Classical-quantum approach to image classification: Autoencoders and quantum SVMs

Despite the current progress in quantum computing, the reliability of quantum computers is very challenging. Near-term quantum computers referred to as Noisy Intermediate-Scale Quantum (NISQ) computers are expected to operate in the presence of errors. To run a quantum circuit on a NISQ computer, the circuit should be mapped to satisfy the physical constraints of the quantum architecture. The mapping process takes into account the error rates of the quantum hardware. It selects physical qubits and their movements, which minimize the circuit error rates. The output of the quantum circuit can be obtained through several runs on NISQ computers. What's important from a security perspective is that the output of the quantum circuit is inherently dependent on the error parameters of the quantum hardware. An adversary can, therefore, leverage such dependency to alter the functional behavior of the quantum circuit. We show that malicious changes in the error rates used for mapping quantum circuits can change their output. To detect this attack on NISQ architectures, we propose inserting test points into the quantum circuits to study their error rates with respect to other qubit allocations. We utilize superposition, classical, and un-compute tests to provide side-channel information of the quantum circuit. We study the effectiveness of our approach using IBMQ 16 Melbourne quantum computer and Qiskit tools as an exemplar.

Gate-based quantum computing is an attractive candidate in the post-Moore era. Noisy intermediate-scale quantum (NISQ) computers are expected to be available in the next few years. It is required to repeatedly execute the target quantum application for reliable NISQ computing, e.g., users can set 1,024 as a repetition parameter in the IBM-Q machine, because NISQ computers output follows the probability distribution of execution trials. Since the distribution depends strongly on the effects of noise, it is difficult to determine a sufficient number of repetitions. This paper proposes a novel statistical approach for efficient NISQ computing. The key idea is to introduce a Bayesian credible interval model to obtain convergence of the probability distributions. We demonstrate that our execution method can detect all significant output values, that occur more often than the random situation (probability is 1/2^n), using a NISQ simulator.

While current quantum computers, referred to as Noisy Intermediate-Scale Quantum (NISQ) computers, are expected to be beneficial for different applications, they are prone to different types of errors. In order to enhance the reliability of quantum systems, noise-aware quantum compilers are used to generate physical quantum circuits to be executed on NISQ computers. The quantum hardware is calibrated very frequently and its error rates are computed accordingly. Based on the hardware error rates, a quantum compiler allocates physical qubits and schedules quantum operations. However, error rates may change post-calibration. To incorporate dynamic error rates into quantum circuit compilation with minimum cost, we propose a Machine Learning (ML)-based scheme to detect the incorrect output of the quantum circuit and predict the Probability of Successful Trials (PST) with high accuracy. Our approach can verify the error rates of the quantum hardware and validate the correctness of the extracted quantum circuit output. We provide a case study of our ML-based reliability models using IBM Q16 Melbourne quantum computer. Our results show that the proposed scheme achieves a very high prediction accuracy.

Simulation of the dynamics of quantum materials is emerging as a promising scientific application for noisy intermediate-scale quantum (NISQ) computers. Due to their high gate-error rates and short decoherence times, however, NISQ computers can only produce high-fidelity results for those quantum circuits smaller than some given circuit size. Dynamic simulations, therefore, pose a challenge as current algorithms produce circuits that grow in size with each subsequent time-step of the simulation. This underscores the crucial role of quantum circuit compilers to produce executable quantum circuits of minimal size, thereby maximizing the range of physical phenomena that can be studied within the NISQ fidelity budget. Here, we present two domain-specific (DS) quantum circuit compilers for the Rigetti and IBM quantum computers, specifically designed to compile circuits simulating dynamics under a special class of time-dependent Hamiltonians. The compilers outperform state-of-the-art general-purpose compilers in terms of circuit size reduction by around 25%–30% as well as wall-clock compilation time by around 40% (dependent on system size and simulation time-step). Drawing on heuristic techniques commonly used in artificial intelligence, both compilers scale well with simulation time-step and system size. Code for both compilers is open-source and packaged into a full-stack quantum simulation software with tutorials included for ease of use for future researchers wishing to perform dynamic simulations of quantum materials on quantum computers. As our DS compilers provide significant improvements in both compilation time and simulation fidelity, they provide a building block for accelerating progress toward physical quantum supremacy.

A universal fault-tolerant quantum computer holds the promise to speed up computational problems that are otherwise intractable on classical computers; however, for the next decade or so, our access is restricted to noisy intermediate-scale quantum (NISQ) computers and, perhaps, early fault tolerant (EFT) quantum computers. This motivates the development of many near-term quantum algorithms including robust amplitude estimation (RAE), which is a quantum-enhanced algorithm for estimating expectation values. One obstacle to using RAE has been a paucity of ways of getting realistic error models incorporated into this algorithm. So far the impact of device noise on RAE is incorporated into one of its subroutines as an exponential decay model, which is unrealistic for NISQ devices and, maybe, for EFT devices; this hinders the performance of RAE. Rather than trying to explicitly model realistic noise effects, which may be infeasible, we circumvent this obstacle by tailoring device noise using randomized compiling to generate an effective noise model, whose impact on RAE closely resembles that of the exponential decay model. Using noisy simulations, we show that our noise-tailored RAE algorithm is able to regain improvements in both bias and precision that are expected for RAE. Additionally, on IBM’s quantum computer ibmq_belem our algorithm demonstrates advantage over the standard estimation technique in reducing bias. Thus, our work extends the feasibility of RAE on NISQ computers, consequently bringing us one step closer towards achieving quantum advantage using these devices.

The calculation of non-covalent interaction energies on noisy intermediate-scale quantum (NISQ) computers appears to be challenging with straightforward application of existing quantum algorithms. For example, the use of the standard supermolecular method with the variational quantum eigensolver (VQE) would require extremely precise resolution of the total energies of the fragments to provide for accurate subtraction to the interaction energy. Here we present a symmetry-adapted perturbation theory (SAPT) method that may provide interaction energies with high quantum resource efficiency. Of particular note, we present a quantum extended random-phase approximation (ERPA) treatment of the SAPT second-order induction and dispersion terms, including exchange counterparts. Together with previous work on first-order terms (Chem. Sci., 2022, 13, 3094), this provides a recipe for complete SAPT(VQE) interaction energies up to second order, which is a well established truncation. The SAPT interaction energy terms are computed as first-level observables with no subtraction of monomer energies invoked, and the only quantum observations needed are the VQE one- and two-particle density matrices. We find empirically that SAPT(VQE) can provide accurate interaction energies even with coarsely optimized, low circuit depth wavefunctions from a quantum computer, simulated through ideal statevectors. The errors of the total interaction energy are orders of magnitude lower than the corresponding VQE total energy errors of the monomer wavefunctions. In addition, we present heme-nitrosyl model complexes as a system class for near term quantum computing simulations. They are strongly correlated, biologically relevant and difficult to simulate with classical quantum chemical methods. This is illustrated with density functional theory (DFT) as the predicted interaction energies exhibit a strong sensitivity with respect to the choice of functional. Thus, this work paves the way to obtain accurate interaction energies on a NISQ-era quantum computer with few quantum resources. It is the first step in alleviating one of the major challenges in quantum chemistry, where in-depth knowledge of both the method and system is required a priori to reliably generate accurate interaction energies.

The development of near-term quantum computers, referred to as Noisy Intermediate-Scale Quantum (NISQ) computers, has progressed rapidly in the past few years resulting in several quantum computers which vary in their underlying technology and physical constraints. The performance of these computers also varies from one quantum algorithm to another. To enable efficient selection of the quantum computer that provides the highest output fidelity for a given application, an accurate noise modeling of each quantum hardware is required. However, noise modeling for a given application is a complex problem because of the unknown interaction between the quantum circuit parameters and the noise parameters of NISQ devices. We propose the use of Machine Learning (ML) to model the performance of different quantum computers at the application level. The ML models predict the output fidelity of the quantum application executed on different quantum computers given their publicly available physical constraints. We use a diverse training dataset to cover the key features for application-level benchmarking of the quantum hardware. Our results obtained from different superconducting quantum devices show that our proposed ML models enable cost-effective quantum computer selection for different quantum applications with different fidelity metrics.

Quantum computing offers promising new avenues for tackling the long-standing challenge of simulating the quantum dynamics of complex chemical systems, particularly open quantum systems coupled to external baths. However, simulating such nonunitary dynamics on quantum computers is challenging since quantum circuits are specifically designed to carry out unitary transformations. Furthermore, chemical systems are often strongly coupled to the surrounding environment, rendering the dynamics non-Markovian and beyond the scope of Markovian quantum master equations like Lindblad or Redfield. In this work, we introduce a quantum algorithm designed to simulate non-Markovian dynamics of open quantum systems. Our approach enables the implementation of arbitrary quantum master equations on noisy intermediate-scale quantum (NISQ) computers. We illustrate the method as applied in conjunction with the numerically exact hierarchical equations of motion (HEOM) method. The effectiveness of the resulting quantum HEOM algorithm is demonstrated as applied to simulations of the non-Lindbladian electronic energy and charge transfer dynamics in models of the carotenoid-porphyrin-C60 molecular triad dissolved in tetrahydrofuran and the Fenna-Matthews-Olson complex.

Quantum computing is a new paradigm for a multitude of computing applications. This study presents the technologies that are currently available for the physical implementation of qubits and quantum gates, establishing their main advantages and disadvantages and the available frameworks for programming and implementing quantum circuits. One of the main applications for quantum computing is the development of new algorithms for machine learning. In this study, an implementation of a quantum circuit based on support vector machines (SVMs) is described for the resolution of classification problems. This circuit is specially designed for the noisy intermediate-scale quantum (NISQ) computers that are currently available. As an experiment, the circuit is tested on a real quantum computer based on superconducting qubits for an application to detect weak signals of the future. Weak signals are indicators of incipient changes that will have a future impact. Even for experts, the detection of these events is complicated since it is too early to predict this impact. The data obtained with the experiment shows promising results but also confirms that ongoing technological development is still required to take full advantage of quantum computing.

Today’s Noisy Intermediate-Scale Quantum (NISQ) computers support only limited sets of available quantum gates and restricted connectivity. Therefore, quantum algorithms must be transpiled in order to become executable on a given NISQ computer; transpilation is a complex and computationally heavy process. Moreover, NISQ computers are affected by noise that changes over time, and periodic calibration provides relevant error rates that should be considered during transpilation. Variational algorithms, which form one main class of computations on NISQ platforms, produce a number of similar yet not identical quantum "ansatz" circuits. In this work, we present a transpilation methodology optimized for variational algorithms under potentially changing error rates. We divide transpilation into three steps: (1) noise-unaware and computationally heavy pre-transpilation; (2) fast noise-aware matching; and (3) fast decomposition followed by heuristic optimization. For a complete run of a variational algorithm under constant error rates, only step (3) needs to be executed for each new ansatz circuit. Step (2) is required only if the error rates reported by calibration have changed significantly since the beginning of the computation. The most expensive Step (1) is executed only once for the whole run. This distribution is helpful for incremental, calibration-aware transpilation when the variational algorithm adapts its own execution to changing error rates. Experimental results on IBM’s quantum computer show the low latency and robust results obtained by calibration-aware transpilation.

The fourth Industrial Revolution (4IR) integrates digital, physical and biological systems to create Cyber-Physical Systems (CPS) that blur the line between the digital, physical and biological systems. One of the drivers of the 4IR is quantum computing; which harnesses quantum mechanical concepts such as entanglement, superposition and tunneling to perform computation. A full-scale quantum computer has not yet been realized. However, Noisy Intermediate-Scale Quantum (NISQ) computers are already in use. In this chapter, we explore NISQ as a disruptive technology of the fourth Industrial Revolution. Furthermore, we discuss the NISQ disruptors together with the applications of the NISQ frameworks. Finally, a novel privacy-preserving quantum machine learning scheme is introduced in this chapter. In essence, the various applications discussed in this chapter show various sectors that are disrupted by NISQ computing. Therefore, the overall objective of this chapter is to provide an exposition to NISQ computing, and demonstrate a link between NISQ computing and the fourth Industrial Revolution.

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.

Noisy intermediate-scale quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving ‘quantum supremacy’, a major milestone in quantum computing. NISQ supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of quantum supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the world. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.

High error-rates preclude the preparation of fully error-corrected logical qubit state on noisy intermediate scale quantum (NISQ) computers. When operand logical qubits inherit large state-preparation noise, it is difficult to show that subsequent logical gate fails less frequently than its physical (unprotected) version. We articulate a scheme of decoupling transversal logical gate errors from state-preparation noise and experimentally validate its use-case for IBM Q quantum processors. We find that in the absence of state preparation noise, the IBM Q processors significantly raise the likelihood of certain two-qubit errors in the operand(s) of [[7, 1, 3]] transversal gates. Yet, encoding can still be shown to improve the gate fidelity provided that the gate operands are strategically decoded/corrected for the likely two-qubit errors in lieu of their less likely single-qubit counterparts. This trade-off enables quantum CSS code to principally correct longer strings of errors without increasing the codeword size and paves new avenues of investigating fault-tolerance in NISQ computers.

Quantum machine learning has experienced significant progress in both software and hardware development in the recent years and has emerged as an applicable area of near-term quantum computers. In this work, we investigate the feasibility of utilizing quantum machine learning (QML) on real clinical datasets. We propose two QML algorithms for data classification on IBM quantum hardware: a quantum distance classifier (qDS) and a simplified quantum-kernel support vector machine (sqKSVM). We utilize these different methods using the linear time quantum data encoding technique ({mathrm{log}}_{2}N) for embedding classical data into quantum states and estimating the inner product on the 15-qubit IBMQ Melbourne quantum computer. We match the predictive performance of our QML approaches with prior QML methods and with their classical counterpart algorithms for three open-access clinical datasets. Our results imply that the qDS in small sample and feature count datasets outperforms kernel-based methods. In contrast, quantum kernel approaches outperform qDS in high sample and feature count datasets. We demonstrate that the {mathrm{log}}_{2}N encoding increases predictive performance with up to + 2% area under the receiver operator characteristics curve across all quantum machine learning approaches, thus, making it ideal for machine learning tasks executed in Noisy Intermediate Scale Quantum computers.