🌐 Quantum Computing Portfolio — Hisham Mansour

This repository serves as a central portfolio linking my quantum computing projects, hackathon submissions, and algorithm-development work.
Each project is kept in its original submitted form, and this repository acts as the unified entry point for professional audiences.

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🚀 Highlight Projects

1. Quantum Galton Board — Womanium Global Quantum Hackathon 2025

🔗 Repo: https://github.com/mnshmnsh/Womanium2025--QuantumGaltonBoard
Implementation of Carney & Varcoe’s Universal Statistical Simulator, reproducing classical and quantum Galton-board distributions using quantum circuits.

🔧 Key Features

• General algorithm for n‑level Galton boards (tested at n=1, 2, and 5).
• Distributions analyzed: Gaussian (Hadamard gates), Exponential (biased RY rotations), and Hadamard quantum walk (post‑processed symmetry).
• Simulations performed under four conditions: noiseless baseline, noisy unoptimized, noisy optimized, and noisy optimized with error mitigation.
• Statistical validation: compared simulated vs theoretical distributions using Total Variation Distance (TVD) and bin‑by‑bin residual analysis.
• Circuit diagrams generated for 1‑ and 2‑level boards, showing gate structure and depth.
• Verified qubit scaling formula (2n+2) and depth growth consistent with O((n^2)) construction.

📈 Results

• Gaussian distributions:
  • n=1: Simulated counts Bin0=4150 vs theory 4096, Bin1=4042 vs theory 4096 → TVD ≈ 0.013.
  • n=2: Simulated counts Bin0=2070, Bin1=4069, Bin2=2053 vs theory (2048, 4096, 2048) → TVD ≈ 0.015.
• Exponential distributions:
  • Bias parameter (p_{\mathrm{right}} \approx 0.90).
  • Noisy runs showed larger deviations, with TVD up to ~0.23–0.33 depending on optimization level.
• Hadamard quantum walk (U‑shape):
  • Post‑processed symmetry produced distributions with TVD < 0.01 in noiseless runs.
• Circuit resources:
  • n=1 circuits: 4 qubits, depth ≈ 5.
  • n=2 circuits: 6 qubits, depth ≈ 14.
  • Scaling confirmed the (2n+2) qubit formula and quadratic depth growth.
• Noise analysis:
  • FakeSherbrooke backend used to emulate hardware constraints.
  • Optimization reduced depth by ~20–40% in some cases, though routing sometimes increased gate counts.
• Residual plots:
  • Highlighted which bins contributed most to distribution differences under noise.

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2. Classiq AztecHacks 2024 — Quantum Hackathon

🔗 Repo: https://github.com/mnshmnsh/Classiq-AztecHacks-2024-Quantum-Hackathon
Hackathon participation solving all challenge tasks using the Classiq SDK.

🔧 Part A — Challenge Functions

• Implemented all 10 progressively difficult functions:
  • inplace_square, inplace_linear, inplace_quadratic, inplace_cubic, inplace_exponential
  • discrete_log_oracle, inplace_discrete_logarithm
  • equality_oracle, inplace_sum, sum_of_squares
• Each function expressed in reversible arithmetic form using Classiq’s symbolic quantum number types (QNum, QArray[QBit]).
• Verified correctness of arithmetic and oracle logic.
• Resource reporting after synthesis:
  • Example: inplace_quadratic synthesized with depth ≈ 12, gate count ≈ 40.
  • inplace_discrete_logarithm synthesized with depth ≈ 60+, gate count ≈ 200+.
  • These values confirmed the circuits scale with function complexity.

🔧 Part B — Bonus Algorithm

• Implemented the W₃ Werner state:
  • Superposition of 001, 010, 100.
  • Constructed via a sequence of RY, X, CH, and CX gates.
  • Synthesized circuit used 3 qubits, depth ≈ 12, with ~8 CX gates.
• Executed with Classiq simulator, producing measurement outcomes distributed across the three target states.

📈 Results

• All 10 challenge functions implemented and tested successfully.
• Resource usage (qubits, depth, gate counts) reported for each synthesized circuit.
• Bonus Werner state prepared and validated, with measurement counts confirming the expected superposition.

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3. Quantum Utility & Error Mitigation — 2D Ising Model

🔗 Repo: https://github.com/mnshmnsh/Development-of-Novel-Quantum-Algorithms
QAOA applied to the 2D transverse‑field Ising model with trotterization and artificial noise injection, guided by Kim et al., Nature 615, 596–600 (2023).

🔧 Key Features

• 2D Ising Hamiltonian (4×4 lattice, periodic boundary conditions) encoded with Pyomo.
• QAOA (Quantum Approximate Optimization Algorithm) used as the hybrid quantum‑classical solver.
• Suzuki–Trotter decomposition for Hamiltonian evolution.
• Circuit synthesized under depth and width constraints.
• Random noise added to Pauli coefficients; Zero‑Noise Extrapolation (ZNE) applied via linear fit.

📈 Results

• Circuit width = 16 qubits, depth ≈ 91.
• Gate composition: 320 CX, 240 RZ, 80 RX, 16 H.
• Best solution cost ≈ –960 with probability ≈ 0.71.
• Energy convergence observed after ~80 iterations.
• Noiseless energy ≈ –699.7; extrapolated energy via ZNE ≈ –670.6.
• ZNE produced extrapolated energies close to the noiseless baseline, demonstrating mitigation of noise effects.

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🧠 Skills & Tools

Quantum

• Qiskit — Galton Board circuits, Aer simulation, error mitigation (qiskit_experiments)
• Classiq SDK — AztecHacks challenge functions, 2D Ising QAOA implementation
• QAOA — Applied in the Ising project (5‑layer optimization)
• Variational circuits — Evident in QAOA layers
• Quantum walks — Hadamard quantum walk distribution in the Galton Board project
• Quantum simulation — AerSimulator (Galton Board), Classiq simulator (Ising)
• ZNE (Zero‑Noise Extrapolation) — Implemented in the Ising project for noise mitigation

Classical / ML

• Python — Core language across all projects
• NumPy — Binomial pmf (Galton Board), polynomial fitting for ZNE (Ising)
• Data visualization — Matplotlib plots, residuals, convergence graphs, energy vs noise plots