Counting , Fanout , and the Complexity of Quantum Acc Frederic

Counting, fanout and the complexity of quantum ACC

We propose definitions of QAC, the quantum analog of the classical class AC of constant-depth circuits with AND and OR gates of arbitrary fan-in, and QACC[q], the analog of the class ACC[q] where Modq gates are also allowed. We prove that parity or fanout allows us to construct quantum MODq gates in constant depth for any q, so QACC[2] = QACC. More generally, we show that for any q, p > 1, MODq...

Quantum Circuits: Fanout, Parity, and Counting

We propose definitions of QAC, the quantum analog of the classical class AC of constant-depth circuits with AND and OR gates of arbitrary fan-in, and QACC[q], where n-ary MODq gates are also allowed. We show that it is possible to make a ‘cat’ state on n qubits in constant depth if and only if we can construct a parity or MOD2 gate in constant depth; therefore, any circuit class that can fan ou...

Quantum Cir uits: Fanout, Parity, and Counting

Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation...

Quantum lower bounds for fanout

We consider the resource bounded quantum circuit model with circuits restricted by the number of qubits they act upon and by their depth. Focusing on natural universal sets of gates which are familiar from classical circuit theory, several new lower bounds for constant depth quantum circuits are proved. The main result is that parity (and hence fanout) requires log depth quantum circuits, when ...