Related papers: Interacting boson problems are QMA-hard
The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\delta$-function interaction there is another…
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…
As the title suggests, this is an attempt at bosonizing fermions in any number of dimensions without paying attention to the fact that the Fermi surface is an extended object. One is tempted to introduce the density fluctuation and its…
There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the…
As an intrinsically-unbiased approach, quantum Monte Carlo (QMC) is of vital importance in understanding correlated phases of matter. Unfortunately, it often suffers notorious sign problem when simulating interacting fermion models. Here,…
We study the role of electron-electron interactions near integer and abelian fractional quantum Hall (QH) transitions using composite fermion (CF) representations. Interaction effects are encapsulated in CF theories as gauge fluctuations.…
A system of N interacting bosons or fermions in a two-dimensional harmonic potential (or, equivalently, magnetic field) whose states are projected onto the lowest Landau level is considered. Generic expressions are derived for matrix…
Equations are proposed for the description of the fermion interaction via massive and massless bosons. These equations lead to the propagators which maintain theory renormalization. These equations are also invariant with respect to the…
The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic…
Computing the state of a quantum mechanical many-body system composed of indistinguishable particles distributed over a multitude of modes is one of the paradigmatic test cases of computational complexity theory: Beyond well-understood…
Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic…
Determinant quantum Monte Carlo (DQMC), formulated in complex-fermion representation, has played a key role in studying strongly-correlated fermion systems. However, its applicability is limited due to the requirement of particle-number…
We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this paper, we show hardness of a classical tiling problem on an N x N…
Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Meron-cluster algorithms lead to an efficient solution of sign problems for both fermionic and bosonic models. Here we apply the meron concept to…
Quantum Monte Carlo simulations of quantum many body systems are plagued by the Fermion sign problem. The computational complexity of simulating Fermions scales exponentially in the projection time $\beta$ and system size. The sign problem…
We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For…
State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks…
We pose a generalized Boson Sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of Bosons. We describe a quantum optical processor that can solve this problem…
It is known that three fundamental questions regarding local Hamiltonians -- approximating the ground state energy (the Local Hamiltonian problem), simulating local measurements on the ground space (APX-SIM), and deciding if the low energy…
Understanding the dynamics of higher-dimensional quantum systems embedded in a complex environment remains a significant theoretical challenge. While several approaches yielding numerically converged solutions exist, these are…