相关论文: No quantum Ramsey theorem for stabilizer codes

It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…

We investigate the Weyl channels being covariant with respect to the maximum commutative group of unitary operators. This class includes the quantum depolarizing channel and the "two-Pauli" channel as well. Then, we show that our estimation…

The Ramsey's theorem says that a graph with sufficiently many vertices contains a clique or stable set with many vertices. Now we attach some parameter to every vertex, such as degree. Consider the case a graph with sufficiently many…

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…

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…

It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…

We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new…

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…

Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…

We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…

Exact quantum codes detecting a prescribed set of Pauli errors are approached through algebraic constructions--stabilizer, codeword-stabilized, permutation-invariant, topological, and related families. Geometrically, exact Pauli detection…

Quantum magic, quantified by nonstabilizerness, measures departures from stabilizer structure and underlies potential quantum speedups. We introduce an efficient classical framework for computing stabilizer R\'enyi entropies and stabilizer…

A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize…

We introduce a novel type of quantum error correcting code, called the spinor code, based on spaces defined by total spin. The code is a nonstabilizer code, and is also a nonlinear quantum error correcting code, meaning that quantum…

A quantum error correction code is assessed over its ability to correct errors in noisy quantum circuits. This task requires extensive simulations of faulty quantum circuits, which are often made tractable by considering stochastic Pauli…

Stabilizer codes allow for non-local encoding and processing of quantum information. Deformations of stabilizer surface codes introduce new and non-trivial geometry, in particular leading to emergence of long sought after objects known as…

We develop the quantum component of Algebraic Phase Theory by showing that quantum phase, Weyl noncommutativity, and stabiliser codes arise as unavoidable algebraic consequences of Frobenius duality. Working over finite commutative…

We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes over $GF_{4}$ and binary quantum codes to one between…

Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…

Quantum magic, or non-stabilizerness, is an important quantum resource that characterizes computational power beyond classically simulable Clifford operations and is therefore essential for achieving quantum advantage. While previous…