Related papers: Simulation of quantum computation with magic state…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
We propose a quantum circuit that creates a pure state corresponding to the quantum superposition of all prime numbers less than 2^n, where n is the number of qubits of the register. This Prime state can be built using Grover's algorithm,…
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…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…
The development of a framework for quantifying "non-stabiliserness" of quantum operations is motivated by the magic state model of fault-tolerant quantum computation, and by the need to estimate classical simulation cost for noisy…
The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with XX and ZZ couplings of neighboring qubits along and between the chains,…
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…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$…
I describe a method of inferring the past of quantum observables given the initial state and the subsequent measurement results using Wigner quasi-probability representations. The method is proved to be compatible with logic for large…
The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of…
There exist many attempts to define a Wigner function for qudits, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are artificial in their construction and do not allow…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…