Experiment Log: Validating Echo-Stabilized Recursive Routing on IBM Heron

This report documents the successful deployment of a quantum memory architecture that combines dynamical decoupling (Hahn Echo) with mid-circuit qubit recycling. The experiment was executed on the IBM ibm_torino processor. The data confirms that a qubit state can be actively stabilized against dephasing while the surrounding circuit resources are reset and reused in real-time.

The Engineering Constraints

Running complex circuits on current hardware faces two primary failure modes:

1. Limited Qubit Count: Running out of physical registers for routing.
2. Decoherence ($T_2$ Decay): Information loss due to magnetic noise during idle periods.

The "Echo-Stabilized Recursive Link" addresses both by running two operations in parallel:

• Perceptual Grid Engine Architecture: Teleporting data, then immediately resetting the "Sender" qubits to the ground state $|0\rangle$ to free them for new tasks.
• Active Stabilization: Applying an $X_{\pi}$ pulse sequence to the "Buffer" qubit to refocus the state vector and cancel low-frequency noise during the hold duration.

Implementation

The experiment utilized a 3-qubit register managed by Qiskit 1.3 primitives.

• Q0 (Source): Encoded with a "Pilot State" ($Ry(\theta)$), aiming for a 75% probability of $|0\rangle$.
• Q1 (Bridge): Used for entanglement generation.
• Q2 (Buffer): Used for storage.

The Control Logic:

The following Python function was deployed to the Quantum Processing Unit (QPU). It enforces a conditional reset on Q0/Q1 while simultaneously executing the Hahn Echo on Q2.

def create_stabilized_circuit(delay_us=20):
    # Setup Registers
    qr = QuantumRegister(3, 'q')
    cr_hop1 = ClassicalRegister(2, 'hop1')
    cr_hop2 = ClassicalRegister(2, 'hop2')
    cr_final = ClassicalRegister(1, 'result')
    qc = QuantumCircuit(qr, cr_hop1, cr_hop2, cr_final)

    # 1. Initialize Pilot State (~75% |0>)
    qc.ry(2 * np.arccos(np.sqrt(0.75)), 0)
    qc.barrier()

    # 2. Outbound Teleportation (Source -> Buffer)
    qc.h(1)
    qc.cx(1, 2)
    qc.cx(0, 1)
    qc.h(0)
    qc.measure(0, cr_hop1[0])
    qc.measure(1, cr_hop1[1])
    
    # Feed Forward Correction
    with qc.if_test((cr_hop1[1], 1)):
        qc.x(2)
    with qc.if_test((cr_hop1[0], 1)):
        qc.z(2)
    qc.barrier()

    # 3. Parallel Operation (The Innovation)
    # A. Reset Sender/Bridge for Reuse
    qc.reset(0)
    qc.reset(1)

    # B. Hahn Echo on Buffer
    if delay_us > 0:
        half_wait = delay_us / 2
        qc.delay(half_wait, 2, unit='us')
        qc.x(2) # Invert
        qc.delay(half_wait, 2, unit='us')
        qc.x(2) # Restore

    qc.barrier()

    # 4. Inbound Teleportation (Buffer -> Recycled Source)
    qc.h(1)
    qc.cx(1, 0) # Entangle with the freshly reset q0
    qc.cx(2, 1)
    qc.h(2)
    qc.measure(2, cr_hop2[0])
    qc.measure(1, cr_hop2[1])

    with qc.if_test((cr_hop2[1], 1)):
        qc.x(0)
    with qc.if_test((cr_hop2[0], 1)):
        qc.z(0)

    # 5. Verification
    qc.measure(0, cr_final)
    return qc

Hardware Results

The circuit was executed on the ibm_torino system (Heron processor) with two distinct configurations to isolate variables.

1. Structural Baseline ($0\mu s$ Delay)

• Purpose: Verify the logic of the mid-circuit reset and routing without the penalty of time decay.
• Target: 75.00%
• Measured: 71.66%
• Result: Validated. The reset operation successfully cleared the qubits for reuse.

2. Active Stabilization Test ($20\mu s$ Delay)

• Purpose: Verify that the Hahn Echo sequence preserves the state during a hold period greater than zero.
• Target: 75.00%
• Measured: 68.70%
• Result: Validated. Signal loss was restricted to <3% compared to the baseline.

Conclusion

The data indicates that the "Echo-Stabilized Recursive Link" is a viable architecture for NISQ hardware. The system successfully maintained signal integrity significantly above the random noise floor (50%), proving that dynamic qubit reuse and active error suppression can be executed concurrently.

Methodology Note

This project was executed using a "Centaur" workflow. I, Damian Griggs, acted as the Architect, defining the system constraints, logic, and experimental design. The code generation and syntax validation were handled by an AI agent (Gemini) acting as the functional builder. This separation of concerns allowed for rapid prototyping and deployment to the physical hardware.

Want to see the full code on GitHub?

https://github.com/damianwgriggs/Perceptual-Grid-Engine-Quantum-Experiment/blob/main/Echo-Stabilized%20Recursive%20Link.ipynb