Quantum power system state estimation (QPSSE) offers an inspiring direction for tackling the challenge of state estimation through quantum computing. Nevertheless, the current bottlenecks originate from the scarcity of practical and scalable QPSSE methodologies in the noisy intermediate-scale quantum (NISQ) era. This paper devises a NISQ-QPSSE algorithm that facilitates state estimation on real NISQ devices. Our new contributions include: (1) A variational quantum circuit (VQC)-based QPSSE formulation that empowers QPSSE analysis utilizing shallow-depth quantum circuits; (2) A variational quantum linear solver (VQLS)-based QPSSE solver integrating QPSSE iterations with VQC optimization; (3) An advanced NISQ-compatible QPSSE methodology for tackling the measurement and coefficient matrix issues on real quantum computers; (4) A noise-resilient method to alleviate the detrimental effects of noise disturbances. The encouraging test results on the simulator and real-scale systems affirm the precision, universality, and scalability of our QPSSE algorithm and demonstrate the vast potential of QPSSE in the thriving NISQ era.
Quantum power system state estimation (QPSSE) offers an inspiring direction for tackling the challenge of state estimation through quantum computing. Nevertheless, the current bottlenecks originate from the scarcity of practical and scalable QPSSE methodologies in the noisy intermediate-scale quantum (NISQ) era. This paper devises a NISQ-QPSSE algorithm that facilitates state estimation on real NISQ devices. Our new contributions include: (1) A variational quantum circuit (VQC)-based QPSSE formulation that empowers QPSSE analysis utilizing shallow-depth quantum circuits; (2) A variational quantum linear solver (VQLS)-based QPSSE solver integrating QPSSE iterations with VQC optimization; (3) An advanced NISQ-compatible QPSSE methodology for tackling the measurement and coefficient matrix issues on real quantum computers; (4) A noise-resilient method to alleviate the detrimental effects of noise disturbances. The encouraging test results on the simulator and real-scale systems affirm the precision, universality, and scalability of our QPSSE algorithm and demonstrate the vast potential of QPSSE in the thriving NISQ era.
Quantum power flow (QPF) offers an inspiring direction for overcoming the computation challenge of power flow through quantum computing. However, the practical implementation of existing QPF algorithms in today's noisy-intermediate-scale quantum (NISQ) era remains limited because of their sensitivity to noise. This paper establishes an NISQ-QPF algorithm that enables power flow computation on noisy quantum devices. The main contributions include: (1) a variational quantum circuit (VQC)-based alternating current (AC) power flow formulation, which enables QPF using short-depth quantum circuits; (2) NISQ-compatible QPF solvers based on the variational quantum linear solver (VQLS) and modified fast decoupled power flow; and (3) an error-resilient QPF scheme to relieve the QPF iteration deviations caused by noise; (3) a practical NISQ-QPF framework for implementable and reliable power flow analysis on noisy quantum machines. Extensive simulation tests validate the accuracy and generality of NISQ-QPF for solving practical power flow on IBM's real, noisy quantum computers.
Quantum computers have the potential to deliver speed-ups for solving certain important problems that are intractable for classical counterparts, making them a promising avenue for advancing modern computation. However, many quantum algorithms require deep quantum circuits, which are challenging to implement on current noisy devices. To address this limitation, variational quantum algorithms (VQAs) have been actively developed, enabling practical quantum computing in the noisy intermediate-scale quantum (NISQ) era. Among them, the variational quantum eigensolver (VQE) stands out as a leading approach for solving problems in quantum chemistry, many-body physics, and even integer factorization. The VQE algorithm can be implemented on various quantum hardware platforms, including photonic systems, quantum dots, trapped ions, neutral atoms, and superconducting circuits. In particular, photonic platforms offer several advantages: they operate at room temperature, exhibit low decoherence, and support multiple degrees of freedom, making them suitable for scalable, high-dimensional quantum computation. Here we present methodologies for realizing VQE on photonic systems, highlighting their potential for practical quantum computing. We first provide a theoretical overview of the VQE framework, focusing on the procedure for variationally estimating ground state energies. We then explore how photonic systems can implement these processes, showing that a wide variety of problems can be addressed using either multiple qubit states or a single qudit state.
Quantum-empowered electromagnetic transients program (QEMTP) is a promising paradigm for tackling EMTP’s computational burdens. Nevertheless, no existing studies truly achieve a practical and scalable QEMTP operable on today’s noisy-intermediate-scale quantum (NISQ) computers. The strong reliance on noise-free and fault-tolerant quantum devices–which appears to be decades away– hinder practical applications of current QEMTP methods. This paper devises a NISQ-QEMTP methodology which for the first time transitions the QEMTP operations from ideal, noise-free quantum simulators to real, noisy quantum computers. The main contributions lie in: (1) design of shallow-depth QEMTP quantum circuits for mitigating noises on NISQ quantum devices; (2) practical QEMTP linear solvers incorporating executable quantum state preparation and measurements for nodal voltage computations; (3) a noise-resilient QEMTP algorithm leveraging quantum resources logarithmically scaled with power system dimension; (4) a quantum shifted frequency analysis (QSFA) for accelerating QEMTP by exploiting dynamic phasor simulations with larger time steps; (5) a systematical analysis on QEMTP’s performance under various noisy quantum environments. Extensive experiments systematically verify the accuracy, efficacy, universality and noise-resilience of QEMTP on both noise-free simulators and IBM real quantum computers.
Abstract \noindent This paper applies the Variational Quantum Linear Solver (VQLS) to the continuous-time Lyapunov equation ATX+XA=−Q. Using the Kronecker product formulation, the matrix equation is transformed into the linear system Hz=b, where H=In⊗AT+AT⊗In and z=vec(X). VQLS approximates the solution via parameterized quantum circuits optimized in a hybrid quantum-classical loop. Numerical experiments on four control system benchmarks with Kronecker dimensions up to 25×25 demonstrate residual norms as low as 10−9, with logarithmic qubit scaling (2-5 qubits) and shallow circuit depths (6-14 layers) suitable for near-term quantum devices. Compared to the HHL algorithm, VQLS offers reduced circuit complexity and qubit overhead, making it practical for noisy intermediate-scale quantum (NISQ) hardware. This paper demonstrates the potential of variational quantum algorithms for solving Lyapunov equations in control and dynamical systems applications.
Variational Quantum Circuits (VQCs) have emerged as a cornerstone of hybrid quantum–classical algorithms designed to harness the computational potential of near-term quantum devices. By combining parameterized quantum gates with classical optimization, VQCs provide a flexible framework for tackling machine learning, chemistry, and optimization problems intractable for classical methods. This review comprehensively overviews VQC design principles, ansatz structures, optimization strategies, and real-world applications. Furthermore, we discuss fundamental challenges such as barren plateaus, the expressibility–trainability trade-off, and current noisy intermediate-scale quantum (NISQ) hardware limitations. Finally, we highlight emerging directions that could enable scalable, noise-resilient, and physically interpretable variational quantum models for future quantum computing applications
Quantum Phase Estimation (QPE) is a foundational algorithm for molecular ground-state energy estimation, but its deep circuit requirements make direct hardware execution impractical on Noisy Intermediate-Scale Quantum (NISQ) devices. We present an analytically grounded variational surrogate framework in which a shallow Variational Quantum Circuit (VQC) is trained to reproduce the QPE measurement distribution without any quantum circuit simulation. The training target is computed entirely classically via the Dirichlet kernel, evaluated directly from the Full Configuration Interaction (FCI) ground-state energy, the ancilla qubit count, and the time evolution parameter, eliminating the exponentially scaling simulation bottleneck of prior surrogate approaches. We apply this framework to the hydrogen molecule (H2) with a symmetry-tapered Hamiltonian, conducting a four-stage experimental investigation on IBM Quantum hardware. Stage 1 compares linear and full entangler topologies for the RY-RZ-CZ ansatz, with and without XpXm Dynamical Decoupling (DD), across four distributional metrics (Hellinger distance, fidelity error, total variation distance, Jensen-Shannon divergence), identifying the linear entangler as optimal. Stage 2 varies VQC layers (p=1 to 5) for the linear-entangler ansatz, identifying single-layer depth as optimal under hardware noise. Stage 3 applies this configuration to the reduced RY-CZ ansatz, comparing ideal and noisy simulator-trained parameters. A supplementary noise analysis at p∈{8,64} characterizes the depth-dependent interplay between circuit depth and DD effectiveness. The framework enables faithful QPE mimicry using a linearly scaling VQC, recovering the ground-state energy within the chemical accuracy threshold (1 kcal/mol), constituting a scalable, hardware-efficient paradigm for QPE-based molecular energy estimation on NISQ devices.