Related papers: Beyond Ans\"atze: Learning Quantum Circuits as Uni…
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…
A major challenge in the training of recurrent neural networks is the so-called vanishing or exploding gradient problem. The use of a norm-preserving transition operator can address this issue, but parametrization is challenging. In this…
Variational quantum algorithms are a promising class of algorithms that can be performed on currently available quantum computers. In most settings, the free parameters of a variational circuit are optimized using a classical optimizer that…
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…
Variational Quantum Algorithms are one of the most promising candidates to yield the first industrially relevant quantum advantage. Being capable of arbitrary function approximation, they are often referred to as Quantum Neural Networks…
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…
Given the rising popularity of quantum machine learning (QML), it is important to develop techniques that effectively simplify commonly adopted families of parameterised quantum circuits (commonly known as ans\"{a}tze). This thesis pioneers…
Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been…
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…
Quantum computers can efficiently solve problems which are widely believed to lie beyond the reach of classical computers. In the near-term, hybrid quantum-classical algorithms, which efficiently embed quantum hardware in classical…
In this work, we propose the first quantum Ans\"atze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding.…
In this thesis we expand upon the results that led to the paper of Lee et al., arXiv:2105.01114 (2021). In particular, we give more details on the oracular formulation of variational quantum algorithms, and the relationship between…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
We introduce multiple parametrized circuit ans\"atze and present the results of a numerical study comparing their performance with a standard Quantum Alternating Operator Ansatz approach. The ans\"atze are inspired by mixing and phase…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
Quantum computation represents an emerging framework to solve lattice gauge theories (LGT) with arbitrary gauge groups, a general and long-standing problem in computational physics. While quantum computers may encode LGT using only…
For a large number of tasks, quantum computing demonstrates the potential for exponential acceleration over classical computing. In the NISQ era, variable-component subcircuits enable applications of quantum computing. To reduce the…
We present quantum circuits with a brick wall structure using the optimal number of parameters and two-qubit gates to parametrize $SU(2^n)$, and provide evidence that these circuits are universal for $n\leq 5$. For this, we successfully…
The classification of quantum states into distinct classes poses a significant challenge. In this study, we address this problem using quantum neural networks in combination with a problem-inspired circuit and customised as well as…