Related papers: Reduced quantum circuits for stabilizer states and…
We introduce a model-checking tool intended specially for the analysis of quantum information protocols. The tool incorporates an efficient representation of a certain class of quantum circuits, namely those expressible in the so-called…
We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX…
We investigate the problem of evaluating the output probabilities of Clifford circuits with nonstabilizer product input states. First, we consider the case when the input state is mixed, and give an efficient classical algorithm to…
We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford…
In this thesis, we study concepts in quantum computing using graphical languages, specifically using the ZX-calculus. The core of the research revolves around (graphical) stabilizer decompositions. The first major focus is on the…
Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
A cluster state is a strongly entangled state, which is a source of measurement-based quantum computation. It is generated by applying controlled-Z (CZ) gates to the state $\left\vert ++\cdots +\right\rangle $. It is protected by the…
Recent completeness results on the ZX-Calculus used a third-party language, namely the ZW-Calculus. As a consequence, these proofs are elegant, but sadly non-constructive. We address this issue in the following. To do so, we first describe…
This paper proposes a new optimized quantum block-ZXZ decomposition method [7,8,10] that results in more optimal quantum circuits than the quantum Shannon decomposition (QSD)[27], which was introduced in 2006 by Shende et al. The…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…
We present a complete optimization procedure for hybrid quantum-classical circuits with classical parity logic. While common optimization techniques for quantum algorithms focus on rewriting solely the pure quantum segments, there is…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure - the stabilizer group - encodes all possible…
In the near term, programming quantum computers will remain severely limited by low quantum volumes. Therefore, it is desirable to implement quantum circuits with the fewest resources possible. For the common Clifford+T circuits, most…
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
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…
Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…
Path sums are a convenient symbolic formalism for quantum operations with applications to the simulation, optimization, and verification of quantum protocols. Unlike quantum circuits, path sums are not limited to unitary operations, but can…