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We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
In this work we study the recurrence problem for quantum Markov chains, which are quantum versions of classical Markov chains introduced by S. Gudder and described in terms of completely positive maps. A notion of monitored recurrence for…
We present the Quantum Paldus Transform: an efficient quantum algorithm for block-diagonalising fermionic, spin-free Hamiltonians in the second quantisation. Our algorithm implements an isometry between the occupation number basis of a…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is central for building scalable quantum information systems. In most state-of-the-art approaches, qubits interact locally,…
We present a method for preparing various exotic modifications of Schr{\"o}dinger cat states by coupling a semiclassical oscillator to a system of qubits. Varying the number of qubits and parameters of the protocol (involving quantum quench…
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
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.…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
We present a hybrid model of the unitary-evolution-based quantum computation model and the measurement-based quantum computation model. In the hybrid model part of a quantum circuit is simulated by unitary evolution and the rest by…
Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…
We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
DNA has been proposed as a chemical platform for computing and data storage, paving the way for building DNA-based computers. Recently, DNA has been hypothesized as an ideal quantum computer with the base pairs working as Josephson…
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…