Related papers: Comprehensive Numerical Studies of Barren Plateau …
Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve…
The state-of-the-art quantum computing hardware has entered the noisy intermediate-scale quantum (NISQ) era. Having been constrained by the limited number of qubits and shallow circuit depth, NISQ devices have nevertheless demonstrated the…
The Variational Quantum Eigensolver (VQE) is a fundamental algorithm in quantum computing, yet a coherent geometric characterization of VQE remains missing due to fragmented analyses across fixed-ansatz and adaptive-circuit formulations. In…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
Variational quantum algorithms are tailored to perform within the constraints of current quantum devices, yet they are limited by performance-degrading errors. In this study, we consider a noise model that reflects realistic gate errors…
We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional…
The execution of quantum algorithms on modern hardware is often constrained by noise and qubit decoherence, limiting the circuit depth and the number of gates that can be executed. Circuit optimization techniques help mitigate these…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized…
Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap,…
The optimization of quantum circuits can be hampered by a decay of average gradient amplitudes with increasing system size. When the decay is exponential, this is called the barren plateau problem. Considering explicit circuit…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
Variational quantum algorithms represent a powerful approach for solving optimization problems on noisy quantum computers, with a broad spectrum of potential applications ranging from chemistry to machine learning. However, their…
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…
The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
Quadratic unconstrained binary optimization (QUBO) tasks are very important in chemistry, finance, job scheduling, and so on, which can be represented using graph structures, with the variables as nodes and the interaction between them as…
Variational quantum algorithms face a fundamental trainability crisis: barren plateaus render optimization exponentially difficult as system size grows. While recent Lie algebraic theory precisely characterizes when and why these plateaus…