Related papers: Mildly-Interacting Fermionic Unitaries are Efficie…

We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial"…

We consider the problem of testing and learning quantum $k$-juntas: $n$-qubit unitary matrices which act non-trivially on just $k$ of the $n$ qubits and as the identity on the rest. As our main algorithmic results, we give (a) a…

We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic…

This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models, within a range of alternative quantum bases. We focus on transitioning these states from the…

The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…

Mean field approach, although a generally reliable tool that captures major short range correlations, often fails in symmetric low dimensional strongly correlated electronic systems like those described by the Hubbard model. In these…

This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve…

Classically hard to simulate quantum states, or "magic states", are prerequisites to quantum advantage, highlighting an apparent separation between classically and quantumly tractable problems. Classically simulable states such as Clifford…

We compute the correlation functions of the eigenvalues in the Gaussian unitary ensemble using the fermionic replica method. We show that non--trivial saddle points, which break replica symmetry, must be included in the calculation in order…

The structure of the group $(\mathbb{Z}/n\mathbb{Z})^\star$ and Fermat's little theorem are the basis for some of best-known primality testing algorithms. Many related concepts arise: Euler's totient function and Carmichael's lambda…

We devise a unitary transformation that replaces the fermionic degrees of freedom of lattice gauge theories by (hard-core) bosonic ones. The resulting theory is local and gauge invariant, with the same symmetry group. The method works in…

In this paper we show that very large mixtures of Gaussians are efficiently learnable in high dimension. More precisely, we prove that a mixture with known identical covariance matrices whose number of components is a polynomial of any…

We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and the…

Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by…

We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the…

Schemes of classical shadows have been developed to facilitate the read-out of digital quantum devices, but similar tools for analog quantum simulators are scarce and experimentally impractical. In this work, we provide a measurement scheme…

The dynamics of fermionic unparticles is developed from first principles. It is shown that any unparticle, whether fermionic or bosonic, can be recast in terms of a canonically quantized field, but with non-local interaction terms. We…

Systems consisting of few interacting fermions are the building blocks of matter with atoms and nuclei being the most prominent examples. We have created an artificial few-body quantum system with complete control over the system's quantum…

Suppose that we are given independent, identically distributed samples $x_l$ from a mixture $\mu$ of no more than $k$ of $d$-dimensional spherical gaussian distributions $\mu_i$ with variance $1$, such that the minimum $\ell_2$ distance…

We consider fermionic systems in which fermion parity is conserved within rigid subsystems, and describe an explicit procedure for gauging such subsystem fermion parity symmetries to obtain bosonic spin Hamiltonians. We show that gauging…