Bennett, Bernstein, Brassard, and Vazirani proved in 1996 that a brute-force key search on a quantum computer cannot be faster than roughly 2 < sup > n / 2 </ sup > invocations of the underlying cryptographic algorithm, compared with roughly 2 < sup > n </ sup > in the classical case.

It was a promise that, in the event, he was unable to keep after his search for alternative landing grounds proved fruitless.

The search for a suitable and affordable place to live proved to be very difficult.

A major search for the stone had been ordered by the British Government, but this proved unsuccessful.

They proved that it is not in fact any faster than performing a single partial search.

An extended search for an anchorage at King Edward VII Land proved equally fruitless, so Shackleton was forced to break his undertaking to Scott and set sail for McMurdo Sound, a decision which, according to second officer Arthur Harbord, was " dictated by common sense " in view of the difficulties of ice pressure, coal shortage and the lack of any nearer known base.

The problem with type B is that it relies on the program being able to decide which moves are good enough to be worthy of consideration (' plausible ') in any given position and this proved to be a much harder problem to solve than speeding up type A searches with superior hardware and search extension techniques.

A massive search and rescue operation proved fruitless.

Despite an initial search for a permanent successor to Deayton, having a different guest host each week proved successful, with average audience figures increasing from 6 million to 7 million.

Gnutella's original design, featuring total elimination of the server network in favor of purely peer-to-peer searching, quickly proved to be infeasible due to massive search traffic overhead between peers.

Gray's cousin Robert Leffingwell was the first on the job but proved inadequate and the strip was handed over to Tribune staff artist Henry Arnold and general manager Henry Raduta as the search continued for a permanent replacement.

When attempts at returning to the drill sites and looking for rocks proved fruitless, Penfield abandoned his search, published his findings and returned to his Pemex work.

Although PageRank was more difficult to game, webmasters had already developed link building tools and schemes to influence the Inktomi search engine, and these methods proved similarly applicable to gaming PageRank.

They started out their life as accidental blackmailers ( all in search of adventure and money ), but the detecting life soon proved more profitable and much more exciting.

They rode on the backs of great dragons, travelling throughout the cosmos in search of plunder, and proved superior to all other races and cultures which they met and destroyed-some of these being themselves highly technological interstellar empires.

This expedition also proved successful in its primary goal by discovering copper in the Coppermine River basin ; however, an intensive search of the area yielded only one four-pound lump of copper and commercial mining was not considered viable.

These efforts proved to be futile, and the search was eventually called off.

Even though normally an Orthodox beth din requires a minimum of three Jews knowledgeable and observant of Halakha ( Jewish Law ), in new communities and exigencies, providing a thorough search has proved unfruitful, halakhah provides that even one Orthodox Jew can establish a beth din, since every Orthodox community is required to establish its own beth din.

The search for a new guitarist proved more difficult.

Sun and his twin brother Sun Zhiwei proved a theorem about what are now known as the Wall-Sun-Sun primes that guided the search for counterexamples to Fermat's last theorem.

Born in Huai ' an, Jiangsu, Sun and his twin brother Sun Zhihong proved a theorem about what are now known as the Wall-Sun-Sun primes that guided the search for counterexamples to Fermat's last theorem.

Throughout the fifty years from 1867 to 1914, it proved difficult to reach adequate compromises in the governance of Austria-Hungary, leading many to search for non-diplomatic solutions.

While it proved unfruitful, Spence became a sailor and Kennedy joined a search for the Arctic explorer, Sir John Franklin.

It also proved successful in the search for a lost hydrogen bomb following the 1966 Palomares B-52 crash in Spain.

The action centers about a group of outspoken and offbeat students sitting around a table in a cafeteria and their collective and ultimately fruitless search for a cup of hot coffee.

Aberration should not be confused with stellar parallax, although it was an initially fruitless search for parallax that first led to its discovery.

After a fruitless search, Kelly returned to Pittsburgh, to his first position as a choreographer with the Charles Gaynor musical revue Hold Your Hats at the Pittsburgh Playhouse in April, 1938.

He is motivated to continue his fruitless search by the promise of a large reward, recently doubled, upon the letter's safe return, and he will pay 50, 000 francs to anyone who can help him.

This turn of events caused him to question the overall utility of demystifying culture for the masses, thinking it might be a fruitless attempt, and drove him deeper in his search for individualistic meaning in art.

A fruitless search for silphium by Romans in the reign of the emperor Vespasian is an amusing sub-plot of the crime novel Two for the Lions by Lindsey Davis.

The search for a fossil showing transitional traits between apes and humans, however, was fruitless until the young Dutch geologist Eugène Dubois found a skullcap, a molar and a femur on the banks of Solo River, Java in 1891.

In 1869, he led a fruitless search for the explorer Ludwig Leichhardt, in the desert west of present-day Leonora.

A comprehensive search of a wide area ( including what is now known to have been the crash site ) was fruitless, and the fate of the aircraft and occupants remained unknown for over 50 years.

After a fruitless trip to England in search of employment, Underhill returned to Boston where he sold his house and land and joined Wheelwright, who had settled in Dover, New Hampshire.

* c. 1575: Martin Frobisher continues the fruitless search for a passage to Asia.

* 1610-11: The English explorer Henry Hudson, in Dutch service, continues the fruitless search for a passage to Asia.

The search proves fruitless.

The Lizard Lifeboat found a serious hole in its hull when it finally returned to its slipway after a fruitless search.

For the postmodernist, no ordering system exists, so a search for order is fruitless and absurd.

Despite this, the fruitless search for a quantitive relationship allowing the logical derivation of prices from values ( a labor theory of price ) with the aid of mathematical functions has occupied many economists, producing the famous transformation problem literature.

The moths inadvertently pollinate them by transferring pollen from flower to flower in their fruitless search for nectar.

In the following year, he took her to sea in a fruitless search for British West Indiamen ; but he and his ship eventually achieved success in 1779.

As Anne's search continues to be fruitless, Jack attempts to persuade her to return with him to the United States and form a family with him and Dominic ; Anne refuses, determined to continue searching for Gilbert in Germany.

Following the first raid on January 7, 500 troops under the command of General Robert B. Mitchell consisting of the Seventh Iowa Cavalry, the First Nebraska Veteran Volunteer Cavalry, and Companies " B " and " C ," First Nebraska Militia ( mounted ) had been removed from the Platte and were engaged in a fruitless search for hostile Indians on the plains south of the Platte.