# Jordan-Wigner transformation and qubits with nontrivial exchange rule

@article{Vlasov2021JordanWignerTA, title={Jordan-Wigner transformation and qubits with nontrivial exchange rule}, author={Alexander Yu. Vlasov}, journal={ArXiv}, year={2021}, volume={abs/2103.04629} }

Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. Even in standard model with local fermionic modes formally only the ‘occupied’ state |1〉 is truly relevant for Fermi–Dirac statistics, but ‘vacuum’ state |0〉 is not. Introduction of exchange rule for such fermionic qubits indexed by some ‘positions’ may look questionable due to general super-selection principle. However, a consistent algebraic construction of such ‘super…

## References

SHOWING 1-10 OF 21 REFERENCES

Fermionic quantum computation

- 2000

We define a model of quantum computation with local fermionic modes (LFMs) — sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m…

Two-bit gates are universal for quantum computation.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1995

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The…

Quantum circuits and Spin(3n) groups

- Computer Science, MathematicsQuantum Inf. Comput.
- 2015

The matrix tensor product implementation of the Spin(3n) group together with relevant models by usual quantum circuits with $2n$ qubits are investigated in such a framework and a possibility of the classical simulation of such circuits in polynomial time is discussed.

Clifford algebras and universal sets of quantum gates

- Physics
- 2001

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for n-qubit systems. It is based on the well-known application of Lie…

Quantum-Mechanical Computers

- Physics
- 1995

E very two years for the past 50, computers have become twice as fast while their components have become half as big. Circuits now contain wires and transistors that measure only one hundredth of a…

Lie groups and Lie algebras

- Mathematics
- 2005

The first example of a Lie group is the general linear group GL(n,R) = {A ∈ Matn(R)| det(A) 6= 0} of invertible n × n matrices. It is an open subset of Matn(R), hence a submanifold, and the…

Simulating physics with computers

- Mathematics, Physics
- 1982

On the program it says this is a keynote speech--and I don't know what a keynote speech is. I do not intend in any way to suggest what should be in this meeting as a keynote of the subjects or…

Supersymmetry for Mathematicians: An Introduction

- Mathematics
- 2004

Introduction The concept of a supermanifold Super linear algebra Elementary theory of supermanifolds Clifford algebras, spin groups, and spin representations Fine structure of spin modules…

Über das Paulische Äquivalenzverbot

- Physics
- 1928

ZusammenfassungDie Arbeit enthält eine Fortsetzung der kürzlich von einem der Verfasser vorgelegten Note „Zur Quantenmechanik der Gasentartung“, deren Ergebnisse hier wesentlich erweitert werden. Es…

Clifford algebras and spinors

- Mathematics
- 2017

1. Quadratic spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Quaternion algebras . . . . . . . . . .…