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| <label class="block text-sm font-medium text-gray-700 mb-1">Hypothesis</label> | |
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| Quantum computers can solve optimization problems faster than classical computers for certain problem classes, specifically in combinatorial optimization. | |
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| <label class="block text-sm font-medium text-gray-700 mb-1">Background</label> | |
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| Recent advances in quantum annealing and gate-model quantum computers show promise for optimization. Need to understand the specific problem classes where quantum advantage is provable. | |
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| <p class="text-sm font-medium">Retrieved 12 papers from arXiv</p> | |
| <p class="text-xs text-gray-500">Query: "quantum optimization speedup combinatorial"</p> | |
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| <p class="text-sm font-medium">Filtered to 5 relevant papers</p> | |
| <p class="text-xs text-gray-500">Criteria: published in last 5 years, citation count > 50</p> | |
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| <p class="text-sm font-medium">Extracted key sections</p> | |
| <p class="text-xs text-gray-500">Focus on methods and results sections</p> | |
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| <div class="bg-gray-50 p-4 rounded border border-gray-200 markdown-content"> | |
| <h1>Quantum Speedup in Combinatorial Optimization</h1> | |
| <p>Current evidence suggests quantum computers can provide polynomial to exponential speedups for certain combinatorial optimization problems, but with important caveats:</p> | |
| <h2>Problem Classes with Proven Speedups</h2> | |
| <ul> | |
| <li><strong>Quadratic Unconstrained Binary Optimization (QUBO)</strong>: Quantum annealing shows 2-5x speedup on D-Wave for specific instances</li> | |
| <li><strong>Graph Isomorphism</strong>: Theoretical speedup possible with Grover's algorithm (√N vs N)</li> | |
| <li><strong>Traveling Salesman</strong>: Hybrid quantum-classical approaches show promise for medium-sized problems</li> | |
| </ul> | |
| <h2>Limitations</h2> | |
| <p>The speedups are highly dependent on:</p> | |
| <ol> | |
| <li>Problem encoding efficiency</li> | |
| <li>Noise levels in current quantum hardware</li> | |
| <li>Comparison to highly optimized classical algorithms</li> | |
| </ol> | |
| <h2>Comparative Analysis</h2> | |
| <pre> | |
| Problem Classical Time Quantum Time Speedup | |
| ------------------------------------------------------- | |
| Graph Partition O(2^n) O(√(2^n)) Exponential | |
| MaxCut O(n^3) O(n^2) Polynomial | |
| TSP O(n!) O(√(n!)) Exponential | |
| </pre> | |
| </div> | |
| </div> | |
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| <p class="text-sm font-medium">"Quantum Algorithms for Combinatorial Optimization" - Nature (2021)</p> | |
| <p class="text-xs text-gray-500">DOI: 10.1038/s41586-021-03222-x | Cited by 142</p> | |
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| <p class="text-sm font-medium">"Practical Quantum Speedups for Optimization" - PRX Quantum (2022)</p> | |
| <p class="text-xs text-gray-500">DOI: 10.1103/PRXQuantum.3.020304 | Cited by 87</p> | |
| </div> | |
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| <p class="text-sm font-medium">"Limits of Quantum Speedup in Optimization" - Quantum (2020)</p> | |
| <p class="text-xs text-gray-500">DOI: 10.22331/q-2020-10-12-342 | Cited by 203</p> | |
| </div> | |
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| <!-- Version History --> | |
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| <span class="text-sm font-medium">Version 1.2</span> | |
| <span class="ml-2 px-2 py-1 text-xs bg-indigo-100 text-indigo-800 rounded-full">Current</span> | |
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| <div class="text-xs text-gray-500">2 hours ago</div> | |
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| <div class="text-sm mb-2">Refined hypothesis and added comparative analysis table</div> | |
| <div class="text-xs text-gray-500">Commit by Dr. Alice Chen</div> | |
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| <span class="text-sm font-medium">Version 1.1</span> | |
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| <div class="text-xs text-gray-500">1 day ago</div> | |
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| <div class="text-sm mb-2">Added limitations section based on peer feedback</div> | |
| <div class="text-xs text-gray-500">Commit by Dr. Bob Johnson</div> | |
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| <span class="text-sm font-medium">Version 1.0</span> | |
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| <div class="text-xs text-gray-500">3 days ago</div> | |
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| <div class="text-sm mb-2">Initial experiment setup and first results</div> | |
| <div class="text-xs text-gray-500">Commit by Dr. Alice Chen</div> | |
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| <div class="text-sm font-medium mb-2">Hypothesis Changes</div> | |
| <div class="text-sm p-3 rounded diff-added"> | |
| <p>Quantum computers can solve optimization problems faster than classical computers for certain problem classes, specifically in combinatorial optimization.</p> | |
| </div> | |
| <div class="text-sm p-3 rounded diff-removed mt-1"> | |
| <p>Quantum computers are faster than classical computers for optimization problems.</p> | |
| </div> | |
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| <div class="text-sm font-medium mb-2">Added Content</div> | |
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| <h3>Comparative Analysis</h3> | |
| <pre> | |
| Problem Classical Time Quantum Time Speedup | |
| ------------------------------------------------------- | |
| Graph Partition O(2^n) O(√(2^n)) Exponential | |
| MaxCut O(n^3) O(n^2) Polynomial | |
| TSP O(n!) O(√(n!)) Exponential | |
| </pre> | |
| </div> | |
| </div> | |
| <div> | |
| <div class="text-sm font-medium mb-2">Modified Content</div> | |
| <div class="text-sm p-3 rounded diff-changed"> | |
| <p>The speedups are highly dependent on:</p> | |
| <ol> | |
| <li>Problem encoding efficiency</li> | |
| <li class="diff-added">Noise levels in current quantum hardware</li> | |
| <li>Comparison to highly optimized classical algorithms</li> | |
| </ol> | |
| </div> | |
| </div> | |
| <div> | |
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| <img class="h-6 w-6 rounded-full mr-2" src="https://images.unsplash.com/photo-1494790108377-be9c29b29330?ixlib=rb-1.2.1&ixid=eyJhcHBfaWQiOjEyMDd9&auto=format&fit=facearea&facepad=2&w=256&h=256&q=80" alt=""> | |
| <div> | |
| <p class="text-sm font-medium">Dr. Sarah Williams</p> | |
| <p class="text-xs text-gray-600">"Consider adding more quantitative comparisons between quantum and classical approaches."</p> | |
| <div class="flex items-center mt-1 text-xs text-gray-500"> | |
| <i class="fas fa-thumbs-up text-blue-500 mr-1"></i> 3 | |
| <i class="fas fa-thumbs-down text-gray-400 ml-2 mr-1"></i> 0 | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| <script> | |
| // Toggle version dropdown | |
| document.getElementById('versionDropdownBtn').addEventListener('click', function() { | |
| const dropdown = document.getElementById('versionDropdown'); | |
| dropdown.classList.toggle('hidden'); | |
| }); | |
| // Close dropdown when clicking outside | |
| document.addEventListener('click', function(event) { | |
| const dropdownBtn = document.getElementById('versionDropdownBtn'); | |
| const dropdown = document.getElementById('versionDropdown'); | |
| if (!dropdownBtn.contains(event.target) && !dropdown.contains(event.target)) { | |
| dropdown.classList.add('hidden'); | |
| } | |
| }); | |
| // New notebook button | |
| document.getElementById('newNotebookBtn').addEventListener('click', function() { | |
| alert('Opening new notebook session...'); | |
| // In a real app, this would open a modal or new page for experiment setup | |
| }); | |
| // Simulate markdown rendering (in a real app, you'd use a proper markdown renderer) | |
| document.querySelectorAll('.markdown-content').forEach(el => { | |
| // This is just a placeholder - in reality you'd use a library like marked.js | |
| // Here we're just demonstrating the styled output | |
| }); | |
| </script> | |
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