Related papers: Efficient classical simulation of quantum computat…
Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state…
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes…
Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device…
In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the…
The Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators, akin to quantum mechanics. Instead of evolving probability densities in phase space (as in…
We develop a general formalism, based on the Wigner function representation of continuous-variable quantum states, to describe the action of an arbitrary conditional operation on a multimode Gaussian state. We apply this formalism to…
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…
Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has…
Quantum computing has potential to provide exponential speedups over classical computing for many important applications. However, today's quantum computers are in their early stages, and hardware quality issues hinder the scale of program…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
Determining the quantum-classical boundary between quantum circuits which can be efficiently simulated classically and those which cannot remains a fundamental question. One approach to classical simulation is to represent the output of a…
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…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
We generalize the polynomial-time outcome-complete simulation algorithm for stabilizer circuits in arXiv:2309.08676 to track global phases exactly, yielding what we call phased outcome-complete simulation. The original algorithm enabled…
Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates…
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…
The classical simulation of highly-entangling quantum dynamics is conjectured to be generically hard. Thus, recently discovered measurement-induced transitions between highly entangling and low-entanglement dynamics are phase transitions in…
Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…