Related papers: Transforming graph states using single-qubit opera…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n,k,d \ge…
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…
We propose a scheme that converts a stabilizer code into another stabilizer code in a fault tolerant manner. The scheme first puts both codes in specific forms, and proceeds the conversion from a source code to a target code by applying…
Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms. We improve on this method by studying stabiliser decompositions of ZX…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing,…
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors that are inherently continuous A powerful method to suppress these effects is to use quantum error correction. Typically,…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Graph states are entangled states useful for several quantum information processing tasks such as measurement-based quantum computation and quantum metrology. As the size of graph states realized in experiments increases, it becomes more…
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the…
Many-body quantum states, as a matter of fact, are extremely essential to solve certain mathematical problems or simulate quantum systems in measurement-based quantum computation. However, how to verify large scale quantum states, such as…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…
The Clifford group is the set of gates generated by controlled-Z gates, the phase gate and the Hadamard gate. We will say that a n-qubit state is a Clifford state if it can be prepared using Clifford gates. These states are known as the…
We report progress on the LU-LC conjecture - an open problem in the context of entanglement in stabilizer states (or graph states). This conjecture states that every two stabilizer states which are related by a local unitary operation, must…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
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…