Related papers: Simulating quantum circuits with ZX-calculus reduc…
The ZX-calculus is a graphical calculus for reasoning about pure state qubit quantum mechanics. It is complete for pure qubit stabilizer quantum mechanics, meaning any equality involving only stabilizer operations that can be derived using…
Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
We start by studying the subgroup structures underlying stabilizer circuits. Then we apply our results to provide two normal forms for stabilizer circuits. These forms are computed by induction using simple conjugation rules in the Clifford…
Traditional quantum circuit optimization is performed directly at the circuit level. Alternatively, a quantum circuit can be translated to a ZX-diagram which can be simplified using the rules of the ZX-calculus, after which a simplified…
The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…
This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational theorem-proving techniques and the extended Wolfram model…
We present a simple and efficient way to reduce the contraction cost of a tensor network to simulate a quantum circuit. We start by interpreting the circuit as a ZX-diagram. We then use simplification and local complementation rules to…
In the noisy intermediate-scale quantum (NISQ) era, two-qubit gates in quantum circuits are more susceptible to noise than single-qubit gates. Therefore, reducing the number of two-qubit gates is crucial for improving circuit efficiency and…
Classical simulation of quantum circuits is a pivotal part of the quantum computing landscape, specially within the NISQ era, where the constraints imposed by available hardware are unavoidable. The Gottesman-Knill theorem further motivates…
Quantum circuit cutting refers to a series of techniques that allow one to partition a quantum computation on a large quantum computer into several quantum computations on smaller devices. This usually comes at the price of a sampling…
The ZX-calculus is a graphical language for suitably represented tensor networks, called ZX-diagrams. Calculations are performed by transforming ZX-diagrams with rewrite rules. The ZX-calculus has found applications in reasoning about…
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 study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative…
Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a…
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…
We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifically, we develop a canonical form in the ZX calculus and…
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…
We present novel algorithms to estimate outcomes for qubit quantum circuits. Notably, these methods can simulate a Clifford circuit in linear time without ever writing down stabilizer states explicitly. These algorithms outperform previous…
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…