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Variational quantum algorithms use non-convex optimization methods to find the optimal parameters for a parametrized quantum circuit in order to solve a computational problem. The choice of the circuit ansatz, which consists of…

For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…

Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are…

Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…

Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the…

Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in…

Variational Quantum Algorithms (VQAs), such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), are widely studied as candidates for near-term quantum advantage. Recent work has shown that…

A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of…

Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…

We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…

We present a detailed numerical study of an alternative approach, named Quantum Non-Demolition Measurement (QNDM), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding…

Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy intermediate-scale quantum (NISQ) devices. Testing these algorithms on relevant hardware is crucial to…

Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…

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,…

The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…

Variational Quantum Algorithms (VQAs) are promising methods for solving combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) devices. However, benchmarking VQAs is difficult due to their stochastic behavior and the…

Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…

Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a…

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…

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…