Canonical quantum algorithms often achieve low execution fidelities on current Noisy Intermediate-Scale Quantum (NISQ) hardware. The standard implementation of Grover's search algorithm, designed for theoretical generality, produces deep, gate-heavy circuits that are susceptible to noise. This paper challenges the "one-size-fits-all" design paradigm by using Grammatical Evolution (GE) to automatically discover hardware-efficient, state-specific quantum circuits. We demonstrate this approach by evolving bespoke circuits for all eight 3-qubit computational basis states and executing them on a 133-qubit IBM Heron quantum processor. To our knowledge, this is the first hardware-validated application of GE for this task. The results indicate significant performance gains: evolved circuits achieve hardware-executed fidelities up to 96.9% (vs. 66.3% baseline) while reducing circuit depth by 82.5–96.6% and gate count by 77.4–94.6% compared to canonical implementations. These findings suggest that automated symbolic search is a viable approach to designing algorithms that can execute on today's NISQ devices.
Canonical quantum algorithms often achieve low execution fidelities on current Noisy Intermediate-Scale Quantum (NISQ) hardware. The standard implementation of Grover's search algorithm, designed for theoretical generality, produces deep, gate-heavy circuits that are susceptible to noise. This paper challenges the "one-size-fits-all" design paradigm by using Grammatical Evolution (GE) to automatically discover hardware-efficient, state-specific quantum circuits. We demonstrate this approach by evolving bespoke circuits for all eight 3-qubit computational basis states and executing them on a 133-qubit IBM Heron quantum processor. To our knowledge, this is the first hardware-validated application of GE for this task. The results indicate significant performance gains: evolved circuits achieve hardware-executed fidelities up to 96.9% (vs. 66.3% baseline) while reducing circuit depth by 82.5–96.6% and gate count by 77.4–94.6% compared to canonical implementations. These findings suggest that automated symbolic search is a viable approach to designing algorithms that can execute on today's NISQ devices.
Noisy Intermediate-Scale Quantum (NISQ) devices are promising platforms for practical quantum computing, but their performance is significantly affected by limited qubit availability, gate errors, decoherence, circuit depth, and hardware-dependent noise. Conventional quantum circuits are generally designed and optimized before execution and may not respond effectively to changing hardware conditions during computation. This research proposes a Self-Adaptive Quantum Circuit framework that dynamically modifies quantum circuits according to the current computational resources and noise characteristics of NISQ devices. The proposed framework monitors parameters such as qubit fidelity, gate error rates, circuit depth, execution time, and resource availability, and automatically selects suitable circuit configurations to improve computational performance. Adaptive mechanisms can be employed to reduce unnecessary gates, optimize qubit utilization, and mitigate the impact of hardware noise while maintaining the required computational accuracy. The framework will be evaluated using simulation platforms and available NISQ quantum hardware, comparing adaptive circuits with conventional static circuits using metrics such as accuracy, fidelity, circuit depth, gate count, execution time, and error rate. The expected outcome is a resource-efficient and noise-aware quantum circuit optimization approach capable of improving the reliability and performance of quantum applications on near-term quantum hardware. The proposed research aims to contribute toward more practical, flexible, and hardware-aware quantum computing systems for NISQ-era applications. Keywords: NISQ Computing, Self-Adaptive Quantum Circuits, Quantum Circuit Optimization, Quantum Error Mitigation, Quantum Noise, Quantum Computing.
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.
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's search algorithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grover's search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grover's search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.
Quantum computing is an emerging technology that combines the principles of both computer science and quantum mechanics to solve computationally challenging problems significantly faster than the current classical computers. In this thesis, a proof of concept to generate hardware-executable quantum circuits for Noisy Intermediate-Scale Quantum (NISQ) devices that follow the paradigm of approximate computing is presented. We adopt a multi-level optimization approach and consider the placement of native quantum gates that can be physically implemented on one of the existing quantum systems (IBM, Rigetti) as a circuit topology optimization problem and the adjustment of parameters of these native quantum gates as a continuous design optimization problem. The outer topology problem is solved with the aid of a genetic algorithm, whereas the gradient-descent method is used for the inner design optimization. Our approach starts from the reference circuit and transforms it into an executable circuit with tunable parameters by replacing the high-level quantum operations with a set of approximate decompositions, e.g., single qubit rotation quantum gates or a combination of single qubit rotation gates (matrix multiplication). Later, the inner design optimization ensures that the circuit created is tuned to be executed to achieve an expectation value close to that of the reference circuit. This is complemented by compiler-based optimizations to further reduce or aggregate the quantum gates of the optimized circuit. This three-step pipeline is embedded into an outer genetic algorithm framework that inspects many different circuit designs (the approximate-decomposition replacements are by no means unique) and returns a set of unique approximate quantum circuits that can be executed on hardware. We have tested our circuit generation approach for superconducting quantum systems such as IBM and Rigetti hardware for many different benchmark circuits such as Quantum Fourier Transform, Toffoli, quantum adder, multi-controlled operations and three oracle-based algorithms, namely, Grover's search algorithm, Deutsch and Bernstein-Vazirani algorithm. In nearly all cases, our approach outperforms the quantum compiler frameworks by IBM and Rigetti even on their highest optimization level and produces significantly smaller circuits, up to 2x reduction in the number of gates. In addition, the circuits generated using the proposed approach provide better (a) performance (on average, improved by 24.25%) and (b) reliability (on average, improved by 23.50%) compared to the IBM generated circuits when executed on the ibmq_5_yorktown physical quantum device.
Grover's quantum search algorithm provides a proven quadratic speedup over classical linear search for unstructured databases. While its theoretical advantage is well established, experimental validation on real noisy intermediate-scale quantum (NISQ) hardware remains limited by noise, decoherence, and hardware constraints. In this work, we present an experimental comparison between classical linear search and Grover's quantum search algorithm executed on IBM Quantum real superconducting hardware using Qiskit Runtime. A four-qubit implementation corresponding to a 16-element search space is evaluated across multiple experimental runs. The results demonstrate consistent amplitude amplification, achieving an average success probability of 54.25% and an amplification factor of 8.68× over random guessing. Although classical execution remains faster in wall-clock time due to quantum hardware overhead, the experiment empirically validates the algorithmic advantage of Grover's search and quantifies the performance gap between ideal and real quantum processors in the NISQ era.
Noisy intermediate-scale quantum (NISQ) devices with limited qubit count and connectivity limit the scale of quantum circuits that can be executed. Circuit cutting methods simulate larger quantum computers by decomposing large circuits into small subcircuits that can be executed on NISQ hardware. Existing circuit cutting methods only consider the qubit count of the target hardware for finding the locations of cuts on the circuits. This can result in deeper subcircuits after mapping on the hardware. Fidelity decays exponentially with circuit depth and diminishes the quality of execution. We propose a circuit-cutting framework that reduces variance in the depth of subcircuits after mapping to the hardware. Our method formulates the initial circuit cutting as a multi-objective optimization problem based on an evolutionary search method with the number of cuts and the maximum depth of individual routed subcircuits as fitness objectives. This method is implemented as an extension to the existing Qiskit Circuit Cutting Addon, which allows for integration in existing flows. Our approach achieves reductions in routed subcircuit depth of up to 9.9% across benchmark circuits compared with baseline methods.