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    "headline": "Every Unitary Fit Into Shallow Quantum Depth",
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    "dek": "The construction parallelized arbitrary operations with exponentially many ancillas—and reached constant depth only with unbounded fan-out.",
    "summary": "The construction parallelized arbitrary operations with exponentially many ancillas—and reached constant depth only with unbounded fan-out.",
    "body_text": "Nehoran and Yuen show that any n-qubit unitary can be approximated with one- and two-qubit gates in polynomial depth, overturning the possibility that exponential depth is universally necessary when unlimited workspace is allowed. The price is 2^O(n) ancilla qubits. If the gate model also permits unbounded fan-out, the depth becomes constant. The proof links unitary synthesis to locally decodable codes and private information retrieval. This is a theoretical existence result with exponential width, not a claim that arbitrary useful circuits have suddenly become practical on current quantum hardware.",
    "why_it_matters": "The construction parallelized arbitrary operations with exponentially many ancillas—and reached constant depth only with unbounded fan-out.",
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      "This is a theoretical existence result with exponential width, not a claim that arbitrary useful circuits have suddenly become practical on current quantum hardware."
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        "text": "The construction parallelized arbitrary operations with exponentially many ancillas—and reached constant depth only with unbounded fan-out.",
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        "qualification": "This is a theoretical existence result with exponential width, not a claim that arbitrary useful circuits have suddenly become practical on current quantum hardware."
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    "tags": [
      "quantum circuits",
      "unitary synthesis",
      "circuit depth"
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      "source_id": "source-2026-10-01-002",
      "title": "arXiv preprint 2609.40351",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2609.40351",
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      "published_at": "2026-09-30T13:59:12.000-04:00",
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    "name": "The Machine Press",
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    "description": "A daily newspaper for the age of artificial intelligence."
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    "title": "Every Unitary Fit Into Shallow Quantum Depth",
    "publisher": "The Machine Press",
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