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Every Unitary Fit Into Shallow Quantum Depth
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.
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.
Limits and context
- This is a theoretical existence result with exponential width, not a claim that arbitrary useful circuits have suddenly become practical on current quantum hardware.
Key claims
The construction parallelized arbitrary operations with exponentially many ancillas—and reached constant depth only with unbounded fan-out.
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.
Evidence: source-2026-10-01-002
Sources
- arXiv preprint 2609.40351arXiv · primary research
Corrections
No corrections have been recorded for this story.