GUgus_massa·Jan 1, 2025
In Show HN: Quantum-Enhanced Mathematical Reasoning System – Expert Verificationnandhakishorm
quantum_reflection
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nandhakishorm / quantum_reflection · Not publicly available
quantum_reflection
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| Period | Start (UTC) | End (exclusive, UTC) | Mentions | Submissions | Comments |
|---|---|---|---|---|---|
| Dec 31, 07:00 | 2024-12-31 07:00:00 UTC | 2024-12-31 08:00:00 UTC | 2 | 2 | 0 |
| Dec 31, 08:00 | 2024-12-31 08:00:00 UTC | 2024-12-31 09:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 09:00 | 2024-12-31 09:00:00 UTC | 2024-12-31 10:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 10:00 | 2024-12-31 10:00:00 UTC | 2024-12-31 11:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 11:00 | 2024-12-31 11:00:00 UTC | 2024-12-31 12:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 12:00 | 2024-12-31 12:00:00 UTC | 2024-12-31 13:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 13:00 | 2024-12-31 13:00:00 UTC | 2024-12-31 14:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 14:00 | 2024-12-31 14:00:00 UTC | 2024-12-31 15:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 15:00 | 2024-12-31 15:00:00 UTC | 2024-12-31 16:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 16:00 | 2024-12-31 16:00:00 UTC | 2024-12-31 17:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 17:00 | 2024-12-31 17:00:00 UTC | 2024-12-31 18:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 18:00 | 2024-12-31 18:00:00 UTC | 2024-12-31 19:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 19:00 | 2024-12-31 19:00:00 UTC | 2024-12-31 20:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 20:00 | 2024-12-31 20:00:00 UTC | 2024-12-31 21:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 21:00 | 2024-12-31 21:00:00 UTC | 2024-12-31 22:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 22:00 | 2024-12-31 22:00:00 UTC | 2024-12-31 23:00:00 UTC | 0 | 0 | 0 |
| Dec 31, 23:00 | 2024-12-31 23:00:00 UTC | 2025-01-01 00:00:00 UTC | 0 | 0 | 0 |
| Jan 1, 00:00 | 2025-01-01 00:00:00 UTC | 2025-01-01 01:00:00 UTC | 0 | 0 | 0 |
| Jan 1, 01:00 | 2025-01-01 01:00:00 UTC | 2025-01-01 02:00:00 UTC | 1 | 0 | 1 |
What Hacker News says
3 sourcesShow HN: Quantum-Enhanced Mathematical Reasoning System – Expert Verification
We've developed an approach combining quantum computing with Meta-Llama-3.1-8B-Instruct to enhance mathematical reasoning. Our system proved that α must be an even integer for IMO 2024 Problem 1, where GPT-4 and Claude 3.5 failed. We seek expert verification of our methodology and results.
The Problem:
Find all real α where ⌊α⌋ + ⌊2α⌋ + ... + ⌊nα⌋ is divisible by n for all positive integers n.
Our Approach:
We represent mathematical reasoning as quantum states in a finite-dimensional Hilbert space, encoding both amplitude (token probabilities) and phase (logical relationships) information. A custom Hamiltonian guides the exploration of mathematical relationships through quantum evolution.
Key Innovation:
The system uses quantum interference to detect mathematical properties:
Valid reasoning shows constructive interference
Contradictions c
Read the rest
reate destructive interference
Patterns emerge through phase relationships
Implementation:
Base: Meta-Llama-3.1-8B-Instruct
Quantum dimension: 512
Convergence threshold: 0.98
Stability window: 3 steps
Results:
GPT-4 (github.com/NandhaKishorM/quantum_reflection/blob/main/gpt4o.md)
Attempted integer proof but missed evenness
Failed to complete proof
Claude 3.5 (github.com/NandhaKishorM/quantum_reflection/blob/main/claude_sonnet_3.5.md)
Made incorrect assumptions
Missed evenness pattern
Our Solution (github.com/NandhaKishorM/quantum_reflection/blob/main/quantum_resoning.md)
Proved α must be even
Showed why odd integers fail
Complete mathematical justification
Areas Needing Verification:
Quantum State Representation:
Is our encoding of mathematical statements sound? Does phase encoding correctly capture logical relationships?
Hamiltonian Design:
Have we correctly designed the evolution operator? Are there missing edge cases?
Interference Analysis:
Is our interpretation of interference patterns rigorous? Are alternative explanations possible?
Proof Completeness:
Have we conclusively proven even integers are the only solutions?
Implementation:
Repository: github.com/NandhaKishorM/quantum_reflection
Architecture: See quantum_system.svg in docs
Full implementation in main.py
Key Questions:
Is our quantum interference interpretation valid as mathematical proof?
Are there failure modes in our state representation?
Can this approach generalize to other problems?
What additional verification steps would you recommend?
We welcome rigorous analysis from:
Quantum computing researchers
Mathematicians
Theoretical computer scientists
AI researchers
The quantum state evolution revealed crucial patterns:
Odd integers → destructive interference
Even integers → quantum coherence
Non-integers → phase decoherence
This led to proving even integers are the only solutions. We seek verification of both our methodology and conclusions.
Technical requirements: Understanding of quantum computing, mathematical logic, number theory, and neural language models.
Quantum-Enhanced Mathematical Reasoning System – Seeking Expert Verification
We've developed an approach combining quantum computing with Meta-Llama-3.1-8B-Instruct to enhance mathematical reasoning. Our system proved that α must be an even integer for IMO 2024 Problem 1, where GPT-4 and Claude 3.5 failed. We seek expert verification of our methodology and results.
The Problem:
Find all real α where ⌊α⌋ + ⌊2α⌋ + ... + ⌊nα⌋ is divisible by n for all positive integers n.
Our Approach:
We represent mathematical reasoning as quantum states in a finite-dimensional Hilbert space, encoding both amplitude (token probabilities) and phase (logical relationships) information. A custom Hamiltonian guides the exploration of mathematical relationships through quantum evolution.
Key Innovation:
The system uses quantum interference to detect mathematical properties:
Valid reasoning shows constructive interference
Contradictions c
Read the rest
reate destructive interference
Patterns emerge through phase relationships
Implementation:
Base: Meta-Llama-3.1-8B-Instruct
Quantum dimension: 512
Convergence threshold: 0.98
Stability window: 3 steps
Results:
GPT-4 (github.com/NandhaKishorM/quantum_reflection/blob/main/gpt4o.md)
Attempted integer proof but missed evenness
Failed to complete proof
Claude 3.5 (github.com/NandhaKishorM/quantum_reflection/blob/main/claude_sonnet_3.5.md)
Made incorrect assumptions
Missed evenness pattern
Our Solution (github.com/NandhaKishorM/quantum_reflection/blob/main/quantum_resoning.md)
Proved α must be even
Showed why odd integers fail
Complete mathematical justification
Areas Needing Verification:
Quantum State Representation:
Is our encoding of mathematical statements sound? Does phase encoding correctly capture logical relationships?
Hamiltonian Design:
Have we correctly designed the evolution operator? Are there missing edge cases?
Interference Analysis:
Is our interpretation of interference patterns rigorous? Are alternative explanations possible?
Proof Completeness:
Have we conclusively proven even integers are the only solutions?
Implementation:
Repository: github.com/NandhaKishorM/quantum_reflection
Architecture: See quantum_system.svg in docs
Full implementation in main.py
Key Questions:
Is our quantum interference interpretation valid as mathematical proof?
Are there failure modes in our state representation?
Can this approach generalize to other problems?
What additional verification steps would you recommend?
We welcome rigorous analysis from:
Quantum computing researchers
Mathematicians
Theoretical computer scientists
AI researchers
The quantum state evolution revealed crucial patterns:
Odd integers → destructive interference
Even integers → quantum coherence
Non-integers → phase decoherence
This led to proving even integers are the only solutions. We seek verification of both our methodology and conclusions.
Technical requirements: Understanding of quantum computing, mathematical logic, number theory, and neural language models.