The Moore parity conjecture asserts that parity cannot be computed exactly by constant-depth quantum
circuits with arbitrary one-qubit gates and unbounded-arity Toffoli gates using
polynomially many qubits, with auxiliary qubits starting
and ending in the zero state. The parity of 
is 
.
Gates within a layer have disjoint supports, so unbounded fanout is not supplied
as a primitive operation. The original clean coherent formulation is related to fanout
by conjugation with Hadamard gates.
Moore Parity Conjecture
See also
Boolean Circuit, Parity, Quantum Circuit, QubitExplore with Wolfram|Alpha
References
Moore, C. "Quantum Circuits: Fanout, Parity, and Counting." 17 Mar 1999. https://arxiv.org/abs/quant-ph/9903046.Cite this as:
Weisstein, Eric W. "Moore Parity Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MooreParityConjecture.html