Related papers: A new algorithm for producing quantum circuits usi…
In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum…
We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\hat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$,…
Learning low dimensional representation is a crucial issue for many machine learning tasks such as pattern recognition and image retrieval. In this article, we present a quantum algorithm and a quantum circuit to efficiently perform…
Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about…
Let $C$ be a symmetrizable generalized Cartan Matrix, and $q$ an indeterminate. ${\fg}(C)$ is the Kac-Moody Lie algebra and $U=U_q({\fg}(C))$ the associated quantum enveloping algebra over $ k={\Bbb Q}(q)$. The quantum function algebra…
In the Noisy Intermediate Scale Quantum (NISQ) era, finding implementations of quantum algorithms that minimize the number of expensive and error prone multi-qubit gates is vital to ensure computations produce meaningful outputs. Unitary…
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
A new algorithm for simulating compact U(1) lattice gauge theory in three dimensions is presented which is based on global changes in the configuration space. We show that this algorithm provides an effective way to extract partition…
We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits…
We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles (circular unitary, orthogonal, and symplectic ensembles; CUE, COE and CSE). We utilise the established model of a…
We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+$T$ basis, that minimize the number of phase-rotation gates in the synthesized approximation circuit.…
Within the general context of the architecture in quantum computer design, this paper aims is to provide a general strategy to obtain a block-matrix representation of quantum gates applied to qubits placed in arbitrary positions over an…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it…
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
Decoupling systems into independently evolving components has a long history of simplifying seemingly complex systems. They enable a better understanding of the underlying dynamics and causal structures while providing more efficient means…