Related papers: Quantum circuits with free fermions in disguise
Local interactions among electrons underlie many complex properties of correlated materials. While the Jordan-Wigner transformation can preserve this locality along one spatial dimension, interactions along the remaining dimensions…
In this paper, we show that the Hamiltonian approach to loop quantum gravity has a fermion doubling problem. To obtain this result, we couple loop quantum gravity to a free massless scalar and a chiral fermion field, gauge fixing the many…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in…
We conjecture that the free-fermion part of the eigenspectrum observed recently for the $SU_q(N)$ Perk-Schultz spin chain Hamiltonian in a finite lattice with $q=\exp (i\pi (N-1)/N)$ is a consequence of the existence of a special simple…
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their…
We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a simple set of equalities between circuits of this fragment,…
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…
The statistical mechanics characterization of a finite subsystem embedded in an infinite system is a fundamental question of quantum physics. Nevertheless, a full closed form { for all required entropic measures} does not exist in the…
All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…
Simulation of fermionic systems is one of the most promising applications of quantum computers. It spans problems in quantum chemistry, high-energy physics and condensed matter. Underpinning the core steps of any quantum simulation…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between…
We present random quantum circuit models for non-unitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends towards steady states with logarithmic violations of the entanglement…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the…
Simulating a fermionic system on a quantum computer requires encoding the anti-commuting fermionic variables into the operators acting on the qubit Hilbert space. The most familiar of which, the Jordan-Wigner transformation, encodes…
We extend the notion of space shifts introduced by L. D. Faddeev and A. Yu. Volkov (Phys. Lett. B 315 (1993)) for certain quantum light cone lattice equations of sine-Gordon type at root of unity. As a result we obtain a compatibility…