The Aaronson-Kuperberg unitary synthesis problem asks whether a polynomial-size quantum oracle circuit can approximate an arbitrary unitary
transformation after a suitable Boolean oracle is
chosen. The oracle may depend on the target transformation,
whereas the circuit is constructed from the number of qubits
alone. For a Boolean function 
, the oracle gate acts by 
.
Unitary Synthesis Problem
See also
Diamond Norm, Oracle, Quantum Channel, Quantum Circuit, Unitary MatrixExplore with Wolfram|Alpha
References
Aaronson, S. "Open Problems Related to Quantum Query Complexity." ACM Trans. Quantum Comput. 2, Article 14, 2021. https://doi.org/10.1145/3488559.Lombardi, A.; Ma, F.; and Wright, J. "A One-Query Lower Bound for Unitary Synthesis and Breaking Quantum Cryptography." In Proc. 56th Annual ACM Symposium on Theory of Computing (Ed. B. Mohar, I. Shinkar, and R. O'Donnell). New York, NY: ACM, pp. 979-990, 2024. https://doi.org/10.1145/3618260.3649650.Cite this as:
Weisstein, Eric W. "Unitary Synthesis Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnitarySynthesisProblem.html