Quantum States

[Inserian]

I am currently testing methods to stabilize qubits' superposition states by embedding multi-dimensional information layers that remain fixed until manipulated while avoiding noise decoherence. A major challenge is accessing and retrieving this information without disturbing the quantum states or affecting retrieval time. Grover's Algorithm, which offers a quadratic speedup for unsorted database searches, could potentially aid in this process. However, scaling Grover's Algorithm to handle larger, more complex systems remains a significant hurdle due to increased computational complexity.

Qubit decoherence isn't a big issue with proper upscaling and correctly monitoring these "states" while implementing other factors. Nevertheless, decoherence remains problematic when using Quantum Processing Units (QPUs) because external environmental factors can induce machine-level decoherence, affecting overall system performance.

If you have any input please feel free to add to the discussion or contact me at [email protected] or [email protected]

[Inserian]

Applying the following attributes to specify points for decode in my newly named qc's (Quantum Channels) that act like neurons.
class GroverOracle:
"""
Oracle for Grover's Algorithm to mark the target state.
"""
def init(self, target_state: str):
"""
:param target_state: Binary string representing the target state to mark.
"""
self.target_state = target_state
self.num_qubits = len(target_state)
self.circuit = QuantumCircuit(self.num_qubits)
self.build_oracle()

def build_oracle(self):
    """
    Constructs the oracle circuit that marks the target state by flipping its amplitude.
    """
    # Apply X gates to flip the qubits where target_state has '0'
    for i, bit in enumerate(self.target_state):
        if bit == '0':
            self.circuit.x(i)

    # Multi-controlled Z gate
    self.circuit.h(self.num_qubits - 1)
    self.circuit.mct(list(range(self.num_qubits - 1)), self.num_qubits - 1)  # Multi-controlled Toffoli
    self.circuit.h(self.num_qubits - 1)

    # Revert X gates
    for i, bit in enumerate(self.target_state):
        if bit == '0':
            self.circuit.x(i)

    self.circuit.barrier()

def get_oracle(self) -> QuantumCircuit:
    """
    Returns the oracle circuit.
    """
    return self.circuit

Then class the diffuser to construct a diffuser circuit.

[Inserian]

Diffuser class, then we can apply the search algo for marked states...

class GroverDiffuser:
"""
Diffuser (inversion about the mean) for Grover's Algorithm.
"""
def init(self, num_qubits: int):
self.num_qubits = num_qubits
self.circuit = QuantumCircuit(self.num_qubits)
self.build_diffuser()

def build_diffuser(self):
    """
    Constructs the diffuser circuit.
    """
    # Apply Hadamard gates
    self.circuit.h(range(self.num_qubits))
    # Apply X gates
    self.circuit.x(range(self.num_qubits))
    # Multi-controlled Z gate
    self.circuit.h(self.num_qubits - 1)
    self.circuit.mct(list(range(self.num_qubits - 1)), self.num_qubits - 1)  # Multi-controlled Toffoli
    self.circuit.h(self.num_qubits - 1)
    # Apply X gates
    self.circuit.x(range(self.num_qubits))
    # Apply Hadamard gates
    self.circuit.h(range(self.num_qubits))
    self.circuit.barrier()

def get_diffuser(self) -> QuantumCircuit:
    """
    Returns the diffuser circuit.
    """
    return self.circui