Related papers: Extending the Graph Formalism to Higher-Order Gate…
We propose an extension to the Pauli stabiliser formalism that includes fractional $2\pi/N$ rotations around the $Z$ axis for some integer $N$. The resulting generalised stabiliser formalism - denoted the XP stabiliser formalism - allows…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
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…
Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph…
We study operator scrambling in quantum circuits built from `super-Clifford' gates. For such circuits it was established in arXiv:2002.12824 that the time evolution of operator entanglement for a large class of many-body operators can be…
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a…
In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states…
The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of…
We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages, such as Cirq and Q#. The computation can then be implemented using a series of non-Pauli…
Quantum entanglement plays an important role in quantum computation and communication. It is necessary for many protocols and computations, but causes unexpected disturbance of computational states. Hence, static analysis of quantum…
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC)…
Superconducting quantum devices are a leading technology for quantum computation, but they suffer from several challenges. Gate errors, coherence errors and a lack of connectivity all contribute to low fidelity results. In particular,…
Following on our previous work arXiv:2204.07593 and arXiv:2306.01043 studying the orbits of quantum states under Clifford circuits via `reachability graphs', we introduce `contracted graphs' whose vertices represent classes of quantum…
Generic quantum-circuit simulation appears intractable for conventional computers and may be unnecessary because useful quantum circuits exhibit significant structure that can be exploited during simulation. For example, Gottesman and Knill…
While all quantum algorithms can be expressed in terms of single-qubit and two-qubit gates, more expressive gate sets can help reduce the algorithmic depth. This is important in the presence of gate errors, especially those due to…
The $n$-qubit stabilizer states are those left invariant by a $2^n$-element subset of the Pauli group. The Clifford group is the group of unitaries which take stabilizer states to stabilizer states; a physically--motivated generating set,…
Fathoming out quantum state space is a challenging endeavor due to its exponentially growing dimensionality. At the expense of being bound in its expressiveness, the discrete and finite subspace of graph states is easier to investigate via…
We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates (including T-gates and $\sqrt{\mathrm{T}}$-gates) can be disentangled completely, provided the number of non-Clifford gates is smaller or…