



01951nas a2200217   4500008004100000245008300041210006900124260001500193490000600208520129200214100002001506700002301526700001701549700002201566700002401588700002301612700001301635700002301648700002501671856003701696       2022                        eng d00aImplementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions0 aImplementing a Fast Unbounded Quantum Fanout Gate Using PowerLaw  c10/27/20220 v43 a<p>The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor&#39;s algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α&le;D. As a corollary, we show that power-law systems with α&le;D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques.&nbsp;</p>1 aGuo, Andrew, Y.1 aDeshpande, Abhinav1 aChu, Su-Kuan1 aEldredge, Zachary1 aBienias, Przemyslaw1 aDevulapalli, Dhruv1 aSu, Yuan1 aChilds, Andrew, M.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2007.0066200982nas a2200169   4500008004100000245008200041210006900123260001500192300001100207490000700218520047100225100002300696700001800719700002100737700001700758856003700775       2013                        eng d00aInterpolatability distinguishes LOCC from separable von Neumann  measurements0 aInterpolatability distinguishes LOCC from separable von Neumann   c2013/06/25  a1122040 v543 a  Local operations with classical communication (LOCC) and separable operations
are two classes of quantum operations that play key roles in the study of
quantum entanglement. Separable operations are strictly more powerful than
LOCC, but no simple explanation of this phenomenon is known. We show that, in
the case of von Neumann measurements, the ability to interpolate measurements
is an operational principle that sets apart LOCC and separable operations.
1 aChilds, Andrew, M.1 aLeung, Debbie1 aMancinska, Laura1 aOzols, Maris  uhttp://arxiv.org/abs/1306.5992v101273nas a2200145   4500008004100000245009500041210006900136260001400205490000700219520078700226100002301013700002401036700002301060856004401083       2007                        eng d00aImproved quantum algorithms for the ordered search problem via  semidefinite programming
0 aImproved quantum algorithms for the ordered search problem via s  c2007/3/260 v753 a  One of the most basic computational problems is the task of finding a desired
item in an ordered list of N items. While the best classical algorithm for this
problem uses log_2 N queries to the list, a quantum computer can solve the
problem using a constant factor fewer queries. However, the precise value of
this constant is unknown. By characterizing a class of quantum query algorithms
for ordered search in terms of a semidefinite program, we find new quantum
algorithms for small instances of the ordered search problem. Extending these
algorithms to arbitrarily large instances using recursion, we show that there
is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433
log_2 N queries, which improves upon the previously best known exact algorithm.
1 aChilds, Andrew, M.1 aLandahl, Andrew, J.1 aParrilo, Pablo, A.  uhttp://arxiv.org/abs/quant-ph/0608161v1