Related papers: Learning the stabilizer group of a Matrix Product …
System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant…
We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…
Magic-state resource theory is a fundamental framework with far-reaching applications in quantum error correction and the classical simulation of quantum systems. Recent advances have significantly deepened our understanding of magic as a…
Magic, capturing the deviation of a quantum state from the stabilizer formalism, is a key resource underpinning the quantum advantage. The recently introduced stabilizer R\'enyi entropy (SRE) offers a tractable measure of magic, avoiding…
We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study…
In this work, we present number-theoretic and algebraic-geometric techniques for bounding the stabilizer rank of quantum states. First, we refine a number-theoretic theorem of Moulton to exhibit an explicit sequence of product states with…
Numerical N-body simulations are commonly used to explore stability regions around exoplanets, offering insights into the possible existence of satellites and ring systems. This study aims to utilize Machine Learning (ML) techniques to…
We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $\rho$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $\rho$ at…
Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…
We introduce a new classical simulation algorithm based on non-signaling polytopes of multipartite Bell scenarios, capable of simulating universal measurement-based quantum computation with single-qubit Pauli measurements. In our model, the…
The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…
The determination of many special types of quantum states has been studied thoroughly, such as the generalized |GHZ> states, |W> states equivalent under stochastic local operations and classical communication and Dicke states. In this…
This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
We demonstrate the use of variational neural network quantum states to study non-stabilizerness in qubit-regularised quantum field theory. Applying the methodology recently introduced by Sinibaldi et al., we numerically compute the…
We use a graphical representation of stabilizer states to describe, simply and efficiently, the effect of measurements of Pauli products on stabilizer states. This work complements our earlier work [Phys. Rev. A 77, 042307 (2008)], which…
The characterization of nonstabilizerness is fruitful due to its application in gate synthesis and classical simulation. In particular, the resource monotone called the stabilizer extent is a useful tool to estimate the simulation cost…
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a…
The stabilizer group of an n-qubit state \psi is the set of all matrices of the form g=g_1\otimes\cdots\otimes g_n, with g_1,...,g_n being any 2x2 invertible complex matrices, that satisfy g\psi=\psi. We show that for 5 or more qubits,…
We develop analytical and algorithmic techniques that enable efficient simulation of a broad class of noisy stabilizer circuits. We derive closed-form expressions of expectation values for tensor product of Paulis in circuits with…