Superquantum iQuHACK 2026 Challenge

This repository contains the solution for the Superquantum iQuHACK 2026 Challenge. The goal of the challenge was to synthesize various quantum unitaries into Clifford+T sequences with high precision.

Repository Structure

• src/: Core Python scripts for synthesis and verification.
  • solver.py: The main script used to synthesize target unitaries.
  • verify_all.py: Wrapper script to verify all 11 tasks.
  • verify_circuits.py: Core logic for norm distance and T-count calculation.
• circuits/: Generated Clifford+T QASM files for all 11 tasks.
• docs/: Challenge description and PDF documentation.
• .gitignore: Standard git ignore file to keep the repository clean.

Getting Started

Prerequisites

• Python 3.8+
• Qiskit
• Scipy
• Numpy
• mpmath
• pygridsynth (for 1-qubit rotation synthesis)

Running the Solver

To regenerate the Clifford+T circuits (outputs will be saved in circuits/), run:

python3 src/solver.py

Verification

To verify the generated circuits and see performance statistics, run:

python3 src/verify_all.py

Performance Results

All tasks were verified using the operator norm distance metric and T-count calculation.

Task	Description	Norm Distance	T-count
1	Controlled-Y	0.0000e+00	4
2	Controlled-Ry(π/7)	6.8145e-13	504
3	exp(i π/7 ZZ)	1.1120e-12	2956
4	exp(i π/7 (XX+YY))	8.1579e-13	2758
5	exp(i π/4 H2)	2.2204e-16	0
6	exp(i π/7 H3)	1.4597e-12	2540
7	State Preparation	6.7878e-07	2522
8	Structured 1	1.9131e-12	2674
9	Structured 2	1.6163e-12	3332
10	Random Unitary	2.4678e-12	5126
11	4-qubit Diagonal	2.6346e-12	3660

Bonus Challenge: Commuting Pauli Phase Program

The bonus challenge involved synthesizing a unitary represented by 255 commuting Pauli strings on 9 qubits, with phase rotation angles quantized to $\pi/8$.

Solution Overview

1. Diagonalization: We implemented a manual Clifford diagonalization algorithm using Gaussian elimination on the symplectic representation of the Pauli subgroup. A Clifford circuit $C$ was constructed to map the basis of the commuting subgroup to $Z$-basis parities.
2. Phase Synthesis: The diagonal phase rotations $\prod \exp(-i \frac{k_j \pi}{8} Z^{v_j})$ were implemented using CNOT ladders and Rz gates. Since $k_j \in {1, 7}$, each term translates to a single $T$ or $T^\dagger$ gate.
3. Clifford+T Decomposition: The final circuit $C^\dagger \text{Diag} C$ was transpiled to the ${H, T, T^\dagger, CNOT}$ gate set.

Running the Bonus Solver

python3 scripts/solve_bonus.py
python3 scripts/verify_bonus.py

Challenge	Desciption	Fidelity	T-count
Bonus	255 Commuting Paulis	1.0000	255

Methodology

1. Decomposition: 2-qubit unitaries are decomposed into CX and 1-qubit U3 gates using Qiskit's transpiler with level 3 optimization.
2. Synthesis: 1-qubit U3 gates are further decomposed into Rz-H-Rz-H-Rz sequences. The Rz rotations are synthesized into Clifford+T sequences using pygridsynth for near-optimal T-count given a target precision.
3. Verification: The resulting QASM files are loaded back into Qiskit operators and compared against the target matrices using the operator norm distance, accounting for global phase.