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Community-contributed installable additions to the Wolfram Language
Fermionic Quantum Computation
Fermionic quantum computation is a model of quantum computation based on local fermionic modes. It was introduced by .
Q3 provides tools to efficiently simulate a subclass of fermionic quantum computation models called Wick circuits, where unitary gates are associated with quadratic Hamiltonian (describing non-interacting fermions) and interspersed complete von Neumann measurement in the computational basis (measurement outcome describing an empty or occupied fermionic mode), which is described in Terhal and DiVincenzo (2002) and Knill (2001).
Random Wick circuits may be one of prototype quantum circuits that exhibit the phenomenon of measurement-induced entanglement transition, a transition between two distinct phases with the entanglement entropy characterized by area- and volume-law scaling. See also Li, Chen, and Fisher (2018), Skinner, Ruhman, and Nahum (2019), Chan et. al. (2019), Sang et al. (2021), and Weinstein, Bao, and Altman (2022).
Elementary Tools
— Represents a fermionic Gaussian state
— Represents a Gaussian-type unitary operator
— Represents a Gaussian-type evolution operator governed by a non-Hermitian Hamiltonian
— Represents a measurement of the occupation number on fermion modes
— Represents a set of quantum jump operators that are linear combinations of Majorana operators
WickOperator
WickDensityMatrix
WickElements
WickCoefficients
Physical Properties
— Single-particle Green's functions with respect to a Wick or BdG state
— Von Neumann entropy in a fermionic Gaussian state
— Entanglement entropy in a Wick or BdG state
— Mutual information in a Wick or BdG state
— Logarithmic negativity in a Wick or BdG state
WickOccupation
Simulations
— Simulates random quantum circuits with fermionic gates and von Neumann measurements in the computational basis
— Simulates the quantum master equation for a non-interacting dissipative fermionic system
— Simulates the continuous monitoring of fermion modes
Numerical Solution of Quantum Master Equation
— Solves numerically fermionic quantum master equations with quantum jump operators that are linear in fermion creation operators or projection operators of dressed fermion modes.
Tools for Bogoliubov-de Gennes (BdG) Models
— Represents an arbitrary matrix in the Nambu space
— Represents a unitary matrix in the Nambu space
— Represents a Hermitian matrix in the Nambu space
— Represents the matrix of Green's function of fermion modes in the Nambu space
NambuOne
NambuZero
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