Volume II · April 2026 · Quantum Computing Research Series

GPU-Accelerated Quantum Circuit Simulation & Experimental Analysis of Foundational Quantum Algorithms

Integrating Qiskit Aer cuQuantum, PennyLane VQE, and Quantum Cryptographic Protocols with direct implications for Post-Quantum Cybersecurity. Executed on consumer-grade hardware — no HPC, no cloud budget.

Author Harsh Patel

Institution CyberMind AI · DigiGlow

Location Ahmedabad, Gujarat, India

Published April 19–20, 2026

Qiskit 2.3.0 PennyLane 0.44.1 RTX 3050 · cuQuantum i5-12450H · 16GB DDR4 Post-Quantum Cryptography Python 3.12 Open Source · $0 Compute Cost

↓ Download Full Paper View Results →

1.53×

GPU speedup at 26 qubits

94.04%

Grover's target accuracy

18.2%

BB84 eavesdropper error rate

99.58%

VQE chemical accuracy

Quantum algorithms validated

₹0

Total compute cost

01 — Abstract

What This Paper Covers

This paper presents an integrated experimental study combining GPU-accelerated quantum circuit simulation benchmarking with hands-on implementation and analysis of five foundational quantum algorithms executed on consumer-grade classical simulation hardware. Using IBM Qiskit 2.3.0 (with Qiskit Aer and the NVIDIA cuQuantum backend) and PennyLane 0.44.1, we report: (1) GPU simulation speedup of up to 1.53× over CPU at 26 qubits, with the crossover point near 22 qubits; (2) Bell State preparation achieving perfect 50/50 entanglement (500|00⟩ : 500|11⟩, zero forbidden states) over 1,000 shots; (3) Grover's Quantum Search reaching 94.04% target-state probability (|101⟩, 963/1024 shots) in exactly 2 oracle iterations; (4) BB84 QKD detecting eavesdropper presence via 18.2% error rate against a 0.0% clean baseline; (5) Shor's Integer Factorization recovering primes p=3, q=5 from N=15 via an 8-qubit QFT; and (6) VQE achieving 99.58% accuracy (absolute error 0.014449 Ha, below the 0.016 Ha chemical accuracy threshold). All experiments were executed on an ASUS laptop with Intel Core i5-12450H, NVIDIA RTX 3050 (4GB GDDR6), and 16GB DDR4 RAM.

02 — Experimental Results

Five Algorithms. One Laptop. Zero Excuses.

Each algorithm was implemented from scratch, debugged against Qiskit Aer 2.x compatibility constraints, and validated against theoretical predictions. Results across all five experiments achieved excellence.

ALGORITHM 01 · 2 QUBITS · 1000 SHOTS

Bell State

500 : 500

Perfect quantum entanglement confirmed. |00⟩ and |11⟩ each measured exactly 500 times. Zero forbidden states (|01⟩ = 0, |10⟩ = 0). Confirms noise-free simulator fidelity. Serves as zero-error calibration baseline for all subsequent experiments.

100% — THEORETICAL MAXIMUM

ALGORITHM 02 · 3 QUBITS · 1024 SHOTS

Grover's Search

94.04%

Target state |101⟩ measured 963/1024 times. Theory predicted 94.5% — we achieved 94.04% (deviation: 0.46 pp). Required exactly 2 oracle iterations vs classical 4-query average. Quadratic speedup over classical search confirmed experimentally.

99.5% OF THEORETICAL MAX

ALGORITHM 03 · 100 QUBITS (SIMULATED)

BB84 QKD

0% → 18.2%

Clean channel: 0.0% error → secure 36-bit key generated. Eavesdropped channel: 18.2% error → channel auto-aborted. Physics-guaranteed security. The Heisenberg Uncertainty Principle itself detects the attacker. No math assumptions required.

EAVESDROPPER DETECTED & BLOCKED

ALGORITHM 04 · 12 QUBITS · 2048 SHOTS

Shor's Factorization

N=15 → 3×5

QFT produced four near-equal peaks at {0, 64, 128, 192}. Period r=4 extracted via continued fractions. gcd(7²−1, 15) = 3, gcd(7²+1, 15) = 5. Succeeded on first run. This is the algorithm that breaks RSA-2048 at sufficient scale.

PRIMES RECOVERED — FIRST RUN

ALGORITHM 05 · 4 QUBITS · 100 EPOCHS

VQE (Ising Model)

99.58%

Final energy: −3.412585 Ha vs exact −3.427034 Ha. Absolute error 0.014449 Ha — below the IUPAC 0.016 Ha chemical accuracy threshold. 24 trainable parameters, Adam optimizer, PennyLane lightning.qubit. QML on a laptop.

BELOW CHEMICAL ACCURACY THRESHOLD

DEBUGGING CONTRIBUTION · AER 2.X

Reproducibility Fixes

2 Fixes Documented

Grover's: AerError: unknown instruction: Oracle |101⟩ — Fix: replace append() with compose() to inline gate primitives.

Shor's: AerError: unknown instruction: IQFT — Fix: QFTGate(n).inverse() + qc.decompose() to expand to native gates.

PRACTITIONER CONTRIBUTION

03 — GPU Benchmarks

When Does the GPU Actually Help?

CPU vs GPU simulation across 20–26 qubits on RTX 3050 (4GB GDDR6). The crossover point is not where most people think it is.

CPU Statevector

GPU Statevector (cuQuantum)

1.53× max GPU speedup at 26Q

GPU is slower below 22 qubits due to PCIe transfer overhead. Crossover occurs at exactly 22Q. Recommend GPU only for ≥24 qubit circuits.

04 — Cybersecurity Implications

The Quantum Threat Is Real. The Timeline Is Now.

Shor's Algorithm at fault-tolerant scale breaks RSA and ECC. Grover's halves symmetric key security. BB84 and NIST PQC standards are the migration path. Here's the complete threat assessment from this research, directly informing the CyberMind AI threat model.

Cryptographic Primitive	Classical Security	Post-Quantum Status	Recommended Action
RSA-2048	112-bit equivalent	✕ BROKEN by Shor's	→ Migrate to CRYSTALS-Kyber immediately
ECC P-256	128-bit equivalent	✕ BROKEN by Shor's	→ Migrate to CRYSTALS-Dilithium
AES-128	128-bit	⚠ Weakened by Grover's (64-bit)	→ Upgrade to AES-256
AES-256	256-bit	✓ Secure (128-bit post-Grover)	→ Retain — no action required
SHA-256	128-bit collision	⚠ Acceptable (64-bit Grover)	→ SHA-3 preferred long-term
BB84 / QKD	N/A — physical law	◈ UNCONDITIONALLY SECURE	→ Deploy where infrastructure permits

NIST finalised post-quantum standards (FIPS 203, 204, 205) in August 2024. Migration begins now.

05 — Author

About the Researcher

Harsh Patel

Founder — DigiGlow Founder — CyberMind AI Ahmedabad, Gujarat 🇮🇳

Harsh Patel is the founder of CyberMind AI — an autonomous cybersecurity intelligence platform anchored at the intersection of AI and quantum-aware threat modeling. His research spans GPU-accelerated quantum simulation, post-quantum cryptography migration, variational quantum ML, and practical cybersecurity tooling. This paper was executed entirely on consumer hardware using free open-source frameworks, validating that meaningful quantum research is accessible to independent researchers across India.

✉ harsh@digiglowmarketing.com LinkedIn DigiGlow

07 — Future Work

What Comes Next

This paper is the beginning of a research program, not a one-time experiment. Planned extensions under CyberMind AI:

Scale GPU to 28–32 qubits

Fully characterise the RTX 3050 simulation ceiling and extrapolate to A100/H100.

Shor's for N=21, N=35

Verify O((log N)³) polynomial scaling in practice across larger composite integers.

VQE on H₂ and LiH molecules

Quantum chemistry benchmarks versus the CCSD(T) classical gold standard.

Real IBM Quantum hardware

Execute all five algorithms on ibm_brisbane to measure decoherence and gate fidelity.

QNN Intrusion Detection

Quantum Neural Network binary classifier for network intrusion detection vs LSTM baseline.

BB84 for CyberMind AI comms

Implement BB84 as the authentication layer for CyberMind AI agent-to-agent communication.