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Q3mini

Guides

  • Fermionic Quantum Computation
  • Q3: Symbolic Quantum Simulation
  • Quantum Information Systems
  • Quantum Many-Body Systems
  • Quantum Spin Systems

Tech Notes

  • About Q3
  • Q3: Quick Start
  • Quantum Fourier Transform
  • Quantum Information Systems with Q3
  • Quantum Many-Body Systems with Q3
  • Quantum Operations
  • Quantum Spin Systems with Q3
  • Quantum States
  • Quantum Teleportation
  • Quick Quantum Computing with Q3

Symbols

  • Basis
  • Boson
  • Bra
  • CNOT
  • ControlledGate
  • ExpressionFor
  • Fermion
  • Heisenberg
  • Ket
  • Let
  • Majorana
  • Matrix
  • Multiply
  • NambuGreen
  • NambuHermitian
  • NambuMatrix
  • NambuUnitary
  • Pauli
  • Phase
  • QuantumCircuit
  • Qubit
  • Qudit
  • RandomWickCircuitSimulate
  • Rotation
  • Species
  • Spin
  • SWAP
  • WickCircuit
  • WickEntanglementEntropy
  • WickEntropy
  • WickGreenFunction
  • WickJump
  • WickLindbladSolve
  • WickLogarithmicNegativity
  • WickMeasurement
  • WickMonitor
  • WickMutualInformation
  • WickNonunitary
  • WickSimulate
  • WickState
  • WickUnitary

Overviews

  • The Postulates of Quantum Mechanics
  • Quantum Algorithms
  • Quantum Computation: Models
  • Quantum Computation: Overview
  • Quantum Error-Correction Codes
  • Quantum Information Theory
  • Quantum Noise and Decoherence
QuantumMob`Q3mini`
WickNonunitary
​
WickNonunitary
[{ham,dmp,gmm}]
describes a non-unitary evolution of
2n
Majorana fermion modes (equivalently,
n
Dirac fermion modes) governed by the non-Hermitian Hamiltonian consisting of the coherent and damping parts specified by
2n×2n
real anti-symmetric matrices
ham
and
dmp
, respectively, plus additional constant damping
gmm
.
​
Details and Options

Examples  
(8)
Basic Examples  
(1)
Set the number of fermion modes to consider.
In[1]:=
$n=4;
Construct a non-unitary time-evolution operator.
In[2]:=
SeedRandom[354];
In[3]:=
ham=Re@RandomAntisymmetric[2$n];​​dmp=Re@RandomAntisymmetric[2$n];​​op=WickNonunitary[{ham,dmp,0}]
Out[3]=
WickNonunitary
Modes: 4
Constant: 0

Set an initial state in the
WickState
form.
In[4]:=
in=WickState[{1,0},$n]
Out[4]=
WickState
Modes: 4
Prefactor: 1

Operate the non-unitary evolution operator.
In[5]:=
out=op**in
Out[5]=
WickState
Modes: 4
Prefactor: 18.4

In[6]:=
cvr=WickCovariance[out];​​cvr//ArrayShort
Out[6]//MatrixForm=
0
-0.192222
-0.52246
-0.354647
…
0.192222
0
0.122955
-0.317998
…
0.52246
-0.122955
0
0.430943
…
0.354647
0.317998
-0.430943
0
…
…
…
…
…
…
Scope  
(4)

Possible Issues  
(3)

SeeAlso
WickState
 
▪
WickUnitary
 
▪
WickSimulate
TechNotes
▪
Quantum Many-Body Systems with Q3
▪
Quantum Information Systems with Q3
▪
Q3: Quick Start
RelatedGuides
▪
Fermionic Quantum Computation
▪
Quantum Many-Body Systems
▪
Quantum Information Systems
▪
Q3: Symbolic Quantum Simulation
RelatedLinks
▪
S. Bravyi and R. König (2012)
, Quantum Information & Computation 12, 925 (2012), "Classical simulation of dissipative fermionic linear optics."
▪
S. Bravyi (2005)
, Quantum Information & Computation 5, 216 (2005), "Lagrangian representation for fermionic linear optics."
▪
S. Bravyi and A. Y. Kitaev (2002)
, Annals of Physics 298, 210 (2002),"Fermionic Quantum Computation."
▪
B. M. Terhal and D. P. DiVincenzo (2002)
, Physical Review A 65, 032325, "Classical simulation of
noninteracting
-fermion quantum circuits."
▪
Mahn-Soo Choi (2022)
, A Quantum Computation Workbook (Springer).
""

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