## Quantum Computing & Neural Networks

- 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[2];
creg c[2];
// Quantum Circuit
// Pauli operations
x q[0];
y q[1];
z q[0];
barrier q;
// Clifford operations
h q;
s q[0];
sdg q[1];
cx q[0],q[1];
barrier q;
// non-Clifford operations
t q[0];
tdg q[1];
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[0])
my_first_score.y(q[1])
my_first_score.z(q[0])
my_first_score.barrier(q)
# Clifford operations
my_first_score.h(q)
my_first_score.s(q[0])
my_first_score.s(q[1]).inverse()
my_first_score.cx(q[0],q[1])
my_first_score.barrier(q)
# non-Clifford operations
my_first_score.t(q[0])
my_first_score.t(q[1]).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)
H=1/√2(11;1−1), Hadamard gate
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

### Neruoscience

- brief about nervous system
- neurons: chemical interactions between neurons as communication, not fixed, multi-connected

### 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

- biological growing: nervous system growth, need to study human baby

## Comments !