QPrize — Shor's ECDLP on Quantum Hardware

Team: Classiq Technologies Submission deadline: April 5, 2026

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Contact Information

Name	Email	Organization
Amir Naveh	amir@classiq.io	Classiq Technologies
Ariel Smoler	ariel@classiq.io	Classiq Technologies
Dor Harpaz	dor@classiq.io	Classiq Technologies
Or Samimi Golan	orsa@classiq.io	Classiq Technologies

GitHub: https://github.com/classiqdor/QPrize

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Professional Background

We are engineers at Classiq Technologies, a quantum computing software company that builds tools for high-level quantum circuit synthesis and optimization. Our team works daily with quantum algorithms, circuit synthesis, and hardware backends including IBM Quantum, IonQ, and Quantinuum.

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Key Length Tackled

4-bit ECC key — competition curve y² = x³ + 7 mod 13, group order n = 7, private key d = 6.

We provide two implementations at different points on the cost/legitimacy spectrum:

Solution	Qubits	CX	Hardware	Result
Scalar oracle	11	716	IBM ibm_torino, IonQ Forte-1, IBM ibm_pittsburgh, Rigetti Ankaa-3 ✅	d=6 recovered
EC arithmetic oracle	28	105,554	Simulator only	d=6 recovered

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Quantum Computers Used

The 4-bit circuit was executed on four devices across three vendors:

Device	Vendor	Type	Qubits	Access
IBM ibm_torino (Heron r1)	IBM Quantum	Superconducting	133	IBM Cloud direct
IonQ Forte-1	IonQ	Trapped-ion	36	Classiq SDK
IBM ibm_pittsburgh	IBM Quantum	Superconducting	127	IBM Cloud direct
Rigetti Ankaa-3	Rigetti / AWS Braket	Superconducting	84	AWS Braket

All runs used the same circuit: 11 qubits, 716 CX, depth 1050. All recovered d=6 ✅.

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Execution Instructions

Prerequisites

# Clone repo
git clone https://github.com/classiqdor/QPrize
cd QPrize

# Install classiq
pip install classiq
python -c "import classiq; classiq.authenticate()"

Run on simulator (no credentials needed)

# Hardware-viable circuit (716 CX, scalar oracle)
python publish/hardware_solution/solution.py

# Scalable genuine-ECDLP circuit (~105k CX, takes ~9 min to synthesize)
python publish/scalable_solution/solution.py 4

Run on real IBM hardware

cp .env.example .env
# fill in IBM_TOKEN, IBM_INSTANCE
set -a; source .env; set +a
python publish/hardware_solution/solution.py --ibm

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Submission Contents

publish/
  hardware_solution/    — 716 CX scalar oracle; verified on IBM, IonQ, Rigetti
  scalable_solution/    — 105k CX genuine EC arithmetic (Roetteler 2017); simulator
  competitor_reviews/   — comparison with other known submissions
  summary/              — full solution writeup
  brief.md              — technical brief (source for brief.pdf)
attempts/RESULTS.md     — all 20+ synthesis runs (qubits, depth, CX, success)
PLAN.md                 — optimization roadmap and decision log
worklog/                — per-session activity logs

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Algorithm Summary

We implement Shor's ECDLP algorithm using two-register quantum phase estimation:

1. Prepare superposition |+⟩^{2·var_len} over registers x1, x2
2. Oracle: ecp = P₀ + x1·G − x2·Q
3. Inverse QFT to extract the period
4. Recover d = −x2_r · x1_r⁻¹ mod n

Full technical details in publish/brief.md and publish/summary/summary.md.