Quantum Network State Transport

Project created for the IISc-IBM Qiskit Fall Fest 2025

📄 Read the Full Problem Statement (PDF)

Note

This repository contains a Qiskit implementation for transporting quantum states across asymmetric directed acyclic graphs (DAG). It addresses the Parity Mismatch problem inherent in specific network topologies using ancilla-assisted interference.

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Introduction

Networks connect nodes, devices, and entities across complex systems — from biological interactions to quantum communication infrastructures. Modeling the dynamics of quantum networks is essential for designing future quantum internet protocols.

This project solves a specific routing challenge: Transporting a quantum state from Node A (Start) to Node B (End) where two distinct paths exist with different lengths.

• Path 1 (Left): 4 steps ($1 \to 2 \to 3/4 \to 5 \to 8$)
• Path 2 (Right): 3 steps ($1 \to 6 \to 7 \to 8$)

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The Physics: Parity Mismatch

In a standard qubit hypercube mapping, a single step corresponds to a bit flip. This creates a parity constraint:

• Odd Path Length (3 steps): Connects states of opposite parity (e.g., Even $\to$ Odd).
• Even Path Length (4 steps): Connects states of same parity (e.g., Even $\to$ Even).

The Conflict

We require the Start Node and End Node to map to the same basis state (e.g., $|000\rangle$). $$\text{Start} \equiv |000\rangle \quad \text{and} \quad \text{End} \equiv |000\rangle$$

However, it is physically impossible to reach $|000\rangle$ from itself in 3 steps using standard unitary evolution without auxiliary degrees of freedom.

The Solution: Ancilla-Assisted Transport

We introduce an Ancilla Qubit ($q_a$) to act as a "success flag" or an extra dimension to resolve the parity conflict.

$$|\psi_{\text{final}}\rangle = \alpha |100\rangle_{data} |1\rangle_{anc} + \beta |000\rangle_{data} |1\rangle_{anc}$$

Where the state $|1\rangle_{anc}$ indicates successful arrival at the target node.

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Circuit Design

The circuit mimics the time-evolution of the particle across the graph layers.

Important

The circuit uses 3 Data Qubits to encode position and 1 Ancilla Qubit for flow control.

Key Stages

1. Superposition Split: A Hadamard operation on $q_2$ creates the initial bifurcation between the Left and Right branches.
2. Propagation: Controlled-Hadamard and CNOT gates evolve the state through the intermediate nodes ($2, 3, 4, 6, 7$).
3. Interference & Detection: We use Multi-Controlled X (MCX) gates to detect arrival at the penultimate nodes ($5$ and $7$) and trigger the Ancilla.
4. Uncomputation: Data qubits are reset conditionally to isolate the path memory.

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Setting up The Repository

Ensure you have Python 3.10+ installed. It is recommended to use a virtual environment.

Clone the repository

git clone [https://github.com/stark-069/quantum-graph-transport.git](https://github.com/stark-069/quantum-graph-transport.git)
cd quantum-graph-transport

Install dependencies

pip install -r requirements.txt

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Results & Analysis

The simulation was run on AerSimulator with 2048 shots. The results confirm that the quantum state successfully traverses both paths and triggers the Ancilla.

Interpretation of States

The x-axis represents the bitstring $|q_{anc} q_2 q_1 q_0\rangle$.

• 1000 (Success via Right Path):

  • The particle took the 3-step path ($1 \to 6 \to 7 \to 8$).
  • The data qubits successfully returned to $|000\rangle$.
  • The Ancilla is 1, indicating successful transport.

• 1100 (Success via Left Path):

  • The particle took the 4-step path ($1 \to 2 \to 3/4 \to 5 \to 8$).
  • The Ancilla is 1.
  • Note: $q_2$ remains flipped ($1$) due to the parity difference between the two paths (Length 4 vs Length 3).

Tip

The presence of state 1100 is a direct experimental witness of the path length asymmetry in the network topology.

Runtime Statistics

• Simulator: AerSimulator (Qiskit)
• Shots: 2048
• Circuit Depth: 18 (unoptimized)
• Success Rate: ~100% (deterministic transport)

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References

• Qiskit Documentation: IBM Quantum
• Quantum Walks on Graphs: Kempe, J. (2003). Quantum random walks: an introductory overview.

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Authored by ABHIROOP GOHAR, IIT INDORE