QUBIT4MATLAB V4.0: c=comm(A,B) - File Exchange

E0=ising_classical_ground(B) ising_classical_ground Ground state energy of the classical Ising model

E0=ising_ground(BField,vararg... ising_ground Ground state energy of the quantum Ising model

E0=ising_thermal(BField,T,var... ising_thermal - Internal energy of the Ising model in thermal equilibrium

E0=xy_classical_ground(Jx,Jy,... xy_classical_ground Ground state energy of the classical xy model

F=ising_free(BField,T) ising_free - Free energy of the Ising model in thermal equilibrium

H=heisenberg(varargin) heisenbergp Hamiltonian for the Heisenberg model with periodic BEC

H=heisenberg(varargin) heisenberg Hamiltonian for the Heisenberg model with non-periodic BEC

H=ising(BField,varargin) ising Hamiltonian for the Ising model with non-periodic boundary

H=isingp(BField,varargin) isingp Hamiltonian for the Ising model with periodic BEC

H=spising(BField,varargin) spising Hamiltonian for the Ising model with non-periodic BEC; sparse

H=spising2D(BField,Nx,Ny) spising2D Hamiltonian for the 2D Ising model with aperiodic boundary condition; sparse

H=spisingp(BField,varargin) spisingp Hamiltonian for the Ising model with periodic boundary condition; sparse

Hzz=splattice(op1,op2,Nx,Ny) splattice Lattice Hamiltonian for a 2D spin model with nn interaction with aperiodic

Hzz=splatticep(op1,op2,Nx,Ny) splatticep Lattice Hamiltonian for a 2D spin model with nn interaction with periodic

P=proj_asym(N,varargin) proj_asym Gives the projector to the antisymmetric subspace

P=proj_sym(N,varargin) proj_sym Gives the projector to the symmetric subspace

U=U_CNOT U_CNOT 4x4 unitary matrix realizing a CNOT gate

U=U_H U_H 2x2 unitary matrix realizing a Hadamard gate

U=runitary(varargin); runitary Random unitary

[Jx,Jy,Jz]=su2(d); su2 SU(2) generators for dxd matrices

[difference,U0]=twirl2(rho,va...

[fmin,f123]=optspinsq(rho) optspinsq(rho) Optimal spin squeezing inequalities

[g,stab]=gstate(Gamma)

[m,fa0]=maxsymsep(op,varargin) maxsymsep Maximum for symmetric multi-qubit product states.

[r,difference]=twirl(rho,vara... twirl Twirling

[witness,alpha2,coeff2]=optwi... optwitness Optimal entanglement witness for detecting genuine

b=braket(phi1,varargin) braket Dirac's bra-ket

c=binom(a,b)

c=ccnr(rho) ccnr Computable cross norm - realignment criterion

c=coll(op,varargin) coll Defines a collective operator which is the sum of single-qudit operators.

c=comm(A,B) comm Commutator of two matrices.

c=concurrence(rho); concurrence Compute the concurrence of a two-qubit density matrix.

c=cstate(varargin) cstate Defines a cluster state.

c=rstate(varargin) rcstate Defines a ring cluster state.

c=spcoll(op,varargin) spcoll Defines a collective operator which is the sum of single-qudit

coeff=schmidt(state,list) schmidt Schmidt coefficients of a pure state.

e=ex(op,rho) ex Expectation value of an operator

g=ghzstate(varargin) ghzstate Defines a GHZ state.

gs=grstate(H) grstate Normalized ground state of a Hamiltonian

h=nnchain(a,b,varargin) nnchain Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor

h=nnchainp(a,b,varargin) nnchainp Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor

h=spnnchain(a,b,varargin) spnnchain Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor

h=spnnchainp(a,b,varargin) spnnchainp Defines a Hamiltonian with a(k)b(k+1) nearest-neighbor

k=ketbra(f); ketbra Creating a density matrix from an unnormalized state vector.

k=ketbra2(f); ketbra2 Creating a density matrix from an unnormalized state vector.

m=maxbisep(op1,list,varargin) maxbisep Maximum for biseparable multi-qubit states.

m=maxeig(M); maxeig Maximum eigenvalue of a matrix

m=maxppt(op,list,varargin) maxppt Maximum for multi-qudit states with a positive partial transpose.

m=maxsep(op,varargin) maxsep Maximum for multi-qudit separable states.

m=mineig(M); mineig Minimum eigenvalue of a matrix

m=pkron(matrix,no_of_repeatat...

matrix=reordermat(pattern,var... reordermat Transformation matrix for reordering the qudits according to

matrix=reordermatsp(pattern,v... spreordermat Transformation matrix for reordering the qudits according to

maxoverlap=overlapb(state) overlapb Maximal overlap with biseparable states

mb=maxb(op1,varargin) maxb(op) gives maximum value for

mkron(A,B,varargin) mkron Kronecker (tensor) product of several matrices.

mm=reorder(m,pattern,varargin) reorder Reorder a state vector or a density matrix according to

mm=shiftquditsleft(m,varargin) shiftquditsleft Shift the qudits to the left

mm=shiftquditsright(m,varargi... shiftquditsright Shift the qudits to the right

mm=swapqudits(m,k,l,varargin) swapqudits Swap two qudits of a qudit register

mop=quditop(op,k1,varargin) quditop Operator acting on a qudit of a qudit register

mop=sptwoquditop(op,k1,k2,var... spquditop Operator acting on a given qudit; sparse version

mop=sptwoquditop(op,k1,k2,var... sptwoquditop Operator on given qudits; sparse version

mop=twoquditop(op,k1,k2,varar... twoquditop(op,k1,k2,n) defines an n-qudit quantum operator

neg=negativity(rho,list,varar... negativity Negativity for a qudit register.

obs=orthogobs(d) orthogobs Orthogonal observables for a qudit

op=interact(op1,op2,n1,n2,var... interact Interaction between two qudits

op=paulistr(pstring) paulistr Converts a Pauli string into an operator.

op=spinteract(op1,op2,n1,n2,v... spinteract Interaction between two qudits; sparse version

p=rproduct(varargin) rproduct Random product state vector for a given number of qubits.

pstring=decompose(rho,varargi... decompose Creates a string with the Pauli decomposition of a

q=qsize(matrix,varargin)

r=keep(rho_in,listneg,varargi... keep Reduced density matrix keeping the given qubits.

r=keep_nonorm(rho_in,listneg,... keep_nonorm Reduced density matrix keeping the given qubits.

r=rdmat(varargin) rdmat Random density matrix

r=remove(rho_in,list,varargin) remove Reduced density matrix

rho=BES_Breuer(lambda,d) BES_Breuer Breuer?s two-qudit bound entangled state

rho=BES_Horodecki2x4(b) BES_Horodecki2x4 Horodecki's 2x4 bound entangled state

rho=BES_Horodecki3x3(a) BES_Horodecki3x3 Horodecki's 3x3 bound entangled state

rho=BES_UPB3x3 BES_UPB3x3 3x3 bound entangled state constructed with UPBs

rho=thstate(H,kT) thstate Thermal state of a system with a given Hamiltonian

rhoR=mrealign(rho,list,vararg... mrealign Generalized realignment of a multipartite operator

rhoR=realign(rho) realign Realignment of the bipartite density matrix.

rhoT=pt(rho,list,varargin) pt partial transposition of a density matrix

rhoT=pt_nonorm(rho,list,varar... pt_nonorm partial transposition of a density matrix

rho_noisy=addnoise(rho,p) addnoise Adds white noise to a density matrix.

s=mestate(d) mestate Maximally entangled state

s=mmstate(varargin) mmstate Density matrix for the maximally mixed state

s=printv(v,varargin); printv Prints a state vector in product basis.

s=qeye(varargin) qeye Identity matrix for a given number of qudits.

s=qvec(varargin) qvec Empty state vector for a given number of qudits.

s=rvec(varargin) rvec Random state vector for a given number of qudits.

s=singlet(varargin) singlet Defines a singlet state.

s=smolinstate smolinstate Gives the four-qubit bound entangled state

stab=gstate_stabilizer(Gamma) gstate_stabilizer Gets the generators for the stabilizer of a graph state.

t=trace2(rho)

t=trnorm(A) trnorm Tracenorm of a matrix

v=va(op,rho) va Variance of an operator

vec=reordermat(pattern,vararg... reordervec Transformation vector for reordering the qudits according to

w=bra(v) bra After element-wise conjugation, transforms a vector into a normalized row vector.

w=dstate(e,varargin) dstate Defines a symmetric Dicke state.

w=ket(v) ket Transforms a vector into normalized column vector.

w=nm(v) nm Normalization

w=wstate(varargin)

contents.m

example1.m

example2.m

example3.m

example_maxppt.m

example_optwitness.m

paulixyz.m

su3.m

su3_alternative.m

ver.m

Highlights from QUBIT4MATLAB V4.0

Highlights from
QUBIT4MATLAB V4.0