Related papers: Mildly-Interacting Fermionic Unitaries are Efficie…
A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity--a strongly coupled regime…
The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high…
In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to…
We study the complexity of learning mixtures of separated Gaussians with common unknown bounded covariance matrix. Specifically, we focus on learning Gaussian mixture models (GMMs) on $\mathbb{R}^d$ of the form $P= \sum_{i=1}^k w_i…
Large N gauge theories with adjoint matter can be numerically studied using lattice techniques. Eguchi-Kawai reductions holds for this theory and one can reduce the lattice model to a single site. Hybrid Monte Carlo algorithm can be used to…
We provide a definition and explicit expressions for $n$-body Gaussian Process (GP) kernels which can learn any interatomic interaction occurring in a physical system, up to $n$-body contributions, for any value of $n$. The series is…
The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
We propose efficient algorithms for classically simulating Gaussian unitaries and measurements applied to non-Gaussian initial states. The constructions are based on decomposing the non-Gaussian states into linear combinations of Gaussian…
We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
Perturbative unitarity is a powerful tool for inferring the range of validity of a given effective field theory. Here, we study such a bound in the parameter space of dimension-5 and dimension-6 effective operators that arise in a scenario…
In quantum information theory and statistical physics, symmetries of multiple copies, or replicas, of a system play a pivotal role. For unitary ensembles, these symmetries are encoded in the replicated commutant: the algebra of operators…
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal quantum simulation of fermionic systems is daunting…
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and…
Quadratic Wasserstein distances are obtained between dynamical systems (with states as special case), on $\mathbb{Z}_2$-graded von Neumann algebras. This is achieved through a systematic translation from non-graded to $\mathbb{Z}_2$-graded…
Quantum generative learning is a promising application of quantum computers, but faces several trainability challenges, including the difficulty in experimental gradient estimations. For certain structured quantum generative models,…
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…
Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…
We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account of both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting…