Related papers: Stabilizer rank and higher-order Fourier analysis

We explore the role of majorization theory in quantum phase space. To this purpose, we restrict ourselves to quantum states with positive Wigner functions and show that the continuous version of majorization theory provides an elegant and…

We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…

Magic states, pivotal for universal quantum computation via classically simulable Clifford gates, often undergo decomposition into resourceless stabilizer states, facilitating simulation through classical means. This approach yields three…

Quantum state discrimination plays a central role in defining the possible and impossible operations through a restricted class of quantum operations. A seminal result by Bennett et al. [Phys. Rev. A 59, 1070 (1999)] demonstrates the…

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…

We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition. Our result relies on the fact that states which are mixed by…

In quantum computing, the nonstabilizerness of quantum operations is crucial for understanding and quantifying quantum speedups. In this study, we explore the phenomena of nonstabilizerness of the quantum SWITCH, a novel structure that…

A new class of quantum states is introduced by demanding that the computational measurement statistics approach the Boltzmann distribution of higher-order strongly coupled Ising models. The states, referred to as $n$-coupled states, are…

Quantum fidelity estimation is essential for benchmarking quantum states and processes on noisy quantum devices. While stabilizer operations form the foundation of fault-tolerant quantum computing, non-stabilizer resources further enable…

We investigate the dynamics of nonstabilizerness - also known as `magic' - in monitored quantum circuits composed of random Clifford unitaries and local projective measurements. For measurements in the computational basis, we derive an…

We consider the following task: suppose an algorithm is given copies of an unknown $n$-qubit quantum state $|\psi\rangle$ promised $(i)$ $|\psi\rangle$ is $\varepsilon_1$-close to a stabilizer state in fidelity or $(ii)$ $|\psi\rangle$ is…

This paper builds on the idea of simulating stabiliser circuits through transformations of quadratic form expansions. This is a representation of a quantum state which specifies a formula for the expansion in the standard basis, describing…

Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…

Magic states enable universal, fault-tolerant quantum computation within the stabilizer framework. Their non-stabilizerness supplies the resource needed to bypass the Eastin-Knill theorem while allowing fault-tolerant distillation. Although…

Phase operators are constructed using a Klauder-Berezin coherent state quantization in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables phase leads…

The Schr\"odinger cat states, constructed from Glauber coherent states and applied for description of qubits, are generalized to the kaleidoscope of coherent states related with regular n-polygon symmetry and the roots of unity. The cases…

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…

Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite Heisenberg group. States that are far from being stabilizer states include magic states in quantum computation, MUB-balanced states, and SIC vectors. In…

We introduce a methodology to estimate non-stabilizerness or "magic", a key resource for quantum complexity, with Neural Quantum States (NQS). Our framework relies on two schemes based on Monte Carlo sampling to quantify non-stabilizerness…

Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards…