Noise resilient approximate quantum circuits for NISQ devices

Abstract

The rapid progress of noisy intermediate-scale quantum (NISQ) devices has enabled the execution of quantum algorithms on real hardware, yet their limited qubit counts, short coherence times, and susceptibility to noise pose major challenges to reliable computation. Circuit complexity—including qubit count, circuit depth, and total gate operations—plays a pivotal role in determining the fidelity of quantum programs. Reducing these complexity metrics helps mitigate the detrimental effects of noise and improves the reliability of quantum computations. To address these challenges, this work introduces a series of optimized designs for quantum arithmetic circuits, quantum neural networks (QNNs), and quantum random access memory (QRAM). We investigate arithmetic circuits, including addition, multiplication, division, and square root operations. By leveraging approximate computing and dynamic circuits, we propose novel designs that significantly reduce depth and gate counts while maintaining acceptable accuracy. Approximate arithmetic units such as quantum adder, multiplier, divider, and square root demonstrate superior performance compared to existing designs, and our quantum division circuits exploit mid-circuit measurement and approximation to enhance fidelity, enabling successful deployment on IBM quantum computers. The proposed designs reduce the complexity of exact circuits while maintaining the same level of precision in outputs. All approximate circuits presented in this work are superior to existing quantum circuits in terms of depth, gate counts, and number of qubits. We show that running proposed approximate circuits on real quantum computers generates meaningful results. Building upon these foundations, we develop a noise-resilient quantum neural network (NR-QNN) framework tailored for NISQ devices. NR-QNN employs quantum pruning, which removes gates with negligible rotation angles, and sensitivity-aware qubit mapping, which allocates critical logical qubits to more reliable physical qubits. These optimizations mitigate the impact of noise, thereby enhancing the robustness of QNNs and enabling them to achieve meaningful inference results on real quantum hardware. Finally, we explore the design of approximate quantum random access memory (QRAM) architectures, a crucial component for enabling large-scale quantum data access. Our approach applies pruning techniques to simplify QRAM circuits and re-trains approximate QNN-based modules to mitigate accuracy loss. This strategy reduces circuit depth and improves error resilience, allowing approximate QRAMs to serve as practical building blocks for QNN applications on NISQ computers.