Quantum Computing

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[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

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
Published: Sun 01 July 2018. By Dongming Jin in

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