Related papers: Permanents, Bosons and Linear Optics
Boson Sampling is a task that is conjectured to be computationally hard for a classical computer, but which can be efficiently solved by linear-optical interferometers with Fock state inputs. Significant advances have been reported in the…
Fermionic linear optics is efficiently classically simulatable. Here it is shown that the set of states achievable with fermionic linear optics and particle measurements is the closure of a low dimensional Lie group. The weakness of…
This paper is concerned with the analysis of linear quantum optical networks. It provides a systematic approach to the construction a model for a given quantum network in terms of a system of quantum stochastic differential equations. This…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and…
Fermionic linear optics is a model of quantum computation which is efficiently simulable on a classical probabilistic computer. We study the problem of a classical simulation of fermionic linear optics augmented with noisy auxiliary states.…
This work proposes a digital quantum simulation protocol for the linear scattering process of bosons, which provides a simple extension to partially distinguishable boson cases. Our protocol is achieved by combining the boson-fermion…
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
Boson-sampling has been presented as a simplified model for linear optical quantum computing. In the boson-sampling model, Fock states are passed through a linear optics network and sampled via number-resolved photodetection. It has been…
We present a comprehensive study of the impact of non-uniform, i.e.\ path-dependent, photonic losses on the computational complexity of linear-optical processes. Our main result states that, if each beam splitter in a network induces some…
The current shift in the quantum optics community towards large-size experiments -- with many modes and photons -- necessitates new classical simulation techniques that go beyond the usual phase space formulation of quantum mechanics. To…
Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and…
We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under the effect of Hamiltonians quadratic in creation and annihilation operators, commonly referred to as linear optics. These anyonic models are…
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples,…
BosonSampling is a restricted model of quantum computation proposed recently, where a non-adaptive linear-optical network is used to solve a sampling problem that seems to be hard for classical computers. Here we show that, even if the…
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples,…
The purpose of this overview article, which can be viewed as a supplement to our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf 21} (2004), 1-35], is to highlight the differences of boson and fermion systems in…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
The increasingly popular concept of a hidden Hermiticity of operators (i.e., of their Hermiticity with respect to an {\it ad hoc} inner product in Hilbert space) is compared with the recently introduced notion of {\em non-linear…