Chinese President Hu Jintao's visit to the United States comes amid rising military tensions between the world's leading powers. And as China flexes its growing might, the Obama administration and the U.S. military are looking for ways to respond.

In a stark reminder of the stakes for U.S.-China military relations, Taiwan attempted to embarrass the Chinese, and perhaps the Pentagon, by testing 19 missiles in response to a host of new Chinese weapons advancements.

One-third of the Taiwanese rockets failed, bolstering the island nation's argument that the U.S. should sell it more F-16 fighter jets, even if it angers China's leaders.

The tests echoed an incident last week when the Chinese military tested a prototype of its J-20 stealth fighter jet during a visit by Defense Secretary Robert Gates to Beijing, a move that those traveling with Gates said surprised China's civilian leaders.

"The civilian leadership has seemed surprised by the test and assured me that it had nothing to do with my visit," said Gates while speaking to a group of reporters at China's Great Wall.

Some China experts, though, argue that it is unlikely that China's civilian leadership was unaware of the test flight.

“Frankly, most intelligence people and China watchers see little if no daylight between Chinese civilian and military leadership with respect to issues of major consequences,” said Lt. Gen.David Deptula, who retired as the Air Force intelligence chief three months ago. “President Hu does not micro-manage the military. Clearly, there is no fissure between Chinese leadership.

What has surprised Pentagon officials more is the similarity between China's J-20, the prototype of China's first stealth fighter jet, and Lockheed Martin's FB-22. Several current and former U.S. Air force commanders say its design was likely obtained through online espionage.

Defense officials say that each day, there are more than 1,000 attempts to break into the Pentagon's classified computers - most of them emanating from China.

“The techniques used in the design of the J-20 actually make it appear to be somewhat more sophisticated design than the Russian T-50,” said Deptula.

What continues to baffle Pentagon officials is China's galloping defense budget, which has risen by 464 percent in the past 20 years, according to the Stockholm International Peace Institute.

The Pentagon's budget rose by 31 percent during the same period and is now facing cuts. China's official budget – $98.8 billion in 2009 – is still a fraction of the size of the U.S. budget of more than $600 billion per year.

But it is the type of weapons that China is acquiring that has the Pentagon most worried.

China has a new mobile, land-based ballistic missile that can sink an aircraft carrier. The Dong Feng 21D, known as a “carrier killer,” was revealed in December and includes technology that even the U.S. does not have.

China has added 30 submarines to its fleet in the past decade, while the U.S. had six newly commissioned Virginia class submarines and one Seawolf class sub during the same period, according to the U.S. Navy.

Chairman of the Joint Chiefs of Staff Adm. Mike Mullen expressed concern last week that China's race to procure state-of-the-art weapons is focused on the U.S.

“China is investing in very high-end, high-tech capabilities. And the question that is always out there is to try to understand exactly why,” Mullen asked. “Many of these capabilities seem to be focused very specifically on the United States.”

Secretary of State Hillary Clinton reiterated Mullen's concerns.

“I would be the first to admit that distrust lingers on both sides,” Clinton said during a speech at the State Department. “The United States and the international community have watched China's efforts to modernize and expand its military, and we have sought clarity as to its intentions.”

Some in the Air Force have argued that they would like to see Gates reconsider his new limits on the F-22 program. Gates halted F-22 production at 187 planes for budgetary reasons, but the Air Force argues that producing 12 planes a year – the equivalent in cost of two weeks of fighting in Afghanistan – would be enough to maintain U.S. air superiority for decades.

"What this should be, is a wake up call for the strategic complacency of those who believe that the U.S. will continue to maintain air and naval dominance in the Pacific," said Deptula.

Asian military expert Gordon Chang says that China is deadly serious about its plans to challenge American military supremacy.

“Since last February, Chinese flag officers and senior colonels have been talking  about waging war against the United States,” said Chang, author of “Nuclear Showdown: North Korea Takes on the World,”

“I think Secretary Gates needs to understand that, of course, the Chinese military is configuring themselves to fight us.”