Anticoncentration and distinctness of depth-one random quantum circuits
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Can a depth-one product ensemble of single-qubit gates satisfy the entangled-anticoncentration and distinctness requirements used in the stated nonadaptive quantum construction? The candidates are independent complex Cliffords or exact one-qubit 2-designs.
Why it matters and what counts as progress
Why it matters: A depth-one product ensemble would show that entangling gates are unnecessary for this specific distinctness ingredient.
What counts as progress: Prove the (2/3)^n anticoncentration error and negligible distinctness for polynomially many queries, or reduce ensemble resources further.
How the problem developed
Zhengyu Ji, Yi-Kai Liu and Fang Song Introduced pseudorandom quantum states and unitaries and proposed phase–Hadamard layers as a route to pseudorandom-unitary constructions.
- 2 Sept 2026 · Reported claim [2]
Asad Raza, Jens Eisert and Bill Fefferman, with ChatGPT 5.6 Sol Showed that independent random one-qubit Clifford gates give depth-one distinctness and entangled anticoncentration error (2/3)^n; the authors credit ChatGPT with proposing this non-entangling construction.
AI contribution
Distinctness threshold for pseudorandom unitaries
Independent random one-qubit complex Cliffords, or exact one-qubit 2-designs, form a depth-one n-qubit tensor-product ensemble with entangled anticoncentration error (2/3)^n and negligible distinctness for polynomially many queries.
Sources
Website timeline
Publication dates and editorial changes.
ChatGPT-origin Clifford construction gives depth-one distinctness