Built on

P. Fendley, “Free fermions in disguise,” J. Phys. A
Original
1901
Earlier work this paper cites.
P. Jordan and E. Wigner, “Über das Paulische Äquivalenzverbot,” Z. Physik
1928
Earlier work this paper cites.
E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Ann. Phys
1961
Earlier work this paper cites.
T. D. Schultz, D. C. Mattis, and E. H. Lieb, “Two-Dimensional Ising Model as a Soluble Problem of Many Fermions,” Rev. Mod. Phys
1964
Earlier work this paper cites.
T. Prosen, “Exact Time-Correlation Functions of Quantum Ising Chain in a Kicking Transversal Magnetic Field —Spectral Analysis of the Adjoint Propagator in Heisenberg Picture—,” Prog. Theor. Phys. Supp
2000
Earlier work this paper cites.
L. G. Valiant, “Quantum Circuits That Can Be Simulated Classically in Polynomial Time,” SIAM Journal on Computing
2002
Earlier work this paper cites.
B. M. Terhal and D. P. Divincenzo, “Classical simulation of noninteracting-fermion quantum circuits,” Phys. Rev. A
2002
Earlier work this paper cites.
A. Chapman and S. T. Flammia, “Characterization of solvable spin models via graph invariants,” Quantum
Original
2003
Earlier work this paper cites.
M. Ogura, Y. Imamura, N. Kameyama, K. Minami, and M. Sato, “Geometric criterion for solvability of lattice spin systems,” Phys. Rev. B
Original
2003
Earlier work this paper cites.
F. C. Alcaraz and R. A. Pimenta, “Free fermionic and parafermionic quantum spin chains with multispin interactions,” Phys. Rev. B
Original
2005
Earlier work this paper cites.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys
2006
Earlier work this paper cites.
P. Fendley and K. Schoutens, “Cooper pairs and exclusion statistics from coupled free-fermion chains,” J. Stat. Mech
2007
Earlier work this paper cites.

Similar

V. Eisler and I. Peschel, “Entanglement in a periodic quench,” Annalen der Physik
Original
2008
Cited alongside, same era.
R. Jozsa and A. Miyake, “Matchgates and classical simulation of quantum circuits,” Proc. Roy. Soc. Lond. A
Original
2008
Cited alongside, same era.
F. C. Alcaraz and R. A. Pimenta, “Integrable quantum spin chains with free fermionic and parafermionic spectrum,” Phys. Rev. B
Original
2010
Cited alongside, same era.
S. J. Elman, A. Chapman, and S. T. Flammia, “Free fermions behind the disguise,” Commun. Math. Phys
Original
2012
Cited alongside, same era.
P. Fendley, “Free parafermions,” J. Phys. A
Original

Then

A. Jahn and J. Eisert, “Holographic tensor network models and quantum error correction: a topical review,” Quantum Sci. Tech
Original
2021
Later among the works it cites.
T. Gombor and B. Pozsgay, “Integrable spin chains and cellular automata with medium-range interaction,” Phys. Rev. E
Original
2021
Later among the works it cites.
A. Chapman, S. T. Flammia, and A. J. Kollár, “Free-Fermion Subsystem Codes,” PRX Quantum
Original
2022
Later among the works it cites.
J. W. P. Wilkinson, T. Prosen, and J. P. Garrahan, “Exact solution of the “Rule 150” reversible cellular automaton,” Phys. Rev. E
Original
2022
Later among the works it cites.
F. C. Alcaraz, R. A. Pimenta, and J. Sirker, “Ising analogs of quantum spin chains with multispin interactions,” Phys. Rev. B

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2024

Quantum circuits with free fermions in disguise

Pozsgay, Balázs, Fukai, Kohei

Understand

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.

Built on

P. Fendley, “Free fermions in disguise,” J. Phys. A
Original
1901
Earlier work this paper cites.
P. Jordan and E. Wigner, “Über das Paulische Äquivalenzverbot,” Z. Physik
1928
Earlier work this paper cites.
E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Ann. Phys
1961
Earlier work this paper cites.
T. D. Schultz, D. C. Mattis, and E. H. Lieb, “Two-Dimensional Ising Model as a Soluble Problem of Many Fermions,” Rev. Mod. Phys
1964
Earlier work this paper cites.
T. Prosen, “Exact Time-Correlation Functions of Quantum Ising Chain in a Kicking Transversal Magnetic Field —Spectral Analysis of the Adjoint Propagator in Heisenberg Picture—,” Prog. Theor. Phys. Supp
2000
Earlier work this paper cites.
L. G. Valiant, “Quantum Circuits That Can Be Simulated Classically in Polynomial Time,” SIAM Journal on Computing
2002
Earlier work this paper cites.
B. M. Terhal and D. P. Divincenzo, “Classical simulation of noninteracting-fermion quantum circuits,” Phys. Rev. A
2002
Earlier work this paper cites.
A. Chapman and S. T. Flammia, “Characterization of solvable spin models via graph invariants,” Quantum
Original
2003
Earlier work this paper cites.
M. Ogura, Y. Imamura, N. Kameyama, K. Minami, and M. Sato, “Geometric criterion for solvability of lattice spin systems,” Phys. Rev. B
Original
2003
Earlier work this paper cites.
F. C. Alcaraz and R. A. Pimenta, “Free fermionic and parafermionic quantum spin chains with multispin interactions,” Phys. Rev. B
Original
2005
Earlier work this paper cites.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys
2006
Earlier work this paper cites.
P. Fendley and K. Schoutens, “Cooper pairs and exclusion statistics from coupled free-fermion chains,” J. Stat. Mech
2007
Earlier work this paper cites.