Quantum Circuits: Fanout, Parity, and Counting

Quantum Cir uits: Fanout, Parity, and Counting

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 ...

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...

Generic parity generators design using LTEx methodology: A quantum-dot cellular automata based approach

Quantum-dot Cellular Automata (QCA) is a prominent paradigm that is considered to continue its dominance in thecomputation at deep sub-micron regime in nanotechnology. The QCA realizations of five-input Majority Voter based multilevel parity generator circuits have been introduced in recent years. However, no attention has been paid towards the QCA instantiation of the generic (n-bit) even and ...

Generic parity generators design using LTEx methodology: A quantum-dot cellular automata based approach

Quantum-dot Cellular Automata (QCA) is a prominent paradigm that is considered to continue its dominance in thecomputation at deep sub-micron regime in nanotechnology. The QCA realizations of five-input Majority Voter based multilevel parity generator circuits have been introduced in recent years. However, no attention has been paid towards the QCA instantiation of the generic (n-bit) even and ...