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qpulba_121.py
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qpulba_121.py
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import numpy as np
import random
from qiskit import QuantumCircuit, Aer, execute
from math import log2, ceil, pi
from numpy import savetxt, save, savez_compressed
#=====================================================================================================================
simulator = Aer.get_backend('statevector_simulator')
def disp_isv(circ, msg="", all=True, precision=1e-8):
sim_res = execute(circ, simulator).result()
statevector = sim_res.get_statevector(circ)
qb = int(log2(len(statevector)))
print("\n============ State Vector ============", msg)
s = 0
for i in statevector:
if (all == True): print(' ({:+.5f}) |{:0{}b}>'.format(i,s,qb))
else:
if (abs(i) > precision): print(' ({:+.5f}) |{:0{}b}>'.format(i,s,qb))
s = s+1
print("============..............============")
return
# 24 qubits with Hadamard on 12 qubits log size: 880 MB csv, 816 MB txt, 256 MB npy, 255 KB npz
def save_isv(statevector, mode=1):
if (mode == 1): savez_compressed('output.npz', statevector)
elif (mode == 2): save('output.npy', statevector)
elif (mode == 3):
qb = int(log2(len(statevector)))
f = open("output.txt", "w")
f.write("============ State Vector ============\n")
s = 0
for i in statevector:
f.write(' ({:+.5f}) |{:0{}b}>'.format(i,s,qb)+'\n')
s = s+1
f.write("============..............============")
f.close()
elif (mode == 4): savetxt('output.csv', statevector, delimiter=',')
else: print('Invalid mode selected')
return
#=====================================================================================================================
def nCX(k,c,t,b):
nc = len(c)
if nc == 1:
k.cx(c[0], t[0])
elif nc == 2:
k.toffoli(c[0], c[1], t[0])
else:
nch = ceil(nc/2)
c1 = c[:nch]
c2 = c[nch:]
c2.append(b[0])
nCX(k,c1,b,[nch+1])
nCX(k,c2,t,[nch-1])
nCX(k,c1,b,[nch+1])
nCX(k,c2,t,[nch-1])
return
#=====================================================================================================================
def U_init(qcirc, circ_width, fsm):
for i in fsm:
qcirc.h(i)
qcirc.barrier()
return
def U_read(qcirc, read, head, tape, ancilla):
# Reset read (prepz measures superposed states... need to uncompute)
for cell in range(0, len(tape)):
enc = format(cell, '#0'+str(len(head)+2)+'b') # 2 for '0b' prefix
for i in range(2, len(enc)):
if(enc[i] == '0'):
qcirc.x(head[(len(head)-1)-(i-2)])
qcirc.barrier(read, head)
nCX(qcirc, head+[tape[cell]], read, [ancilla[0]])
qcirc.barrier(read, head)
for i in range(2, len(enc)):
if(enc[i] == '0'):
qcirc.x(head[(len(head)-1)-(i-2)])
qcirc.barrier(read, head, tape, ancilla)
qcirc.barrier()
return
def U_fsm(qcirc, tick, fsm, state, read, write, move, ancilla):
# Description Number Encoding: {M/W}{R}
# [ M1 W1 M0 W0 ] LSQ = W0 = fsm[0]
qcirc.x(read[0]) # If read == 0
nCX(qcirc, [fsm[0],read[0]], write, [ancilla[0]]) # Update write
nCX(qcirc, [fsm[1],read[0]], move, [ancilla[0]]) # Update move
qcirc.x(read[0]) # If read == 1
nCX(qcirc, [fsm[2],read[0]], write, [ancilla[0]]) # Update write
nCX(qcirc, [fsm[3],read[0]], move, [ancilla[0]]) # Update move
qcirc.barrier()
return
def U_write(qcirc, write, head, tape, ancilla):
# Reset write (prepz measures superposed states... need to uncompute)
for cell in range(0, len(tape)):
enc = format(cell, '#0'+str(len(head)+2)+'b') # 2 for '0b' prefix
for i in range(2, len(enc)):
if(enc[i] == '0'):
qcirc.x(head[(len(head)-1)-(i-2)])
qcirc.barrier(write, head)
nCX(qcirc, head+write, [tape[cell]], [ancilla[0]])
qcirc.barrier(write, head)
for i in range(2, len(enc)):
if(enc[i] == '0'):
qcirc.x(head[(len(head)-1)-(i-2)])
qcirc.barrier(write, head, tape, ancilla)
qcirc.barrier()
return
def U_move(qcirc, move, head, ancilla):
# Increment/Decrement using Adder
reg_a = move
reg_a.extend([-1]*(len(head)-len(move)))
reg_b = head
reg_c = [-1] # No initial carry
reg_c.extend(ancilla)
reg_c.append(-1) # Ignore Head position under/overflow. Trim bits. Last carry not accounted, All-ones overflows to All-zeros
def q_carry(qcirc, q0, q1, q2, q3):
if (q1 != -1 and q2 != -1 and q3 != -1): qcirc.toffoli(q1, q2, q3)
if (q1 != -1 and q2 != -1): qcirc.cx(q1, q2)
if (q0 != -1 and q2 != -1 and q3 != -1): qcirc.toffoli(q0, q2, q3)
def q_mid(qcirc, q0, q1):
if (q0 != -1 and q1 != -1): qcirc.cx(q0, q1)
def q_sum(qcirc, q0, q1, q2):
if (q0 != -1 and q2 != -1): qcirc.cx(q0, q2)
if (q1 != -1 and q2 != -1): qcirc.cx(q1, q2)
def q_rcarry(qcirc, q0, q1, q2, q3):
if (q0 != -1 and q2 != -1 and q3 != -1): qcirc.toffoli(q0, q2, q3)
if (q1 != -1 and q2 != -1): qcirc.cx(q1, q2)
if (q1 != -1 and q2 != -1 and q3 != -1): qcirc.toffoli(q1, q2, q3)
# Quantum Adder
for i in range(0,len(head)):
q_carry(qcirc,reg_c[i],reg_a[i],reg_b[i],reg_c[i+1])
q_mid(qcirc,reg_a[i],reg_b[i])
q_sum(qcirc,reg_c[i],reg_a[i],reg_b[i])
for i in range(len(head)-2,-1,-1):
q_rcarry(qcirc,reg_c[i],reg_a[i],reg_b[i],reg_c[i+1])
q_sum(qcirc,reg_c[i],reg_a[i],reg_b[i])
qcirc.x(reg_a[0])
# Quantum Subtractor
for i in range(0,len(head)-1):
q_sum(qcirc,reg_c[i],reg_a[i],reg_b[i])
q_carry(qcirc,reg_c[i],reg_a[i],reg_b[i],reg_c[i+1])
q_sum(qcirc,reg_c[i+1],reg_a[i+1],reg_b[i+1])
q_mid(qcirc,reg_a[i+1],reg_b[i+1])
for i in range(len(head)-2,-1,-1):
q_rcarry(qcirc,reg_c[i],reg_a[i],reg_b[i],reg_c[i+1])
qcirc.x(reg_a[0])
qcirc.barrier()
return
def U_rst(qcirc, tick, fsm, state, read, write, move, ancilla):
# Reset write and move
qcirc.x(read[0])
nCX(qcirc, [fsm[0],read[0]], write, [ancilla[0]])
nCX(qcirc, [fsm[1],read[0]], move, [ancilla[0]])
qcirc.x(read[0])
nCX(qcirc, [fsm[2],read[0]], write, [ancilla[0]])
nCX(qcirc, [fsm[3],read[0]], move, [ancilla[0]])
qcirc.barrier()
return
#=====================================================================================================================
def Test_cfg(block):
global fsm, state, move, head, read, write, tape, ancilla, test
if (block == 'none'):
return
elif (block == 'read'):
fsm = []
state = []
move = []
head = [0,1,2,3]
read = [4]
write = []
tape = [5,6,7,8,9,10,11,12,13,14,15,16]
ancilla = [17]
test = [18]
elif (block == 'fsm'):
fsm = [0,1,2,3,4,5,6,7,8,9,10,11]
state = [12,13]
move = [14]
head = []
read = [15]
write = [16]
tape = []
ancilla = [17]
test = [18,19,20]
elif (block == 'move'):
fsm = []
state = []
move = [0]
head = [1,2,3,4]
read = []
write = []
tape = []
ancilla = [5,6,7]
test = [8,9,10,11]
elif (block == 'write'):
fsm = []
state = []
move = []
head = [0,1,2,3]
read = []
write = [4]
tape = [5,6,7,8,9,10,11,12,13,14,15,16]
ancilla = [17]
test = []#[18,19,20,21,22,23,24,25,26,27,28,29]
elif (block == 'rst'):
fsm = [0,1,2,3,4,5,6,7,8,9,10,11]
state = [12,13]
move = [14]
head = []
read = [15]
write = [16]
tape = []
ancilla = [17]
test = [18,19,20,21]
print("\n\nTEST CONFIGURATION\n\tFSM\t:",fsm,"\n\tSTATE\t:",state,"\n\tMOVE\t:",move,"\n\tHEAD\t:",head,"\n\tREAD\t:",read,"\n\tWRITE\t:",write,"\n\tTAPE\t:",tape,"\n\tANCILLA :",ancilla,"\n\tTEST\t:",test)
def Test_read(qcirc, read, head, tape, ancilla, test):
# Test using full superposition of head and some random tape qubits
# Test associated to read
for i in range(0,len(head)):
qcirc.h(head[i])
# Create random binary string of length tape
randbin = ""
for i in range(len(tape)): randbin += str(random.randint(0, 1))
for i in range(0,len(tape)):
if (randbin[i] == '1'):
qcirc.h(tape[i]) # Replace H with X for ease
qcirc.cx(read[0],test[0])
print("Test tape:",randbin)
qcirc.barrier()
return
def Test_fsm(qcirc, tick, fsm, state, read, write, move, ancilla, test):
# Test using full superposition of fsm, current state, read
# Test associated to move, write, new state
# fsm superposition part of U_init
qcirc.barrier()
qcirc.h(state[0])
qcirc.h(read[0])
qcirc.barrier()
qcirc.cx(write[0],test[0])
qcirc.cx(move[0],test[1])
qcirc.cx(state[1],test[2])
qcirc.barrier()
return
def Test_write(qcirc, write, head, tape, ancilla, test):
# Test using full superposition of head and write
# Test associated to tape (optional)
for i in range(0,len(head)):
qcirc.h(head[i])
qcirc.h(write)
# for i in range(0,len(tape)):
# qcirc.cx(tape[i],test[i])
return
def Test_move(qcirc, move, head, ancilla, test):
# Test using full superposition of head, both inc/dec
# Test associated to head
for i in range(0,len(head)):
qcirc.h(head[i])
qcirc.cx(head[i],test[i])
qcirc.h(move[0])
qcirc.barrier()
return
def Test_rst(qcirc, tick, fsm, state, read, write, move, ancilla, test):
# Test using full superposition of fsm, current state, read
# Test associated to move, write, new state
# fsm superposition part of U_init
for i in range(0,len(state)):
qcirc.h(state[i])
qcirc.h(read[0])
qcirc.h(write[0])
qcirc.h(move[0])
qcirc.barrier()
for i in range(0,len(state)):
qcirc.cx(state[i],test[i])
qcirc.cx(write[0],test[len(state)])
qcirc.cx(move[0],test[len(state)+1])
qcirc.barrier()
return
#=====================================================================================================================
asz = 2 # Alphabet size: Binary (0 is blank/default)
ssz = 1 # State size (Initial state is all 0)
tdim = 1 # Tape dimension
csz = ceil(log2(asz)) # Character symbol size
senc = ceil(log2(ssz)) # State encoding size
transitions = ssz * asz # Number of transition arrows in FSM
dsz = transitions * (tdim + csz + senc) # Description size
machines = 2 ** dsz
print("\nNumber of "+str(asz)+"-symbol "+str(ssz)+"-state "+str(tdim)+"-dimension Quantum Parallel Universal Linear Bounded Automata: "+str(machines))
tsz = dsz # Turing Tape size (same as dsz to estimating self-replication and algorithmic probability)
hsz = ceil(log2(tsz)) # Head size
sim_tick = tsz # Number of ticks of the FSM before abort
#sim_tick = 1 # Just 1 QPULBA cycle for proof-of-concept
tlog = (sim_tick+1) * senc # Transition log # required?
nanc = 3
qnos = [dsz, tlog, tdim, hsz, csz, csz, tsz, nanc]
fsm = list(range(sum(qnos[0:0]),sum(qnos[0:1])))
state = list(range(sum(qnos[0:1]),sum(qnos[0:2]))) # States (Binary coded)
move = list(range(sum(qnos[0:2]),sum(qnos[0:3])))
head = list(range(sum(qnos[0:3]),sum(qnos[0:4]))) # Binary coded, 0-MSB 2-LSB, [001] refers to Tape pos 1, not 4
read = list(range(sum(qnos[0:4]),sum(qnos[0:5])))
write = list(range(sum(qnos[0:5]),sum(qnos[0:6]))) # Can be MUXed with read?
tape = list(range(sum(qnos[0:6]),sum(qnos[0:7])))
ancilla = list(range(sum(qnos[0:7]),sum(qnos[0:8])))
print("\nFSM\t:",fsm,"\nSTATE\t:",state,"\nMOVE\t:",move,"\nHEAD\t:",head,"\nREAD\t:",read,"\nWRITE\t:",write,"\nTAPE\t:",tape,"\nANCILLA :",ancilla)
#=====================================================================================================================
test = []
unit = 'none' # 'read', 'fsm', 'write', 'move', 'rst'
Test_cfg(unit)
qcirc_width = sum(qnos[0:8]) + len(test)
qcirc = QuantumCircuit(qcirc_width)
# 1. Initialize
U_init(qcirc, qcirc_width, fsm)
# 2. Run machine for n-iterations:
for tick in range(0, sim_tick):
# 2.1 {read} << U_read({head, tape})
if (unit == 'read'): Test_read(qcirc, read, head, tape, ancilla, test)
U_read(qcirc, read, head, tape, ancilla)
# 2.2 {write, state, move} << U_fsm({read, state, fsm})
if (unit == 'fsm'): Test_fsm(qcirc, tick, fsm, state, read, write, move, ancilla, test)
U_fsm(qcirc, tick, fsm, state, read, write, move, ancilla)
# 2.3 {tape} << U_write({head, write})
if (unit == 'write'): Test_write(qcirc, write, head, tape, ancilla, test)
U_write(qcirc, write, head, tape, ancilla)
# 2.4 {head, err} << U_move({head, move})
if (unit == 'move'): Test_move(qcirc, move, head, ancilla, test)
U_move(qcirc, move, head, ancilla)
# 2.5 reset
if (unit == 'rst'): Test_rst(qcirc, tick, fsm, state, read, write, move, ancilla, test)
U_rst(qcirc, tick, fsm, state, read, write, move, ancilla)
print()
print(qcirc.draw())
print()
print(qcirc.qasm())
print()
disp_isv(qcirc, "Step: Test all", all=False, precision=1e-4)
#=====================================================================================================================