally verify that optimizing the number of controlled-X gates decreases hardware errors that impact routing performance. Our results indicate that near-term realization of quantum routing using noisy superconducting quantum devices within real-world quantum networks is possible.

Insights from incorporating quantum computing into drug design workflows

MOTIVATION

While many quantum computing (QC) methods promise theoretical advantages over classical counterparts, quantum hardware remains limited. Exploiting near-term QC in computer-aided drug design (CADD) thus requires judicious partitioning between classical and quantum calculations.

RESULTS

We present HypaCADD, a hybrid classical-quantum workflow for finding ligands binding to proteins, while accounting for genetic mutations. We explicitly identify modules of our drug-design workflow currently amenable to replacement by QC: non-intuitively, we identify the mutation-impact predictor as the best candidate. HypaCADD thus combines classical docking and molecular dynamics with quantum machine learning (QML) to infer the impact of mutations. We present a case study with the coronavirus (SARS-CoV-2) protease and associated mutants. We map a classical machine-learning module onto QC, using a neural network constructed from qubit-rotation gates. We have implemented this in simulation and on two commercial quantum computers. We find that the QML models can perform on par with, if not better than, classical baselines. In summary, HypaCADD offers a successful strategy for leveraging QC for CADD.

AVAILABILITY AND IMPLEMENTATION

Jupyter Notebooks with Python code are freely available for academic use on GitHub: https://www.github.com/hypahub/hypacadd_notebook.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Stable Many-Body Resonances in Open Quantum Systems

Periodically driven quantum many-body systems exhibit novel nonequilibrium states, such as prethermalization, discrete time crystals, and many-body localization. Recently, the general mechanism of fractional resonances has been proposed that leads to slowing the many-body dynamics in systems with both U(1) and parity symmetry. Here, we show that fractional resonance is stable under local noise models. To corroborate our finding, we numerically study the dynamics of a small-scale Bose–Hubbard model that can readily be implemented in existing noisy intermediate-scale quantum (NISQ) devices. Our findings suggest a possible pathway toward a stable nonequilibrium state of matter, with potential applications of quantum memories for quantum information processing.

Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Quantum state preparation is an important subroutine for quantum computing. We show that any n-qubit quantum state can be prepared with a Θ(n)-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with d⩾2 nonzero entries, we can reduce the circuit depth to Θ(log(nd)) with O(ndlogd) ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.

Biology and medicine in the landscape of quantum advantages

Quantum computing holds substantial potential for applications in biology and medicine, spanning from the simulation of biomolecules to machine learning methods for subtyping cancers on the basis of clinical features. This potential is encapsulated by the concept of a quantum advantage, which is contingent on a reduction in the consumption of a computational resource, such as time, space or data. Here, we distill the concept of a quantum advantage into a simple framework to aid researchers in biology and medicine pursuing the development of quantum applications. We then apply this framework to a wide variety of computational problems relevant to these domains in an effort to (i) assess the potential of practical advantages in specific application areas and (ii) identify gaps that may be addressed with novel quantum approaches. In doing so, we provide an extensive survey of the intersection of biology and medicine with the current landscape of quantum algorithms and their potential advantages. While we endeavour to identify specific computational problems that may admit practical advantages throughout this work, the rapid pace of change in the fields of quantum computing, classical algorithms and biological research implies that this intersection will remain highly dynamic for the foreseeable future.

Generalization Performance of Quantum Metric Learning Classifiers

Quantum computing holds great promise for a number of fields including biology and medicine. A major application in which quantum computers could yield advantage is machine learning, especially kernel-based approaches. A recent method termed quantum metric learning, in which a quantum embedding which maximally separates data into classes is learned, was able to perfectly separate ant and bee image training data. The separation is achieved with an intrinsically quantum objective function and the overall approach was shown to work naturally as a hybrid classical-quantum computation enabling embedding of high dimensional feature data into a small number of qubits. However, the ability of the trained classifier to predict test sample data was never assessed. We assessed the performance of quantum metric learning on test ants and bees image data as well as breast cancer clinical data. We applied the original approach as well as variants in which we performed principal component analysis (PCA) on the feature data to reduce its dimensionality for quantum embedding, thereby limiting the number of model parameters. If the degree of dimensionality reduction was limited and the number of model parameters was constrained to be far less than the number of training samples, we found that quantum metric learning was able to accurately classify test data.

An ultra-high gain single-photon transistor in the microwave regime

A photonic transistor that can switch or amplify an optical signal with a single gate photon requires strong non-linear interaction at the single-photon level. Circuit quantum electrodynamics provides great flexibility to generate such an interaction, and thus could serve as an effective platform to realize a high-performance single-photon transistor. Here we demonstrate such a photonic transistor in the microwave regime. Our device consists of two microwave cavities dispersively coupled to a superconducting qubit. A single gate photon imprints a phase shift on the qubit state through one cavity, and further shifts the resonance frequency of the other cavity. In this way, we realize a gain of the transistor up to 53.4 dB, with an extinction ratio better than 20 dB. Our device outperforms previous devices in the optical regime by several orders in terms of optical gain, which indicates a great potential for application in the field of microwave quantum photonics and quantum information processing.

Successfully controlling an optical signal by a single gate photon would have great applicability for quantum networks and all-optical computing. Here, the authors realise a single-photon transistor in the microwave regime based on superconducting quantum circuits.

An optimizing method for performance and resource utilization in quantum machine learning circuits

Quantum computing is a new and advanced topic that refers to calculations based on the principles of quantum mechanics. It makes certain kinds of problems be solved easier compared to classical computers. This advantage of quantum computing can be used to implement many existing problems in different fields incredibly effectively. One important field that quantum computing has shown great results in machine learning. Until now, many different quantum algorithms have been presented to perform different machine learning approaches. In some special cases, the execution time of these quantum algorithms will be reduced exponentially compared to the classical ones. But at the same time, with increasing data volume and computation time, taking care of systems to prevent unwanted interactions with the environment can be a daunting task and since these algorithms work on machine learning problems, which usually includes big data, their implementation is very costly in terms of quantum resources. Here, in this paper, we have proposed an approach to reduce the cost of quantum circuits and to optimize quantum machine learning circuits in particular. To reduce the number of resources used, in this paper an approach including different optimization algorithms is considered. Our approach is used to optimize quantum machine learning algorithms for big data. In this case, the optimized circuits run quantum machine learning algorithms in less time than the original ones and by preserving the original functionality. Our approach improves the number of quantum gates by 10.7% and 14.9% in different circuits respectively. This is the amount of reduction for one iteration of a given sub-circuit U in the main circuit. For cases where this sub-circuit is repeated more times in the main circuit, the optimization rate is increased. Therefore, by applying the proposed method to circuits with big data, both cost and performance are improved.

Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to non-ergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.

Multilevel 2-D Quantum Wavelet Transforms

Wavelet transform is being widely used in classical image processing. One-dimension quantum wavelet transforms (QWTs) have been proposed. Generalizations of the 1-D QWT into multilevel and multidimension have been investigated but restricted to the quantum wavelet packet transform (QWPTs), which is the direct product of 1-D QWPTs, and there is no transform between the packets in different dimensions. A 2-D QWT is vital for image processing. We construct the multilevel 2-D QWT's general theory. Explicitly, we built multilevel 2-D Haar QWT and the multilevel Daubechies D4 QWT, respectively. We have given the complete quantum circuits for these wavelet transforms, using both noniterative and iterative methods. Compared to the 1-D QWT and wavelet packet transform, the multilevel 2-D QWT involves the entanglement between components in different degrees. Complexity analysis reveals that the proposed transforms offer exponential speedup over their classical counterparts. Also, the proposed wavelet transforms are used to realize quantum image compression. Simulation results demonstrate that the proposed wavelet transforms are significant and obtain the same results as their classical counterparts with an exponential speedup.

Variational quantum evolution equation solver

Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. The use of encoded source states informed by preceding solution vectors results in faster convergence compared to random re-initialization. Through statevector simulations of the heat equation, we demonstrate how the time complexity of our algorithm scales with the Ansatz volume for gradient estimation and how the time-to-solution scales with the diffusion parameter. Our proposed algorithm extends economically to higher-order time-stepping schemes, such as the Crank-Nicolson method. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction-diffusion and the incompressible Navier-Stokes equations, and demonstrate its validity by proof-of-concept results.

Quantum Natural Language Processing: Challenges and Opportunities

The meeting between Natural Language Processing (NLP) and Quantum Computing has been very successful in recent years, leading to the development of several approaches of the so-called Quantum Natural Language Processing (QNLP). This is a hybrid field in which the potential of quantum mechanics is exploited and applied to critical aspects of language processing, involving different NLP tasks. Approaches developed so far span from those that demonstrate the quantum advantage only at the theoretical level to the ones implementing algorithms on quantum hardware. This paper aims to list the approaches developed so far, categorizing them by type, i.e., theoretical work and those implemented on classical or quantum hardware; by task, i.e., general purpose such as syntax-semantic representation or specific NLP tasks, like sentiment analysis or question answering; and by the resource used in the evaluation phase, i.e., whether a benchmark dataset or a custom one has been used. The advantages offered by QNLP are discussed, both in terms of performance and methodology, and some considerations about the possible usage QNLP approaches in the place of state-of-the-art deep learning-based ones are given.

Quantum-effective exact multiple patterns matching algorithms for biological sequences

This article presents efficient quantum solutions for exact multiple pattern matching to process the biological sequences. The classical solution takes Ο(mN) time for matching m patterns over N sized text database. The quantum search mechanism is a core for pattern matching, as this reduces time complexity and achieves computational speedup. Few quantum methods are available for multiple pattern matching, which executes search oracle for each pattern in successive iterations. Such solutions are likely acceptable because of classical equivalent quantum designs. However, these methods are constrained with the inclusion of multiplicative factor m in their complexities. An optimal quantum design is to execute multiple search oracle in parallel on the quantum processing unit with a single-core that completely removes the multiplicative factor m, however, this method is impractical to design. We have no effective quantum solutions to process multiple patterns at present. Therefore, we propose quantum algorithms using quantum processing unit with C quantum cores working on shared quantum memory. This quantum parallel design would be effective for searching all t exact occurrences of each pattern. To our knowledge, no attempts have been made to design multiple pattern matching algorithms on quantum multicore processor. Thus, some quantum remarkable exact single pattern matching algorithms are enhanced here with their equivalent versions, namely enhanced quantum memory processing based exact algorithm and enhanced quantum-based combined exact algorithm for multiple pattern matching. Our quantum solutions find all t exact occurrences of each pattern inside the biological sequence in O ( ( m / C ) N ) and O ( ( m / C ) t ) time complexities. This article shows the hybrid simulation of quantum algorithms to validate quantum solutions. Our theoretical-experimental results justify the significant improvements that these algorithms outperform over the existing classical solutions and are proven effective in quantum counterparts.

Quantum OPTICS and deep self-learning on swarm intelligence algorithms for Covid-19 emergency transportation

In this paper, the quantum technology is exploited to empower the OPTICS unsupervised learning algorithm, which is a density-based clustering algorithm with numerous applications in the real world. We design an algorithm called Quantum Ordering Points To Identify the Clustering Structure (QOPTICS) and demonstrate that its computational complexity outperforms that of its classical counterpart. On the other hand, we propose a Deep self-learning approach for modeling the improvement of two Swarm Intelligence Algorithms, namely Artificial Orca Algorithm (AOA) and Elephant Herding Optimization (EHO) in order to improve their effectiveness. The deep self-learning approach is based on two well-known dynamic mutation operators, namely Cauchy mutation operator and Gaussian mutation operator. And in order to improve the efficiency of these algorithms, they are hybridized with QOPTICS and executed on just one cluster it yields. This way, both effectiveness and efficiency are handled. To evaluate the proposed approaches, an intelligent application is developed to manage the dispatching of emergency vehicles in a large geographic region and in the context of Covid-19 crisis in order to avoid an important loss in human lives. A theoretical model is designed to describe the issue mathematically. Extensive experiments are then performed to validate the mathematical model and evaluate the performance of the proposed deep self-learning algorithms. Comparison with a state-of-the-art technique shows a significant positive impact of hybridizing Quantum Machine Learning (QML) with Deep Self Learning (DSL) on solving the Covid-19 EMS transportation.

A Cost-Efficient Approach towards Computational Fluid Dynamics Simulations on Quantum Devices

Numerical simulations of physical systems are found in many industries, as they currently play a crucial role in product development. There are many numerical methods for solving differential equations that describe the underlying physics behind the mathematical models in the simulation, among which, the finite element method (FEM) is one of the most commonly used. Although in many applications the FEM seems to provide an acceptable solution to the problem, there are still many complex real-life processes that can be challenging to simulate numerically due to their complexity and large size. Recently, there has been a shift in research towards efficiently applying quantum algorithms in finite element analysis (FEA), as the potential and speedup that they could offer have been shown, but little to no effort has been made towards the applicability and cost efficiency of these algorithms in real-world quantum devices. In this paper, we propose a cost-efficient method for applying quantum algorithms in FEA for industrial problems post-processed by classical algorithms in order to address the limitations of available quantum hardware and their cost when accessing them through different cloud-based services. We carry this out by approximating the solution of the initially large system with a suitable quantum algorithm and using the obtained solutions to generate a set of reduced-order models (ROMs) that are much smaller in complexity and size than the original model. This allows the simulation of the original model with different parameter sets and excitations to be run efficiently on classical computers without having the need to access quantum subroutines again. This way, we have reduced the usage of quantum hardware (and thus the development cost) while still taking advantage of its quantum speedup.

Quantum semi-supervised generative adversarial network for enhanced data classification

In this paper, we propose the quantum semi-supervised generative adversarial network (qSGAN). The system is composed of a quantum generator and a classical discriminator/classifier (D/C). The goal is to train both the generator and the D/C, so that the latter may get a high classification accuracy for a given dataset. Hence the qSGAN needs neither any data loading nor to generate a pure quantum state, implying that qSGAN is much easier to implement than many existing quantum algorithms. Also the generator can serve as a stronger adversary than a classical one thanks to its rich expressibility, and it is expected to be robust against noise. These advantages are demonstrated in a numerical simulation.

Quantum Principal Component Analysis Only Achieves an Exponential Speedup Because of Its State Preparation Assumptions

A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC 2019.], we introduce such a model, where we assume we can efficiently perform ℓ^{2}-norm samples of input data, a natural analog to quantum algorithms that assume efficient state preparation of classical data. Though this model produces less practical algorithms than the (stronger) standard model of classical computation, it captures versions of many of the features and nuances of quantum linear algebra algorithms. With this model, we describe classical analogs to Lloyd, Mohseni, and Rebentrost's quantum algorithms for principal component analysis [S. Lloyd, M. Mohseni, and P. Rebentrost, Nat. Phys. 10, 631 (2014).NPAHAX1745-247310.1038/nphys3029] and nearest-centroid clustering [S. Lloyd, M. Mohseni, and P. Rebentrost, Quantum algorithms for supervised and unsupervised machine learning]. Since they are only polynomially slower, these algorithms suggest that the exponential speedups of their quantum counterparts are simply an artifact of state preparation assumptions.

Resonant quantum principal component analysis

Principal component analysis (PCA) has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e., the eigenvectors of the density matrix with the largest eigenvalues. However, because of the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with minimal resource for ancillary qubits, in which only one frequency-scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4 × 4 density matrix, with an efficiency of 86.0% and a fidelity of 0.90. This work shows the speedup ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.

Coreset Clustering on Small Quantum Computers

Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare the performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.

Quantum computing at the frontiers of biological sciences

Computing plays a critical role in the biological sciences but faces increasing challenges of scale and complexity. Quantum computing, a computational paradigm exploiting the unique properties of quantum mechanical analogs of classical bits, seeks to address many of these challenges. We discuss the potential for quantum computing to aid in the merging of insights across different areas of biological sciences.

Experimental Quantum Principal Component Analysis via Parametrized Quantum Circuits

Principal component analysis (PCA) is a widely applied but rather time-consuming tool in machine learning techniques. In 2014, Lloyd, Mohseni, and Rebentrost proposed a quantum PCA (qPCA) algorithm [Lloyd, Mohseni, and Rebentrost, Nat. Phys. 10, 631 (2014)NPAHAX1745-247310.1038/nphys3029] that still lacks experimental demonstration due to the experimental challenges in preparing multiple quantum state copies and implementing quantum phase estimations. Here, we propose a new qPCA algorithm using the hybrid classical-quantum control, where parameterized quantum circuits are optimized with simple measurement observables, which significantly reduces the experimental complexity. As one important PCA application, we implement a human face recognition process using the images from the Yale Face Dataset. By training our quantum processor, the eigenface information in the training dataset is encoded into the parameterized quantum circuit, and the quantum processor learns to recognize new face images from the test dataset with high fidelities. Our work paves a new avenue toward the study of qPCA applications in theory and experiment.

Quantum computing model of an artificial neuron with continuously valued input data

Artificial neural networks have been proposed as potential algorithms that could benefit from being implemented and run on quantum computers. In particular, they hold promise to greatly enhance Artificial Intelligence tasks, such as image elaboration or pattern recognition. The elementary building block of a neural network is an artificial neuron, i.e. a computational unit performing simple mathematical operations on a set of data in the form of an input vector. Here we show how the design for the implementation of a previously introduced quantum artificial neuron [npj Quant. Inf. 5, 26], which fully exploits the use of superposition states to encode binary valued input data, can be further generalized to accept continuous- instead of discrete-valued input vectors, without increasing the number of qubits. This further step is crucial to allow for a direct application of gradient descent based learning procedures, which would not be compatible with binary-valued data encoding.

Implementation of a Hamming distance-like genomic quantum classifier using inner products on ibmqx2 and ibmq_16_melbourne

Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we present relatively efficient general purpose inner product-based kernel classifiers to classify the test as a normal or disease sample. We encode each training sample as a string of 1 s (presence) and 0 s (absence) representing the attribute's existence across ordered physical blocks of the subdivided genome. Having binary-valued features allows for highly efficient data encoding in the computational basis for classifiers relying on binary operations. Given that a natural distance between binary strings is Hamming distance, which shares properties with bit-string inner products, our two classifiers apply different inner product measures for classification. The active inner product (AIP) is a direct dot product-based classifier whereas the symmetric inner product (SIP) classifies upon scoring correspondingly matching genomic attributes. SIP is a strongly Hamming distance-based classifier generally applicable to binary attribute-matching problems whereas AIP has general applications as a simple dot product-based classifier. The classifiers implement an inner product between N = 2 ⁿ dimension test and train vectors using n Fredkin gates while the training sets are respectively entangled with the class-label qubit, without use of an ancilla. Moreover, each training class can be composed of an arbitrary number m of samples that can be classically summed into one input string to effectively execute all test-train inner products simultaneously. Thus, our circuits require the same number of qubits for any number of training samples and are O ( log N ) in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). The latter allowed encoding of 64 training features across the genome.