Related papers: Extending the Graph Formalism to Higher-Order Gate…
Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states.…
We describe a procedure for graph state quantum computing that is tailored to fully exploit the physics of optically active multi-level systems. Leveraging ideas from the literature on distributed computation together with the recent work…
In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on…
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 propose protocols to implement non-Clifford logical gates between stabilizer codes by entangling into a non-Abelian topological order as an intermediate step. Generalizing previous approaches, we provide a framework that generates a…
The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field $\Gal{2^n}$ to endow it with proper geometrical properties. We analyze the…
Nonstabilizerness, also known as magic, plays a central role in universal quantum computation. Hypergraph states are nonstabilizer generalizations of graph states and constitute a key class of quantum states in various areas of quantum…
In this work, we study the complexity of graph-state preparation. We consider general quantum algorithms consisting of Clifford operations acting on at most two qubits for graph-state preparations. We define the CZ-complexity of a graph…
Graph states are key resources for measurement-based quantum computing, which is particularly promising for photonic systems. Fusions are probabilistic Bell state measurements, measuring pairs of parity operators of two qubits. Fusions can…
Graph states are entangled states that are essential for quantum information processing. As experimental advances enable the realization of large-scale graph states, efficient fidelity estimation methods are crucial for assessing their…
The progress in building quantum computers to execute quantum algorithms has recently been remarkable. Grover's search algorithm in a binary quantum system provides considerable speed-up over classical paradigm. Further, Grover's algorithm…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. By integrating these techniques, we enhance our ability to accurately…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Graph states are a large class of multipartite entangled quantum states that form the basis of schemes for quantum computation, communication, error correction, metrology, and more. In this work, we consider verification of graph states…