Related papers: Quantum circuits with free fermions in disguise
The realistic free fermionic models have had remarkable success in providing plausible explanations for various properties of the Standard Model which include the natural appearance of three generations, the explanation of the heavy top…
It is known that a single quantum harmonic oscillator is characterized by a hidden spectrum generating superconformal symmetry, but its origin has remained rather obscure. We show how this hidden superconformal symmetry can be derived by…
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle…
This thesis studies the role of free fermions in certain classical and quantum integrable models. The classical models studied are the KP and BKP hierarchies of partial differential equations. We review the presence of free fermions in the…
Free fermions in disguise (FFD) Hamiltonians describe spin chains which can be mapped to free fermions, but not via a Jordan-Wigner transformation. Although the mapping gives access to the full Hamiltonian spectrum, the computation of spin…
The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin-1/2 $XX$ model on the diamond chain. Generally, the Hamiltonian of this quantum spin system can be represented in terms of spinless fermions in the…
We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof…
Exactly solvable models are essential in physics. For many-body spin-1/2 systems, an important class of such models consists of those that can be mapped to free fermions hopping on a graph. We provide a complete characterization of models…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…
Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement…
Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in…
The inherent properties of specific physical systems can be used as metaphors for investigation of the behavior of complex networks. This insight has already been put into practice in previous work, e.g., studying the network evolution in…
In this paper, we present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We focus on the use of multi-level qudits, specifically ququarts. Traditional mappings, such as the Jordan-Wigner…
In this article we are concerned with finite dimensional Fermions, by which we mean vectors in a finite dimensional complex space embedded in the exterior algebra over itself. These Fermions are spinless but possess the characterizing…
Modern understanding of symmetry in quantum field theory includes both invertible and non-invertible operations. Motivated by this, we extend Nielsen's geometric approach to quantum circuit complexity to incorporate non-invertible gates.…
We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional…
A large family of multispin interacting one-dimensional quantum spin models with $Z(N)$ symmetry and a free-particle eigenspectra are known in the literature. They are free-fermionic ($N=2$) and free-parafermionic ($N\geq 2$) quantum…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main…