Related papers: Stabilizer extent is not multiplicative

We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…

In this paper we analyze the classical limit of the Nelson model with cut off, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum observables to the solutions of classical…

By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. Furthermore, we introduce a new class of codes which we have called weak…

Classical computers can simulate models of quantum computation with restricted input states. The identification of such states can sharpen the boundary between quantum and classical computations. Previous works describe simulable states of…

A complex projective $t$-design is a configuration of vectors which is ``evenly distributed'' on a sphere in the sense that sampling uniformly from it reproduces the moments of Haar measure up to order $2t$. We show that the set of all…

Circuit cutting partitions a large quantum circuit into smaller subcircuits that can be executed independently and recombined by classical post-processing. In classical state-vector simulation with full-state reconstruction, the runtime is…

We present a discussion of the generalized Clifford group over non-cyclic finite abelian groups. These Clifford groups appear naturally in the theory of topological error correction and abelian anyon models. We demonstrate a generalized…

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…

Clifford codes can be understood as a generalization of stabilizer codes. To show the existence of a true Clifford code which is better than any stabilizer code is a well known open problem in the theory of Clifford codes. One of the main…

We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of…

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have…

Description of nonclassicality of states has hitherto been through violation of Bell inequality and non-separability, with the latter being a stronger constraint. In this paper, we show that this can be further sharpened, by introducing the…

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 describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the…

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…

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for…

We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…

In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in…

Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the…

Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…