Note: This section is still in a draft form.
from qiskit import QuantumCircuit, execute, Aer
from math import pi
from tools import plot_height
import random
from qiskit.providers.aer.noise import NoiseModel
from qiskit.providers.aer.noise.errors import pauli_error
import scipy.linalg as la
import numpy as np
p
.def get_noise(p):
error_meas = pauli_error([('X',p), ('I', 1 - p)])
noise_model = NoiseModel()
noise_model.add_all_qubit_quantum_error(error_meas, "measure")
return noise_model
noise_model = get_noise(0.1)
circuits
, two additional circuits are run: one for which all outputs should be 0
, and one for which all should be 1
.circuits
, the probability that each qubit outputs a 1
is calculated (and cleaned up).p
for each circuit, for which the probability p[j]
refers to qubit j
.probs
contains these lists for each circuit, with probs[k]
containing the p
for the k
th circuit.raw_probs
contains the same lists of probabilities, but without the error mitigation. The results for the all 0
and all 1
circuits are also appended to this.def get_probs(circuits,backend=Aer.get_backend('qasm_simulator'),noise_model=None):
def get_raw_p(counts):
n = len(list(counts.keys())[0])
shots = sum(counts.values())
p = [0]*n
for bitstring in counts:
for j in range(n):
if bitstring[::-1][j]=='1':
p[j] += counts[bitstring]/shots
return p
n = circuits[0].n_qubits
qc0 = QuantumCircuit(n,n)
qc1 = QuantumCircuit(n,n)
for j in range(n):
qc0.measure(j,j)
qc1.x(j)
qc1.measure(j,j)
benchmarks = [qc0,qc1]
if noise_model:
result = execute(circuits+benchmarks,backend,noise_model=noise_model,shots=8192).result()
else:
result = execute(circuits+benchmarks,backend,shots=8192).result()
p0 = get_raw_p(result.get_counts(-2))
p1 = get_raw_p(result.get_counts(-1))
Minv = []
for j in range(n):
Minv.append( la.pinv( [[1-p0[j],1-p1[j]],[p0[j],p1[j]]] ) )
raw_probs = []
probs = []
raw_probs = []
for k in range(len(circuits)):
mitigated_p = []
raw_p = get_raw_p(result.get_counts(k))
for j in range(n):
p = np.dot( Minv[j], [1-raw_p[j],raw_p[j]] )[1]
p = min(max(p,0),1)
mitigated_p.append( p )
probs.append( mitigated_p )
raw_probs.append( raw_p )
raw_probs.append( get_raw_p(result.get_counts(-2)) )
raw_probs.append( get_raw_p(result.get_counts(-1)) )
return probs, raw_probs
0
s and all 1
s (get_probs
will still run its own versions of these).n = 4
qc0 = QuantumCircuit(n,n)
qc0.measure(qc0.qregs[0],qc0.cregs[0])
qc1 = QuantumCircuit(n,n)
qc1.x(qc1.qregs[0])
qc1.measure(qc1.qregs[0],qc1.cregs[0])
probs, raw_probs = get_probs([qc0,qc1],noise_model=noise_model)
/usr/local/lib/python3.7/site-packages/scipy/linalg/basic.py:1321: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver. x, resids, rank, s = lstsq(a, b, cond=cond, check_finite=False)
1
should be zero.print(raw_probs[0])
[0.1014404296875, 0.0947265625, 0.099609375, 0.099365234375]
print(probs[0])
[0.0009215174320381936, 0, 0, 0.006853487663722069]
1
with certainty.print(raw_probs[1])
[0.9005126953125, 0.90185546875, 0.9002685546875, 0.9005126953125]
print(probs[1])
[1, 1, 1, 1]
rochester = {
(2,1):5,(6,1):6,(2,5):28,(6,5):29,(2,7):51,(6,7):52,
(0,3):16,(4,3):17,(8,3):18,(0,7):39,(4,7):40,(8,7):41}
for j in range(0,5):
rochester[2+j,0] = j
for j in range(7,16):
rochester[j-7,2] = j
for j in range(19,28):
rochester[j-19,4] = j
for j in range(30,39):
rochester[j-30,6] = j
for j in range(42,51):
rochester[j-42,8] = j
1
on each qubit will be used as the height for a height map.height[x,y]=1
wherever there is a qubit, and has no entry otherwise (implying a height of zero).height = {}
for x in range(9):
for y in range(9):
if (x,y) in rochester:
height[x,y] = 1
plot_height(height,color_map='gray')
p
, from a device whose mapping between qubits and positions is specified by device
.def make_height(p,device):
L = max(max(device.keys()))+1
height = {}
for pos in device:
height[pos] = p[device[pos]]
all_full = False
while not all_full:
all_full = True
extra_height = {}
for x in range(L):
for y in range(L):
if (x,y) not in height:
total = 0
num = 0
for (dx,dy) in [(0,1),(0,-1),(1,0),(-1,0)]:
if (x+dx,y+dy) in height:
total += height[x+dx,y+dy]
num += 1
if num==0:
all_full = False
else:
extra_height[x,y] = total/(num)
for pos in extra_height:
height[pos] = extra_height[pos]
return height
def height2circuit_temp_1(height,device,limit=np.Inf):
n = min( len(device), limit )
qc = QuantumCircuit(n,n)
for pos in height:
if pos in device:
j = device[pos]
if j<limit:
qc.ry(2*np.arcsin(np.sqrt(height[pos])),j)
qc.measure(j,j)
return qc
height_initial = {}
L = 9
for x in range(L):
for y in range(L):
height_initial[x,y] = (1 + np.cos( np.sqrt( (x-(L-1)/2)**2 + (y-(L-1)/2)**2 )/(L/5) ) )/2
height_initial[x,y] = height_initial[x,y]*(1 + np.cos( ( abs(x+(L-1)/2) + abs(y-(L-1)/2) )/((L-1)/5) ) )/2
plot_height(height_initial)
limit
keyword is for in the above function.limit = 27
qc = height2circuit_temp_1(height_initial,rochester,limit=limit)
probs,raw_probs = get_probs([qc])
p = probs[0] + [0]*(53-limit)
height = make_height(p,rochester)
plot_height(height)
p=[0.10919456219850923, 0.16044568245125349, 0.09048625792811826, 0.11478420569329661, 0.01750400855157675, 0.17499999999999982, 0.11574979056129564, 0.007768721344880438, 0.08535402521823476, 0.3501374885426216, 0.5677950594693499, 0.7200184501845022, 0.5024050422955714, 0.3711212246586675, 0.10785066830542339, 0.01569726699369308, 0, 0.799728813559322, 0.07532605802502002, 0.03544720311097811, 0.0007676560900716691, 0.07124372050540444, 0.3079360506985453, 0.6212898497618173, 0.8309606258817493, 0.7347986312187418, 0.4237070807807376, 0.18767772511848335, 0.20848918523337134, 0.6287630189756027, 0.061037913417585465, 0.100013194352817, 0.34700485698866695, 0.6118154842190453, 0.7705248990578735, 0.6120502817511918, 0.3511696692659317, 0.1114186851211074, 0.022350530825107295, 0.010901728702694527, 0.43033920512447255, 0.005681818181818239, 0.0005247966413016135, 0.02600000000000008, 0.12480810561866737, 0.16719559044596638, 0.11907040328092963, 0.07396630934150084, 0.01814696485623008, 0.008415147265077194, 0, 0.31355697255336856, 0.11640714014432188]
height = make_height(p,rochester)
plot_height(height)
cz
gate on the device, just before measurement.def height2circuit_temp_2(height,device,limit=np.Inf):
red = [(0, 1), (2, 3), (4, 6), (13, 12), (11, 10), (9, 5), (21, 22), (23, 24), (25, 29), (36, 35), (34, 33), (32, 28), (44, 45), (46, 47), (48, 52), (7, 16), (30, 39), (18, 27), (41, 50)]
green = [(7, 8), (9, 10), (11, 17), (22, 23), (21, 20), (16, 19), (30, 31), (32, 33), (34, 40), (45, 46), (43, 44), (39, 42), (15, 14), (13, 6), (25, 26), (38, 37), (36, 29), (48, 49), (2, 1)]
blue = [(0, 5), (9, 8), (19, 20), (21, 28), (32, 31), (42, 43), (44, 51), (11, 12), (13, 14), (15, 18), (27, 26), (25, 24), (23, 17), (34, 35), (36, 37), (38, 41), (50, 49), (48, 47), (46, 40), (4, 3)]
n = min( len(device), limit )
qc = QuantumCircuit(n,n)
for pos in height:
if pos in device:
j = device[pos]
if j<limit:
qc.ry(2*np.arcsin(np.sqrt(height[pos])),j)
for pairs in [red,green,blue]:
for pair in pairs:
if pair[0]<limit and pair[1]<limit:
qc.cz(pair[0],pair[1])
for pos in height:
if pos in device:
j = device[pos]
if j<limit:
qc.measure(j,j)
return qc
qc = height2circuit_temp_2(height_initial,rochester,limit=limit)
probs,raw_probs = get_probs([qc])
p = probs[0] + [0]*(53-limit)
height = make_height(p,rochester)
plot_height(height)
p = [0.009271721250186687, 0.12571347031963487, 0, 0.11378687537627952, 0.11220366379310348, 0.16896345116836464, 0.19807037457434734, 0.1080806799441838, 0.0542184607246759, 0.4533512464546947, 0.6510054501033639, 0.6864168271367205, 0.49212417800886976, 0.41575859178541497, 0.12443894134034998, 0.039715719063544874, 0.31570404436629257, 0.7955108785458552, 0.09762639131017838, 0.026998961578400885, 0.0476251114223862, 0.12394067796610185, 0.21739753511034693, 0.5995431382885258, 0.7080310551100926, 0.6775725593667545, 0.33528404224950037, 0.08964501881236696, 0.26531620553359686, 0.5159870250231695, 0.13996763754045305, 0.0779101741521539, 0.3371308016877635, 0.5970209884901827, 0.7207501019160213, 0.4394103620203772, 0.39190687361419063, 0.1193887297039159, 0.06800556770729752, 0.10569610429923938, 0.3264977296030467, 0.028944911297852392, 0.04038814581694213, 0.052019278710320804, 0.13344441078461078, 0.3722366710013004, 0.11908528692650666, 0.11099187490418526, 0.06481123566550703, 0.05513666352497655, 0.03586081142683477, 0.2545377796538624, 0.27651361235270205]
height = make_height(p,rochester)
plot_height(height)
height2circuit
will have some random single qubit rotations after the cz
gates.def height2circuit(height,device,limit=np.Inf,theta=np.pi/2):
red = [(0, 1), (2, 3), (4, 6), (13, 12), (11, 10), (9, 5), (21, 22), (23, 24), (25, 29), (36, 35), (34, 33), (32, 28), (44, 45), (46, 47), (48, 52), (7, 16), (30, 39), (18, 27), (41, 50)]
green = [(7, 8), (9, 10), (11, 17), (22, 23), (21, 20), (16, 19), (30, 31), (32, 33), (34, 40), (45, 46), (43, 44), (39, 42), (15, 14), (13, 6), (25, 26), (38, 37), (36, 29), (48, 49), (2, 1)]
blue = [(0, 5), (9, 8), (19, 20), (21, 28), (32, 31), (42, 43), (44, 51), (11, 12), (13, 14), (15, 18), (27, 26), (25, 24), (23, 17), (34, 35), (36, 37), (38, 41), (50, 49), (48, 47), (46, 40), (4, 3)]
n = min( len(device), limit )
qc = QuantumCircuit(n,n)
for pos in height:
if pos in device:
j = device[pos]
if j<limit:
qc.ry(2*np.arcsin(np.sqrt(height[pos])),j)
for pairs in [red,green,blue]:
for pair in pairs:
if pair[0]<limit and pair[1]<limit:
qc.cz(pair[0],pair[1])
for pos in height:
if pos in device:
j = device[pos]
if j<limit:
rand_theta = theta*2*(random.random()-0.5)
if random.random()<0.5:
qc.rx(rand_theta,j)
else:
qc.ry(rand_theta,j)
qc.measure(j,j)
return qc
height2circuit
.for j in range(3):
qc = height2circuit(height_initial,rochester,limit=limit)
probs,raw_probs = get_probs([qc])
p = probs[0] + [0]*(53-limit)
height = make_height(p,rochester)
plot_height(height)
probs = [[0, 0.19980438731311997, 0.1119966442953022, 0.21462029808374739, 0.21212121212121224, 0.24343083787803665, 0.2839741708247726, 0.25150698986789777, 0.20750605326876514, 0.4778840406455469, 0.6301094890510947, 0.5461853259280911, 0.5143323926927077, 0.5697781885397412, 0.5143587430461585, 0.10184799221898017, 0.5930624915643137, 0.7625086147484492, 0.1973737103041672, 0.045274725274725036, 0.1667731629392972, 0.3367891446866902, 0.33649683649683637, 0.640562597673207, 0.5971293199554069, 0.5477222003413416, 0.369032258064516, 0.16890783863561826, 0.3180645161290323, 0.5593991807009557, 0.6222222222222223, 0.40617608409986855, 0.39308893176635673, 0.5183673469387756, 0.7164975974372665, 0.5398078975453575, 0.4958256686005375, 0.27778591301801153, 0.4005019720329868, 0.3007471980074722, 0.46801444043321316, 0.2579929531515073, 0.20536663124335813, 0.0476190476190477, 0.24824026278742387, 0.42695278969957084, 0.3217508417508419, 0.13518770667185356, 0.07979341510652026, 0.28387703889585947, 0.09453940402359687, 0.7278629644978588, 0.20491273432449914], [0, 0.277350845326254, 0.04865771812080566, 0.20880056777856643, 0.4573863636363638, 0.18393653941497268, 0.30217199882594664, 0.14479928177504156, 0.06464891041162235, 0.5650029886431559, 0.5669708029197078, 0.6052323881905874, 0.5893361057478095, 0.5055452865064696, 0.3486693730266125, 0.16729192719188551, 0.23053043595626926, 0.677050310130944, 0.1362722765643843, 0.2128937728937726, 0.4724600638977636, 0.3322152767190122, 0.23643023643023633, 0.6318805348150719, 0.6815774804905239, 0.7081528160693185, 0.5767741935483869, 0.16693998032141688, 0.255, 0.5336822940373235, 0.2423025435073629, 0.12391590013140605, 0.3425714786879494, 0.5925170068027211, 0.7261078483715964, 0.49754535752401285, 0.4598839677373707, 0.2057402255088594, 0.4523126568662604, 0.19863013698630153, 0.47754512635379076, 0.23789638522771764, 0.22143995749202977, 0.2716894977168951, 0.16048803378695464, 0.23931330472103013, 0.32026936026936037, 0.22641509433962248, 0.31530019367333756, 0.18506900878293603, 0.06489184692179682, 0.511120320486255, 0.48243912949795315], [0.8556851311953357, 0.2410227749056867, 0.4072986577181211, 0.2824698367636622, 0.21076839826839838, 0.28507684680218126, 0.31127091282653363, 0.1923816852635628, 0.499273607748184, 0.4620442319187089, 0.6264598540145982, 0.5575855013154047, 0.5737412743205111, 0.45425138632162665, 0.10434521124642905, 0.3362512157843545, 0.20394115265217966, 0.7546519641626463, 0.15771137612220285, 0.5369963369963366, 0.15527156549520774, 0.33145296539106583, 0.3876123876123875, 0.578225386351797, 0.6896599777034559, 0.6979125640015753, 0.4755555555555554, 0.14758937356510332, 0.2880645161290323, 0.5625853436504323, 0.24497991967871496, 0.4102496714848883, 0.33695842834590417, 0.5961904761904762, 0.7147624132407902, 0.4529348986125934, 0.4808263761143341, 0.20676526577829854, 0.21871638580136255, 0.06870070568700726, 0.3757400722021662, 0.23711340206185566, 0.42893198724760895, 0.07893020221787356, 0.12185202565305818, 0.3378540772532189, 0.1991919191919193, 0.3244504960124488, 0.2871530019367333, 0.11841279799247183, 0.3128119800332777, 0.1418704240917254, 0.32105149752208584], [4.440892098500626e-16, 0.3636998742489869, 0.351090604026846, 0.1792760823278922, 0.493641774891775, 0.18691125433812583, 0.4223657176401526, 0.4110555341798126, 0.14140435835351095, 0.47803347280334724, 0.6403284671532845, 0.5704472376498099, 0.5025991385712165, 0.34334565619223656, 0.5296947827394377, 0.11532583020703074, 0.24686192468619236, 0.657339765678842, 0.43507972665148054, 0.1047619047619045, 0.3375079872204473, 0.15230980332367752, 0.27322677322677313, 0.6256294495572147, 0.5816610925306578, 0.678613627412367, 0.5161290322580644, 0.2622171203673336, 0.5885483870967743, 0.49135184342284927, 0.18045515394912987, 0.09093298291721422, 0.38765128924750036, 0.5053061224489797, 0.6599038974906567, 0.5705442902881537, 0.45875194566294025, 0.16327427148923718, 0.0855145213338114, 0.17766708177667098, 0.6551624548736464, 0.2397233459480621, 0.5162061636556855, 0.4359099804305285, 0.45096198967620843, 0.15982832618025758, 0.39326599326599343, 0.12799066329507863, 0.05526145900581012, 0.38299874529485567, 0.12600211768264996, 0.2467191601049869, 0.24218918336565404], [0.6064139941690962, 0.27134274137208325, 0.6346476510067116, 0.24215755855216473, 0.18709415584415598, 0.23847297967278136, 0.2917522747285002, 0.384891624983968, 0.4440677966101695, 0.46383741781231325, 0.5952554744525544, 0.6835720549546914, 0.4871528293479877, 0.5743992606284658, 0.10374379792512398, 0.05738502153675148, 0.14900796328789295, 0.7258442453480357, 0.4163205145383893, 0.23882783882783853, 0.07884984025559111, 0.11007775575545067, 0.23576423576423566, 0.564855009550269, 0.6846432552954291, 0.6218983851910199, 0.36702508960573466, 0.42046572646769437, 0.3340322580645162, 0.5671370050068274, 0.3887550200803214, 0.1258869908015769, 0.388528328363445, 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for _ in range(3):
j = random.randint(0,69)
height = make_height(probs[j],rochester)
plot_height(height)
blobs = []
for p in probs:
blobs.append(make_height(probs[j],rochester))
from island import island
plot_height(island)
quantum_island
below is made using the second method from the last section, in which the texture is positioned randomly.size = max(max(island))+1
quantum_island = {}
for xx in range(size):
for yy in range(size):
quantum_island[xx,yy] = 0
for _ in range(int(20*size**2/L**2)):
chosen = False
while not chosen:
x0 = random.randint(0,size-1)
y0 = random.randint(0,size-1)
chosen = (random.random()<island[x0,y0])
blob = random.choice(blobs)
for (x,y) in blob:
xx = x-int(L/2)+x0
yy = y-int(L/2)+y0
if (xx,yy) in quantum_island:
quantum_island[xx,yy] += blob[x,y]
else:
quantum_island[xx,yy] = blob[x,y]
max_height = max(quantum_island.values())
for (xx,yy) in quantum_island:
quantum_island[xx,yy] = quantum_island[xx,yy]/max_height
plot_height(quantum_island)
with open('quantum_island.py', 'w') as file:
file.write('quantum_island='+str(quantum_island))