New lower bounds for quantum Hamiltonians

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 ...

A new proto ol and lower bounds for quantum oin

Some Lower Bounds for Estrada Index

New Lower Bounds for -Nets

Following groundbreaking work by Haussler and Welzl (1987), the use of small -nets has become a standard technique for solving algorithmic and extremal problems in geometry and learning theory. Two significant recent developments are: (i) an upper bound on the size of the smallest -nets for set systems, as a function of their so-called shallow-cell complexity (Chan, Grant, Könemann, and Sharpe)...

Lower Bounds for Quantum Search and Derandomization

We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T ∈ O( √ N) then the error is lower bounded by a constant. If we want error ≤ 1/2 then we need T ∈ Ω(N) queries. We apply this to show that a quantum computer cannot do much better than a classical computer...