Running AQC (Adiabatic Quantum Computation) on spin chain of size N=8 and N=2 for debugging. Printing probabilities of each sping configuration for N=8 in the middle of time evolution and for N=2 at the end of time evolution (for debugging).

aqc.py

import matplotlib
import matplotlib.pyplot as plt

import numpy as np

from qutip import *
from scipy import *

def operators(N) :
    si = qeye(2)
    sx = sigmax()
    sy = sigmay()
    sz = sigmaz()
    sx_list = []
    sy_list = []
    sz_list = []
    for n in range(N):
        op_list = []
        for m in range(N):
            op_list.append(si)
        op_list[n] = sx
        sx_list.append(tensor(op_list))
        op_list[n] = sy
        sy_list.append(tensor(op_list))
        op_list[n] = sz
        sz_list.append(tensor(op_list))
    psi_list = [basis(2,0) for n in range(N)]
    psi0 = tensor(psi_list)
    return sx_list, sy_list, sz_list, psi_list, psi0

def solve(H0, H1, N, M, psi0, taulist, taumax) :
    args = {'t_max': max(taulist)}
    h_t = [[H0, lambda t, args : (args['t_max']-t)/args['t_max']],
           [H1, lambda t, args : t/args['t_max']]]
    evals_mat = np.zeros((len(taulist),M))
    P_mat = np.zeros((len(taulist),M))
    idx = [0]
    def process_rho(tau, psi):
        # evaluate the Hamiltonian with gradually switched on interaction
        H = qobj_list_evaluate(h_t, tau, args)
        # find the M lowest eigenvalues of the system
        evals, ekets = H.eigenstates(eigvals=M)
        evals_mat[idx[0],:] = real(evals)
        # find the overlap between the eigenstates and psi
        for n, eket in enumerate(ekets):
            P_mat[idx[0],n] = abs((eket.dag().data * psi.data)[0,0])**2
        idx[0] += 1
    mesolve(h_t, psi0, taulist, [], process_rho, args)
    return evals_mat, P_mat

def plot(evals_mat, taulist, taumax, P_mat, N, M) :
    fig, axes = plt.subplots(2, 1, figsize=(12,10))
    #
    # plot the energy eigenvalues
    #
    # first draw thin lines outlining the energy spectrum
    for n in range(len(evals_mat[0,:])):
        ls,lw = ('b',1) if n == 0 else ('k', 0.25)
        axes[0].plot(taulist/max(taulist), evals_mat[:,n] / (2*pi), ls, lw=lw)
    # second, draw line that encode the occupation probability of each state in
    # its linewidth. thicker line => high occupation probability.
    for idx in range(len(taulist)-1):
        for n in range(len(P_mat[0,:])):
            lw = 0.5 + 4*P_mat[idx,n]
            if lw > 0.55:
               axes[0].plot(array([taulist[idx], taulist[idx+1]])/taumax,
                            array([evals_mat[idx,n], evals_mat[idx+1,n]])/(2*pi),
                            'r', linewidth=lw)
    axes[0].set_xlabel(r'$\tau$')
    axes[0].set_ylabel('Eigenenergies')
    axes[0].set_title("Energyspectrum (%d lowest values) of a chain of %d spins.\n " % (M,N)
                    + "The occupation probabilities are encoded in the red line widths.")
    #
    # plot the occupation probabilities for the few lowest eigenstates
    #
    for n in range(len(P_mat[0,:])):
        if n == 0:
            axes[1].plot(taulist/max(taulist), 0 + P_mat[:,n], 'r', linewidth=2)
        else:
            axes[1].plot(taulist/max(taulist), 0 + P_mat[:,n])
    axes[1].set_xlabel(r'$\tau$')
    axes[1].set_ylabel('Occupation probability')
    axes[1].set_title("Occupation probability of the %d lowest " % M +
                      "eigenstates for a chain of %d spins" % N)
    axes[1].legend(("Ground state",));
    plt.show()

def printProbabilities(taulist, P_mat, idx, N) :
    print 'propabilities of each spin configuration at t=%s\n' % str(idx)
    s = 0.
    for n in range(len(P_mat[0,:])):
        lw = P_mat[idx,n]
        s += lw
        print "{0:{fill}{n}b} - ".format(n, fill='0', n=N), lw
    print '\nsums up to %s' % str(s)

res2q.png

res2q.txt

propabilities of each spin configuration at t=99

00 -  0.9994490956271472
01 -  0.00027541278731277574
10 -  0.00027541278731277574
11 -  7.879822735150804e-08

sums up to 1.0000000000000002

res8q.png

res8q.txt

propabilities of each spin configuration at t=49

00000000 -  0.003906462465320872
00000001 -  1.1045557664927843e-19
00000010 -  1.4295080344534068e-08
00000011 -  4.6609294371895095e-08
00000100 -  1.5235258405150954e-11
00000101 -  4.656877716123509e-12
00000110 -  0.030708506395049507
00000111 -  0.0005412100498141933
00001000 -  1.342594983171164e-22
00001001 -  4.678192967812127e-30
00001010 -  1.2764704097068673e-22
00001011 -  5.510153279366488e-32
00001100 -  6.929612509977237e-26
00001101 -  1.1719517873133457e-09
00001110 -  4.0586899484759796e-15
00001111 -  2.913078729784403e-06
00010000 -  0.00047421700085367713
00010001 -  3.248182166940278e-23
00010010 -  2.6018597717822735e-15
00010011 -  6.383654903002076e-32
00010100 -  2.449060747697179e-22
00010101 -  1.5096682619922724e-23
00010110 -  0.008366309633835983
00010111 -  0.08546814413276474
00011000 -  3.2096649905275904e-30
00011001 -  3.7834574117600816e-24
00011010 -  7.377651044640432e-17
00011011 -  3.2722052173373266e-06
00011100 -  0.015057606677999292
00011101 -  4.21049607408217e-31
00011110 -  7.219862988427224e-16
00011111 -  1.993021637108723e-31
00100000 -  3.9235404907935154e-07
00100001 -  8.933449994355897e-13
00100010 -  2.4440438725386756e-22
00100011 -  3.3278782897094846e-14
00100100 -  1.5892618210972276e-15
00100101 -  9.750194830764778e-19
00100110 -  1.9170443825893702e-32
00100111 -  6.485484746004345e-32
00101000 -  3.723262759845694e-13
00101001 -  5.496255409656716e-32
00101010 -  1.2940417806083644e-32
00101011 -  1.937219392132533e-32
00101100 -  2.866224332530895e-31
00101101 -  1.0362150311674495e-15
00101110 -  3.071158475874862e-26
00101111 -  1.0798222762020825e-31
00110000 -  4.666015327937644e-28
00110001 -  7.584019775810523e-25
00110010 -  2.5554578776510706e-16
00110011 -  1.4005596842689667e-11
00110100 -  1.9691317127686566e-32
00110101 -  7.305620249179311e-10
00110110 -  0.0005418899514782906
00110111 -  5.359903352107817e-25
00111000 -  1.7812902645962147e-13
00111001 -  5.4181075516041506e-17
00111010 -  1.0796035322529038e-16
00111011 -  0.00047636900377845317
00111100 -  2.7084060216474284e-05
00111101 -  1.5786080338718004e-07
00111110 -  3.718562918272181e-17
00111111 -  2.8452132787873956e-05
01000000 -  0.001433776683087685
01000001 -  3.3083836164310145e-26
01000010 -  1.0305833631165545e-07
01000011 -  5.772406735486936e-18
01000100 -  0.0007783560638988486
01000101 -  1.212361335365758e-22
01000110 -  9.89895551771929e-09
01000111 -  2.644187286831022e-12
01001000 -  1.819477141712068e-13
01001001 -  1.1008560271861586e-11
01001010 -  0.034080677746419555
01001011 -  1.3160990064107862e-11
01001100 -  2.2144116821181034e-10
01001101 -  8.558314425635619e-26
01001110 -  2.080535663384786e-32
01001111 -  4.66555646350809e-10
01010000 -  0.022664784162521493
01010001 -  1.9367177344185657e-22
01010010 -  9.026458268142445e-13
01010011 -  2.2630717764470422e-11
01010100 -  1.7489851307466586e-32
01010101 -  0.008307905118284074
01010110 -  0.15040803516842272
01010111 -  1.6012031428701363e-14
01011000 -  1.6317215758905498e-31
01011001 -  8.665520657357805e-27
01011010 -  7.387476532347223e-33
01011011 -  8.127109332828114e-32
01011100 -  1.2067342886897408e-32
01011101 -  1.8722068816763566e-32
01011110 -  5.6860542540235356e-33
01011111 -  5.009994539023816e-32
01100000 -  4.537042312281863e-25
01100001 -  4.2363053162109e-33
01100010 -  4.491798313996533e-11
01100011 -  6.920788714416906e-24
01100100 -  4.751815909919558e-29
01100101 -  2.4498487046179763e-25
01100110 -  1.0658912575516172e-33
01100111 -  1.034143506124609e-32
01101000 -  2.5582566851083996e-31
01101001 -  1.1703713999451865e-21
01101010 -  2.0471573850526149e-22
01101011 -  9.240325992943837e-32
01101100 -  4.915254974999177e-12
01101101 -  6.05332874046635e-09
01101110 -  2.5847021728692966e-06
01101111 -  2.601887734273869e-19
01110000 -  2.3678683233786993e-06
01110001 -  1.3371818046913952e-27
01110010 -  0.005321933122407188
01110011 -  2.375752658270128e-13
01110100 -  1.3815273324513494e-08
01110101 -  1.538425433962114e-29
01110110 -  8.158463441377404e-23
01110111 -  1.5425238148306824e-28
01111000 -  6.813245990317991e-30
01111001 -  2.9587497351565745e-23
01111010 -  0.0006324253702772711
01111011 -  0.04661754405304573
01111100 -  0.0004284207359789199
01111101 -  5.1876449863126266e-27
01111110 -  0.0035707923678424476
01111111 -  2.0045507786810107e-09
10000000 -  4.393649307272989e-21
10000001 -  1.4805327838719697e-31
10000010 -  0.02859365636760421
10000011 -  1.219201560304031e-07
10000100 -  0.02882815206911526
10000101 -  3.85617368369541e-17
10000110 -  0.0006473157480817158
10000111 -  2.0543546672671867e-16
10001000 -  1.6423400648771556e-13
10001001 -  1.1408632107059559e-17
10001010 -  1.2969280562227035e-07
10001011 -  6.99246091353701e-05
10001100 -  0.07149696852475254
10001101 -  2.6034140872341597e-15
10001110 -  6.489163082610122e-18
10001111 -  2.3167472544352636e-16
10010000 -  1.9195330922305632e-24
10010001 -  2.391673628153468e-16
10010010 -  3.6189363586682664e-25
10010011 -  0.08650893443805473
10010100 -  9.406982880026019e-32
10010101 -  0.0007139910442780133
10010110 -  4.629791818645832e-29
10010111 -  3.0043863973452523e-13
10011000 -  2.8304211434061656e-06
10011001 -  8.510579099953362e-32
10011010 -  1.0017142758838365e-12
10011011 -  6.852774715011286e-32
10011100 -  9.605148734488975e-17
10011101 -  5.446770623970151e-34
10011110 -  1.5668900601087792e-24
10011111 -  8.603737027256028e-33
10100000 -  7.211187644554405e-33
10100001 -  8.468825540612154e-33
10100010 -  1.3383181859253068e-31
10100011 -  4.4323777739280584e-33
10100100 -  1.9513793078687333e-19
10100101 -  1.1942740485710242e-31
10100110 -  1.4954098403759763e-31
10100111 -  1.1600029383033344e-14
10101000 -  1.8458242256846013e-12
10101001 -  1.5848532055300442e-32
10101010 -  4.794750493822471e-24
10101011 -  3.9713195021767875e-34
10101100 -  1.3190244783056374e-12
10101101 -  7.794888268566871e-11
10101110 -  1.0016545557471463e-11
10101111 -  1.7695018108094462e-32
10110000 -  4.1269003254490172e-19
10110001 -  1.8943991617241293e-09
10110010 -  1.966196397096475e-09
10110011 -  1.5591757069306822e-34
10110100 -  2.1951262469103093e-09
10110101 -  1.2199668285969471e-32
10110110 -  0.022709102823521683
10110111 -  0.0017093278334326288
10111000 -  0.026442552353328232
10111001 -  0.0036905669301959534
10111010 -  1.5212906509441506e-19
10111011 -  1.5858605891774823e-12
10111100 -  0.0005002105974949734
10111101 -  7.671791548666362e-15
10111110 -  1.8871933324456426e-10
10111111 -  0.0004583118549683788
11000000 -  0.00044784549705660024
11000001 -  3.413337355283073e-14
11000010 -  6.266501085368213e-09
11000011 -  0.10943168046428982
11000100 -  4.4148328903799014e-07
11000101 -  0.0001221679520230828
11000110 -  6.85136900514097e-26
11000111 -  9.72453446531925e-07
11001000 -  8.408894371070423e-26
11001001 -  0.04317033908257296
11001010 -  0.0001228592504257116
11001011 -  5.90198980957429e-16
11001100 -  0.007124383926931651
11001101 -  6.39645666466671e-28
11001110 -  4.222948145784682e-26
11001111 -  2.487636227097162e-16
11010000 -  1.9585859705057416e-19
11010001 -  0.0027973347279851724
11010010 -  3.5393711725292775e-32
11010011 -  2.4316281731024935e-05
11010100 -  1.0666640686181611e-27
11010101 -  1.6581785923814883e-17
11010110 -  2.3786491777238042e-26
11010111 -  1.7589224778698656e-30
11011000 -  6.926622038530165e-17
11011001 -  9.641307644713357e-27
11011010 -  4.0531797532737e-32
11011011 -  2.873813324059804e-31
11011100 -  4.346177168193797e-15
11011101 -  1.9908898108432438e-20
11011110 -  1.7109106396050214e-18
11011111 -  7.4076315599512e-21
11100000 -  0.00495346920392532
11100001 -  1.4598431245078052e-09
11100010 -  9.40503759901495e-18
11100011 -  0.027763742961467046
11100100 -  7.319695394307264e-17
11100101 -  0.018637625652596163
11100110 -  4.9010798465479096e-14
11100111 -  2.916629236492447e-17
11101000 -  0.0001565246523697966
11101001 -  2.151591166185074e-06
11101010 -  3.7342699414438066e-07
11101011 -  0.016995495837825753
11101100 -  1.1487181915591664e-07
11101101 -  0.004778126877400488
11101110 -  0.001909558727537797
11101111 -  0.025446297207534607
11110000 -  0.008723941004699816
11110001 -  2.0331157781350488e-26
11110010 -  8.889970609699356e-06
11110011 -  2.330272726419925e-12
11110100 -  8.296564190338841e-32
11110101 -  4.973187459910869e-33
11110110 -  1.0789027996753311e-11
11110111 -  2.3651266024214562e-12
11111000 -  0.0003940709182304036
11111001 -  0.00012387355797407678
11111010 -  2.285524160791754e-06
11111011 -  0.0002834484368186283
11111100 -  2.6379109939493125e-11
11111101 -  0.03044651575201581
11111110 -  5.302360935102528e-15
11111111 -  0.003906252743384673

sums up to 1.000000000000011

run2q.py

import numpy as np

from aqc import operators, solve, printProbabilities, plot

N = 2   # number of spins
M = 4  # number of eigenenergies to plot

# increase taumax to get make the sweep more adiabatic
taumax = 5.0
taulist = np.linspace(0, taumax, 100)

sx, sy, sz, psi_list, psi0 = operators(N)
H0 = 0
for n in range(N):
    H0 += - 0.5 * 2.5 * sx[n]
H1 = 0
#interactions = [(0, 4), (0, 5), (1, 4), (1, 6), (2, 5), (2, 7), (3, 6), (3, 7)]
interactions = [(0, 1)]
for j1, j2 in interactions :
    H1 += -2. * sz[j2] * sz[j2]

evals_mat, P_mat = solve(H0, H1, N, M, psi0, taulist, taumax)
printProbabilities(taulist, P_mat, len(taulist)-1, N)
plot(evals_mat, taulist, taumax, P_mat, N, M)

run8q.py

import numpy as np

from aqc import operators, solve, printProbabilities, plot

N = 8   # number of spins
M = 256  # number of eigenenergies to plot

# increase taumax to get make the sweep more adiabatic
taumax = 5.0
taulist = np.linspace(0, taumax, 100)

sx, sy, sz, psi_list, psi0 = operators(N)
H0 = 0
for n in range(N):
    H0 += - 0.5 * 2.5 * sx[n]
H1 = 0
interactions = [(0, 4), (0, 5), (1, 4), (1, 6), (2, 5), (2, 7), (3, 6), (3, 7)]
for j1, j2 in interactions :
    H1 += -2. * sz[j2] * sz[j2]

evals_mat, P_mat = solve(H0, H1, N, M, psi0, taulist, taumax)
printProbabilities(taulist, P_mat, (len(taulist)/2)-1, N)
plot(evals_mat, taulist, taumax, P_mat, N, M)