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Integrated photonic circuits have a strong potential to perform quantum information processing. Indeed, the ability to manipulate quantum states of light by integrated devices may open new perspectives both for fundamental tests of quantum…
A projective hypersurface is nodal if it does not have singularities worse than simple nodes. We calculate the rational cohomology of the spaces of equations of nodal cubic and quartic plane curves and also nodal cubic surfaces in the…
We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
We consider the general problem of the optimal transformation of N uses of (possibly different) unitary channels to a single use of another unitary channel in any finite dimension. We show how the optimal transformation can be fully…
We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-dimensional qudits (i.e. qupits). We derive a simplified rule set that closely resembles the original rules of qubit ZX-calculus. Using these rules, we…
The phase folding optimization is a circuit optimization used in many quantum compilers as a fast and effective way of reducing the number of high-cost gates in a quantum circuit. However, existing formulations of the optimization rely on…
The well-known theory of "rational canonical form of an operator" describes the invariant factors, or elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space $\V$ over a…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at…
In this work, we propose three-dimensional photonic circuit designs that guarantee a considerable reduction in the complexity of circuits for the purpose of performing quantum state tomography of N-dimensional path qudits. The POVM…
Reconfigurable quantum circuits are fundamental building blocks for the implementation of scalable quantum technologies. Their implementation has been pursued in linear optics through the engineering of sophisticated interferometers. While…
Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose…
Developing quantum computers for real-world applications requires understanding theoretical sources of quantum advantage and applying those insights to design more powerful machines. Toward that end, we introduce a high-fidelity gate set…
Quantum convolutional neural networks (QCNNs) are quantum circuits for characterizing complex quantum states. They have been proposed for recognizing quantum phases of matter at low sampling cost and have been designed for condensed matter…
Recently, it was shown that the qudits used in circuits of a convolutional form (e.g., Matrix Product State sand Multi-scale Entanglement Renormalization Ansatz) can be reset unitarily…
For years, the quantum/reversible circuit community has been convinced that: a) the addition of auxiliary qubits is instrumental in constructing a smaller quantum circuit; and, b) the introduction of quantum gates inside reversible circuits…
It is shown that the two qubit CNOT (controlled NOT) gate can also be realised using q-deformed angular momentum states via the Jordan-Schwinger mechanism.Thus all the three gates necessary for universality i.e. Hadamard, Phase Shift and…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…