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Quantum Approximate Optimization Algorithm (QAOA) provides a way to solve combinatorial optimization problems using quantum computers. QAOA circuits consist of time evolution operators by the cost Hamiltonian and of state mixing operators,…
Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization…
Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing…
Variational quantum algorithms are ubiquitous in applications of noisy intermediate-scale quantum computers. Due to the structure of conventional parametrized quantum gates, the evaluated functions typically are finite Fourier series of the…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. The barren plateau phenomenon manifests as an exponentially…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
Variational Quantum Circuits (VQCs) have emerged as a promising paradigm for quantum machine learning in the NISQ era. While parameter sharing in VQCs can reduce the parameter space dimensionality and potentially mitigate the barren plateau…
We propose a technique for optimizing parameterized circuits in variational quantum algorithms based on the probabilistic tensor sampling optimization. This method allows one to relax random initialization issues or heuristics for…
In the search for quantum advantage with near-term quantum devices, navigating the optimization landscape is significantly hampered by the barren plateaus phenomenon. This study presents a strategy to overcome this obstacle without changing…
The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at…
The training of a parameterized model largely depends on the landscape of the underlying loss function. In particular, vanishing gradients are a central bottleneck in the scalability of variational quantum algorithms (VQAs), and are known…
Despite its popularity, several empirical and theoretical studies suggest that the quantum approximate optimization algorithm (QAOA) has persistent issues in providing a substantial practical advantage. Numerical results for few qubits and…
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…
We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…
The Quantum Alternating Operator Ansatz (QAOA) represents a branch of quantum algorithms for solving combinatorial optimization problems. A specific variant, the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA), ensures uniform…
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is…
QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum…
Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum…