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Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
The gradient mapping norm is a strong and easily verifiable stopping criterion for first-order methods on composite problems. When the objective exhibits the quadratic growth property, the gradient mapping norm minimization problem can be…
Quantum algorithms are of great interest for their possible use in optimization problems. In particular, variational algorithms that use classical counterparts to optimize parameters hold promise for use in currently existing devices.…
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
The emergence of the Barren Plateau phenomenon poses a significant challenge to quantum machine learning. While most Barren Plateau analyses focus on single-qubit rotation gates, the gradient behavior of Parameterized Quantum Circuits built…
We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected - Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection…
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…
In the present noisy intermediate scale quantum computing era, there is a critical need to devise methods for the efficient implementation of gate-based variational quantum circuits. This ensures that a range of proposed applications can be…
Quantum Machine Learning is an emerging sub-field in machine learning where one of the goals is to perform pattern recognition tasks by encoding data into quantum states. This extension from classical to quantum domain has been made…
The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…
Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as "the quantum variational eigensolver" was developed…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
The barren plateau phenomenon, where the gradients of parametrized quantum circuits become vanishingly small, poses a significant challenge in quantum machine learning. While previous studies attempted to explain the barren plateau…
Hybrid quantum-classical algorithms hold great promise for solving quantum control problems on near-term quantum computers. In this work, we employ the hybrid framework that integrates digital quantum simulation with classical optimization…
Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…