Related papers: Unified framework for efficiently computable quant…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
Checking whether two quantum circuits are equivalent is important for the design and optimization of quantum-computer applications with real-world devices. We consider quantum circuits consisting of Clifford gates, a practically-relevant…
C++QED is a framework for simulating open quantum dynamics in general. Historically, it has in the first place been developed for problems in moving-particle cavity QED, but since then has been applied in other fields as well. It is known…
We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…
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…
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
We present a low-depth randomised algorithm for the estimation of entanglement fidelity between an $n$-qubit matchgate circuit $\mathcal{U}$ and its noisy implementation $\mathcal{E}$. Our procedure makes use of a modified Pauli-Liouville…
The Toffoli gate is an important universal quantum gate, and will alongside the Clifford gates be available in future fault-tolerant quantum computing hardware. Many quantum algorithms rely on performing arbitrarily small single-qubit…
We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of…
A quantum computing simulation provides the opportunity to explore the behaviors of quantum circuits, study the properties of quantum gates, and develop quantum computing algorithms. Simulating quantum circuits requires geometric time and…
A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more…
Fault-tolerant quantum computing hinges on efficient logical compilation, in particular, translating high-level circuits into code-compatible implementations. Gate-by-gate compilation often yields deep circuits, requiring significant…
The performance of quantum algorithms for ground-state energy estimation is directly impacted by the quality of the initial state, where quality is traditionally defined in terms of the overlap of the input state with the target state. An…
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
The development of a framework for quantifying "non-stabiliserness" of quantum operations is motivated by the magic state model of fault-tolerant quantum computation, and by the need to estimate classical simulation cost for noisy…
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters…
Application-specific quantum computers offer the most efficient means to tackle problems intractable by classical computers. Realizing these architectures necessitates a deep understanding of quantum circuit properties and their…
IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement…
Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access…