Related papers: Algebraic and Logical Methods in Quantum Computati…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…
A quantum compiling algorithm is an algorithm for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose $U_{in}$ is an $\nb$-bit unstructured unitary matrix (a unitary matrix with no…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We introduce a type system for the Quipper language designed to derive upper bounds on the size of the circuits produced by the typed program. This size can be measured according to various metrics, including width, depth and gate count,…
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…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
We present an algorithm for performing quantum process tomography on an unknown $n$-qubit unitary $C$ from the Clifford group. Our algorithm uses Bell basis measurements to deterministically learn $C$ with $4n + 3$ queries, which is the…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum…
We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…
Equational reasoning is central to quantum circuit optimisation and verification: one replaces subcircuits by provably equivalent ones using a fixed set of rewrite rules viewed as equations. A finite rule set is most informative when it…
The quantum programming language Quipper supports circuit operations such as reversing and controlling certain quantum circuits. Additionally, Quipper provides a function called with-computed, which can be used to program circuits of the…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…