Quantum computing is on the cusp of reality with Noisy Intermediate-Scale Quantum (NISQ) machines currently under development and testing. Some of the most promising algorithms for these machines are variational algorithms that employ classical optimization coupled with quantum hardware to evaluate the quality of each candidate solution. Recent work used GRadient Descent Pulse Engineering (GRAPE) to translate quantum programs into highly optimized machine control pulses, resulting in a significant reduction in the execution time of programs. This is critical, as quantum machines can barely support the execution of short programs before failing.
Quantum computing is on the cusp of reality with Noisy Intermediate-Scale Quantum (NISQ) machines currently under development and testing. Some of the most promising algorithms for these machines are variational algorithms that employ classical optimization coupled with quantum hardware to evaluate the quality of each candidate solution. Recent work used GRadient Descent Pulse Engineering (GRAPE) to translate quantum programs into highly optimized machine control pulses, resulting in a significant reduction in the execution time of programs. This is critical, as quantum machines can barely support the execution of short programs before failing.
First quantum computers very recently have demonstrated “quantum supremacy” or “quantum advantage Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several NISQ-era algorithms” are assumed to match the specifics of such computers; for instance, variational optimisers are based on intertwining relatively short quantum and classical computations, thus maximizing the chances of success. This paper will critically assess the promise and challenge of NISQ computing. What has this field achieved so far, what are we likely to achieve soon, where do we have to be skeptical and wait for the advent of larger-scale fully error-corrected architectures?
Variational quantum algorithms (VQAs) are the leading candidates for practical applications of noisy intermediate-scale quantum (NISQ) devices. Recently, pulse-based variational quantum algorithms (p-VQAs) have emerged as a compelling alternative to traditional gate-based VQAs. By optimizing continuous control fields directly on hardware-native Hamiltonians, pulse-based methods are easy to implement and can significantly reduce quantum resource overhead, thereby enhancing the overall performance of quantum algorithms on NISQ devices. In this review, we present a comprehensive survey over recent advances in p-VQAs, covering theory, algorithms, and hardware deployments across various quantum computing platforms. We also review applications of p-VQAs to variational quantum eigensolver in quantum chemistry, quantum approximate optimization algorithm for combinatorial optimization, and quantum machine learning tasks.
Noisy Intermediate-Scale Quantum (NISQ) devices show great promise for quantum advantage via Parametrized Quantum Circuits (PQCs) and Variational Quantum Algorithms (VQAs). Due to hardware imperfections, however, especially barren plateaus and environmental Pauli noise, the cost landscape is highly distorted, resulting in inaccurate classical optimization during training. To overcome these challenges, a robust quantum gradient descent framework is presented with the integration of error mitigation directly within the optimization loop. A noise-resilient parameter-shift rule is defined and modeled analytically, as is a variant of stochastic gradient descent with real-time Pauli noise mitigation. The framework is based on a 6-qubit system, which is tested on the Max-Cut problem in the presence of different amounts of depolarizing noise. It is shown experimentally that the proposed algorithm is able to achieve the final cost error of 0.045 under significant noise, whereas the standard quantum gradient descent fails to achieve better than 0.320 under this noise. Moreover, the methodology is consistent, converging without a noise-induced flat landscape and without local minima. The method offers a scalable route towards future applications of quantum machine learning on non-fault-tolerant hardware that does not suffer from the large sampling overhead often associated with conventional error mitigation techniques.
The rapid advancement of Noisy Intermediate-Scale Quantum (NISQ) devices has driven the need for efficient design automation tools that can translate complex engineering models into executable quantum circuits. This study explores the development of automated quantum circuit design frameworks focused on gate optimization and noise-aware compilation, enabling practical quantum computation for engineering applications such as optimization, simulation, and control systems. Traditional circuit design methods often fail to account for hardware constraints, decoherence, and gate infidelity, which significantly affect computational accuracy on NISQ devices. To address these challenges, this research introduces a hybrid automation approach combining quantum transpilation, variational circuit pruning, and error-aware synthesis algorithms to enhance circuit reliability and scalability. The framework integrates quantum-classical co-design principles to optimize both logical and physical circuit layers, leveraging hardware-specific calibration data to adapt compilation strategies dynamically. Through simulations and benchmark analysis, the proposed system demonstrates significant improvements in quantum resource utilization, error mitigation, and gate depth reduction compared to conventional compilation methods. This work underscores the growing importance of design automation in quantum engineering, where algorithmic efficiency must be harmonized with physical constraints to realize functional and scalable quantum workflows. By establishing a methodology for gate-level optimization and noise-adaptive design, the study contributes to bridging the gap between theoretical quantum algorithms and real-world engineering implementations within the NISQ computing era.
We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits.
A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time or error rates, it is of pressing importance to map computations onto them in ways that use resources efficiently and maximize the likelihood of successful runs. This paper proposes and evaluates backend compiler approaches to map and optimize high-level QC programs to execute with high reliability on NISQ systems with diverse hardware characteristics. Our techniques all start from an LLVM intermediate representation of the quantum program (such as would be generated from high-level QC languages like Scaffold) and generate QC executables runnable on the IBM Q public QC machine. We then use this framework to implement and evaluate several optimal and heuristic mapping methods. These methods vary in how they account for the availability of dynamic machine calibration data, the relative importance of various noise parameters, the different possible routing strategies, and the relative importance of compile-time scalability versus runtime success. Using real-system measurements, we show that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average 2.9x (and up to 18x) improvement in program success rate over the industry standard IBM Qiskit compiler. Despite small qubit counts, NISQ systems will soon be large enough to demonstrate "quantum supremacy", i.e., an advantage over classical computing. Tools like ours provide significant improvements in program reliability and execution time, and offer high leverage in accelerating progress towards quantum supremacy.