Related papers: Equivalence between fermion-to-qubit mappings in t…
We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford…
We present a wide array of quantum measures on numerical solutions of 1D Bose- and Fermi-Hubbard Hamiltonians for finite-size systems with open boundary conditions. Finite size effects are highly relevant to ultracold quantum gases in…
We initiate the study of Majorana fermion codes. These codes can be viewed as extensions of Kitaev's 1D model of unpaired Majorana fermions in quantum wires to higher spatial dimensions and interacting fermions. The purpose of Majorana…
One of the methods used to extend two-dimensional bosonization to four space-time dimensions involves a transformation to new spatial variables so that only one of them appears kinematically. The problem is then reduced to an Abelian…
Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper we perform a thorough study of general (nonlinear) canonical transformations…
The quantum link~\cite{Brower:1997ha} Hamiltonian was introduced two decades ago as an alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. When generalized this new…
Starting from a general, microscopic fermion-to-boson mapping that preserves Hermitian conjugation, we discuss truncations of the boson Fock space basis. We give conditions under which the exact boson images of finite fermion operators are…
The optimal regularization of infinite-dimensional degrees of freedom is a central open problem in the tractable simulation of lattice gauge theories on quantum computers. Here, we consider regularizing the gauge field by replacing the…
Preserving spin symmetry in variational quantum algorithms is essential for producing physically meaningful electronic wavefunctions. Implementing spin-adapted transformations on quantum hardware, however, is challenging because the…
The overlap fermion offers the considerable advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given…
The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker,…
We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation category $\mathrm{Rep}(H)$ of a semisimple…
Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a…
We give a simplified proof for the equivalence of loop-erased random walks to a lattice model containing two complex fermions, and one complex boson. This equivalence works on an arbitrary directed graph. Specifying to the $d$-dimensional…
Majorana fermions and their generalizations to $\mathbb{Z}_n$ parafermions are considered promising building blocks of fault-tolerant quantum computers for their ability to encode quantum information nonlocally. In such topological quantum…
We consider the fermion spectrum in the strong coupling vortex phase of a lattice fermion-scalar model with a global $U(1)_L\times U(1)_R$, in 2D, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers…
We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2) and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and…
We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing.…
We investigate various variants of the Hermitean version of the Local Bosonic Algorithm proposed by M. L\"uscher. The model used is two-dimensional Quantum Electrodynamics (QED) with two flavours of massive Wilson fermions. The simplicity…
We write down a class of two-dimensional quantum spin-1/2 Hamiltonians whose eigenspectra are exactly solvable via the Jordan-Wigner transformation. The general structure corresponds to a suitable grid composed of XY or XX-Ising spin chains…