Related papers: Quantum circuits with free fermions in disguise

Quantum circuits with free fermions in disguise

URL: http://arxiv.org/abs/2402.02984v1
Date: Mon, 5 Feb 2024 13:15:52 GMT
Title: Quantum circuits with free fermions in disguise
Authors: Bal\'azs Pozsgay
Abstract summary: Multiple families of spin chain models have a free fermionic spectrum, even though they are not solvable by a Jordan-Wigner transformation. We construct circuits using local unitary gates built from the terms in the local Hamiltonians of the respective models. We find that many standard brickwork circuits are not free fermionic, but we identify certain symmetric constructions which are.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Recently multiple families of spin chain models were found, which have a free fermionic spectrum, even though they are not solvable by a Jordan-Wigner transformation. Instead, the free fermions emerge as a result of a rather intricate construction. In this work we consider the quantum circuit formulation of the problem. We construct circuits using local unitary gates built from the terms in the local Hamiltonians of the respective models, and ask the question: which circuit geometries (sequence of gates) lead to a free fermionic spectrum? Our main example is the 4-fermion model of Fendley, where we construct free fermionic circuits with various geometries. In certain cases we prove the free fermionic nature, while for other geometries we confirm it numerically. Surprisingly, we find that many standard brickwork circuits are not free fermionic, but we identify certain symmetric constructions which are.

Related papers

Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
arXiv Detail & Related papers (2024-06-06T18:04:39Z)
Brick Wall Quantum Circuits with Global Fermionic Symmetry [0.0]
We study brick wall quantum circuits enjoying a global fermionic symmetry. Fermionic symmetry pins $H_gamma$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases.
arXiv Detail & Related papers (2024-02-28T16:09:54Z)
Free fermions beyond Jordan and Wigner [0.0]
We compute the exact spectrum, and generalise an elegant graph-theory construction. We also explain how this family admits an N=2 lattice supersymmetry.
arXiv Detail & Related papers (2023-10-30T18:07:36Z)
Quantum circuits for solving local fermion-to-qubit mappings [0.0]
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining locality comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. We demonstrate how maintaining locality allows one to carry out a Trotterized time-evolution with constant circuit depth per time step.
arXiv Detail & Related papers (2022-08-15T13:50:33Z)
Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
arXiv Detail & Related papers (2022-04-11T18:00:01Z)
Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z)
Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
arXiv Detail & Related papers (2021-07-20T18:44:06Z)
Jordan-Wigner transformation and qubits with nontrivial exchange rule [91.3755431537592]
Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. considered method has some relation with construction of super-spaces, but it has some differences with standard definition of supersymmety sometimes used for generalizations of qubit model.
arXiv Detail & Related papers (2021-03-08T09:31:03Z)
The principle of majorization: application to random quantum circuits [68.8204255655161]
Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. We verified that all the families of circuits satisfy on average the principle of majorization. Clear differences appear in the fluctuations of the Lorenz curves associated to states.
arXiv Detail & Related papers (2021-02-19T16:07:09Z)
The coset construction for particles of arbitrary spin [0.0]
When a system spontaneously breaks Poincar'e symmetry, excitations that satisfy Goldstone's theorem can be quite unusual. We propose a novel coset construction for systems that spontaneously break Poincar'e symmetry. We derive a novel action for such particles and find a spin-orbital' coupling between the intrinsic quantum spin and the physical-rotation degrees of freedom.
arXiv Detail & Related papers (2020-10-21T18:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.