## Quantum Computing & Neural Networks

basic concepts

• Superposition: $$\ket{+}, \ket{-}$$
• Phase: $$T$$
• Bloch Sphere
• Decoherence
• Energy relaxation: $$T_1 := \ket{1} \rightarrow \ket{0}$$
• Dephasing: $$T_2$$

Resources

### IBM Open Quantum

OpenQasm Input

// My First Score
OPENQASM 2.0;
include "qelib1.inc";

// Register declarations
qreg q;
creg c;

// Quantum Circuit
// Pauli operations
x q;
y q;
z q;
barrier q;
// Clifford operations
h q;
s q;
sdg q;
cx q,q;
barrier q;
// non-Clifford operations
t q;
tdg q;
barrier q;
// measurement operations
measure q -> c;

# my_first_score.py
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, execute

# Define the Quantum and Classical Registers
q = QuantumRegister(2)
c = ClassicalRegister(2)

# Build the circuit
my_first_score = QuantumCircuit(q, c)
# Pauli operations
my_first_score.x(q)
my_first_score.y(q)
my_first_score.z(q)
my_first_score.barrier(q)
# Clifford operations
my_first_score.h(q)
my_first_score.s(q)
my_first_score.s(q).inverse()
my_first_score.cx(q,q)
my_first_score.barrier(q)
# non-Clifford operations
my_first_score.t(q)
my_first_score.t(q).inverse()
my_first_score.barrier(q)
# measurement operations
my_first_score.measure(q, c)

# Execute the circuit
job = execute(my_first_score, backend = 'local_qasm_simulator', shots=1024)
result = job.result()

# Print the result
print(result.get_counts(my_first_score))


Operations

  X=(01;10), control-not, CNOT gate
T=(10;0eiπ/4)
S=(10;0i):=T^2
Z=(10;0−1):=T^4
S†=(10;0−i):=T^6
T†=(10;0e−iπ/4):=T^7
Y=(0i−i0):=XZ


### Quantum Algorithms

• Shor's algorithm: ordering, factoring
• period finding: modular exponential function, $$a^r = 1 (\mod N)$$
• steps
• pick $$a$$, compute $$\gcd(N,a)$$
• if not co-prime
• do find period $$r$$ so that $$a^r = 1 (\mod N)$$
• until $$r$$ is even
• check $$\gcd(a^{r/2}\pm 1, N)$$ for prime factor
• quadratic sieve method $$\exp(d^{1/3})$$
• Grover's algorithm: reflection^n to amplify the matched state
• Quantum Annealing

### Technicals

Building blocks - Discussion of transistor

### Ideas

• 3D transistor to resemble neuro, spiking instead
• growing network, mimic brain development, let network layers to change & train
• biological growing: nervous system growth, need to study human baby
• timeline
• day 13: • embryonic day 42 - midgestation: establishing rudimentary neural networks
• 3rd gestational week: differentiation of neural progenitor cells
• 8th GW: rudimentary structures of the brain and central nervous system
• rapid growth and elaboration
• end of the prenatal period: major fiber pathways complete
• before preschool: increases in size by four-fold
• by age 6: ~ 90% of adult, structural changes continue
• 100GB neurons, 60TB connections: ~ 600 link per neuron, multiple-in-guided-one-out
• distribution out + spiking activation
• sectioning during training: vision, language, motion and so on. develop as grow, over the cause of infant
• self-sectioning: train as needed
• resonance ignition: transfer learning & creativity