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Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study…

Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling…

We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on…

This paper presents an easy-to-implement approach to mitigate the challenges posed by barren plateaus (BPs) in randomly initialized parameterized quantum circuits (PQCs) within variational quantum algorithms (VQAs). Recent state-of-the-art…

Variational quantum algorithms, which utilize Parametrized Quantum Circuits (PQCs), are promising tools to achieve quantum advantage for optimization problems on near-term quantum devices. Their PQCs have been conventionally constructed…

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…

ReLU neural networks define piecewise linear functions of their inputs. However, initializing and training a neural network is very different from fitting a linear spline. In this paper, we expand empirically upon previous theoretical work…

The barren plateau phenomenon; where cost function gradients vanish exponentially with system size; remains a fundamental obstacle to training variational quantum circuits (VQCs) at scale. We demonstrate, both theoretically and numerically,…

To study generator design for parameterized unitaries in quantum machine learning (QML), we propose an observable-guided generator selection algorithm for $ n $-qubit Pauli-string generator pools. The proposed method selects generators…

Improving the efficiency and accuracy of energy calculations has been of significant and continued interest in the area of materials informatics, a field that applies machine learning techniques to computational materials data. Here, we…

Practical Quantum Machine Learning (QML) is challenged by noise, limited scalability, and poor trainability in Variational Quantum Circuits (VQCs) on current hardware. We propose a multi-chip ensemble VQC framework that systematically…

Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator…

Herein, we introduce a strategy to decompose an arbitrary square matrix into a linear combination of non-unitaries (LCNU) where each non-unitary term is embedded into a unitary matrix. The result is a linear combination of unitaries (LCU)…

We present a novel method for determining gradients of parameterised quantum circuits (PQCs) in hybrid quantum-classical machine learning models by applying the multivariate version of the simultaneous perturbation stochastic approximation…

Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for…

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 that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here, we propose the rules for differentiating…

We introduce fermionic machine learning (FermiML), a machine learning framework based on fermionic quantum computation. FermiML models are expressed in terms of parameterized matchgate circuits, a restricted class of quantum circuits that…

Variational (or, parameterized) quantum circuits are quantum circuits that contain real-number parameters, that need to be optimized/"trained" in order to achieve the desired quantum-computational effect. For that training, analytic…

We study the optimization landscape and the stability properties of training problems with squared loss for neural networks and general nonlinear conic approximation schemes. It is demonstrated that, if a nonlinear conic approximation…