(Fortune Magazine) -- She awakes early on the morning of April 10, 2030, in the capable hands of her suburban Chicago apartment. All night, microscopic sensors in her bedside tables have monitored her breathing, heart rate, and brain activity.

The tiny blood sample she gave her bathroom sink last night has been analyzed for free radicals and precancerous cells; the appropriate preventative drugs will be delivered to her hotel in Atlanta this evening. It's an expensive service, but as a gene therapist, Sharon Oja knows it's worth it.

She steps into the shower. The tiles inside detect her presence and start displaying the day's top headlines. The manned mission to Mars is going to launch ahead of schedule. U.S. military drones have destroyed another terrorist training camp using smart dust. A top Manhattan banker has been found guilty of fraud and sentenced to 10 years of low tech.

And today is the 20th anniversary of the very first quantum computer.

Sharon laughs. It is her 24th birthday, and she has little idea what the world was like before the qubits - the smallest pieces of quantum information - took over.

She dresses and picks out a stylish straw fedora. Quantum computing has brought an unexpected revival in haberdashery: Inside the hatband is Sharon's communication center and intelligent assistant, which has scanned and sorted the 500,000 e-mails she received overnight.

By the time she reaches the car, it has beamed the 10 most urgent ones and her travel schedule to her visual cortex. The text scrolls down in the bottom of her field of vision.

The Hydrogen Honda knows it is going to be an unseasonably warm day - indeed, thanks to quantum computer simulations it has known today's temperature for five years - and rolls the top down for her. Sharon drives to the freeway, steers into the Smart Lane, then relinquishes the wheel. The hatband screens a birthday video from her parents and a super-encrypted memo from her boss.

At the airport there is no ticket check-in or security line. Sharon simply walks through the revolving door, which scans her for dangerous items, picks up her identity, confirms her reservation, and delivers her gate number, all in the space of a second. She doesn't even bother to check whether the plane is on time - since flight patterns are as computable as the weather, O'Hare hasn't had a late departure in five years.

At the bag drop-off, she sees a familiar man in a yarmulke-like brain cap. The hatband is already on the case and flashes his virtual business card alongside his top 10 Google (Charts) results. "Dr. Horton," she calls out. "So nice to see you again. How was the diabetes conference?" Only the slightest flicker of Horton's eyes betrays that he is Googling her details too. "Hello, Ms. Oja," he says. "Many happy returns of the day." Sharon grins and gives silent thanks to the quantum computer's creators.

Science fiction, right? Sure - just like satellites, moon shots, and the original microprocessor once were. To scientists on the quantum computing frontier, this scenario is conservative.

"The age of computing has not even begun," says Stan Williams, a research scientist at Hewlett-Packard (Charts). "What we have today are tiny toys not much better than an abacus. The challenge is to approach the fundamental laws of physics as closely as we can."

Traditional computing, with its ever more microscopic circuitry etched in silicon, can take us only so far: Moore's law, which dictates that the amount of computing power you can squeeze into the same space will double every 18 months, is set to run into a silicon wall by 2015. (The chief culprit is overheating, caused by electrical charges running through ever more tightly packed circuits.)

If we want to keep computer progress on track after that and be able to do all the amazing things in Sharon's life, we have to figure out how to manipulate the brain-bending rules of the quantum realm - an Alice in Wonderland world of subatomic particles that can be in two places at once.

Luckily some of the world's leading research agencies and technology companies are on the case. Single electrons have been made to adjust their spin. Subatomic circuitry is within our grasp. But because the breakthroughs are hidden in esoteric journals and described in language that can give even today's savviest computer users headaches, it is easy to miss the significance of what is going on.

Tangible evidence of the quantum revolution hit the market in July, when Freescale Semiconductor, a Motorola (Charts) spinoff, began commercial shipments of magnetic random-access memory (MRAM) chips. You'll probably notice MRAM first when you buy a digital camera that doesn't take any time to store a picture. Within a matter of years, your new laptop will switch on like a light.

MRAM gets its speed from something called the giant magnetoresistive effect, or GMR. Although it sounds like something out of an X-Men film, GMR has to do with the fact that if you place layers of ultrathin magnetic film on top of one another and alternate their polarity, you get resistance. That is, the electrons can be spun in one direction or the other. Electrons spin like a top or a billiard ball in some direction relative to a magnetic field. Flip the direction of the field, and the electron flips the direction of its spin. This very basic quantum effect can be used like a binary bit, its direction labeled "0" or "1" and employed to store digital information.

In conventional computing these zeroes and ones are created by switching an electric current on and off. Spins are less affected by the environment than electric charges and take longer to decay. Also, keeping an electric charge in position requires continuous power; when computers lose power, the charge goes away. With a magnetic device the memory stays put when the power shuts off.

As a bonus - and it's a fairly major bonus - if you take electricity out of the equation, you get rid of the overheating problem that is undercutting Moore's law.

This memory breakthrough was in large part the doing of DARPA, the Defense Advanced Research Projects Agency - the same Pentagon gang that gave us the Internet. In particular, it's due to a 62-year-old physicist named Stuart Wolf, who recently left DARPA for the University of Virginia. Since 1993 the agency has invested more than $200 million in Wolf-created quantum research programs.

While MRAM is just about memory, the ability to control spin in a computational device - "spintronics" is the word Wolf has coined to describe this work - has huge implications.

The next step: putting spin to work in actual computation. A team at the University of California at Santa Barbara, led by David Awschalom, has made big progress in this direction by controlling electron spins in semiconductors and other materials a few nanometers in size. This could mean not just an end to overheating worries but the possibility of moving computer technology into the molecular realm. With molecular-level chips, a laptop could have more computing power than trillions of today's supercomputers.

And even molecular-level computers could soon be outmoded behemoths. In 2004, Dan Rugar of IBM (Charts) performed what the American Institute of Physics dubbed the most important experiment of the year by using a magnet to control the spin of a single electron. In theory, that means we could have subatomic-scale circuitry. At that level the behavior of particles is more complicated and can - again, in theory - do even more powerful things.

Down in the subatomic world, the same magnetic spin can be up and down and everything in between - all at the same time. It's a strange piece of quantum mechanics known as superposition, made possible because electrons sometimes behave more like waves than particles.

Try picturing a piece of string, fixed at both ends and vibrating. If you get the vibration right, the string will be moving up at one end and down at the other. And as a wave, it will have every value in between.

In the binary math of today's computers, each bit is either a zero or a one. But if each electron in a row of atoms can be in two or more places at once, and we can use these positions for computing, the power of exponential math kicks in.

Consider a quantum bit, or qubit, that can represent two values simultaneously. Two qubits linked together could represent four values at once, three could represent eight, and so on. Twenty qubits could represent almost a million numbers (two to the power of 20) simultaneously.

Harnessing the power of this exponential growth means you can tackle any problem that gets exponentially larger, and there are lots of important ones. We can't reliably predict weather or traffic or the mutation of viruses today because the number of variables and possible interactions is too massive for current computers. Qubits would change that.

Another potential advance involves something called entanglement - what Einstein famously described as "spooky action at a distance." It is a sort of particle love: Once they have become entangled, two subatomic particles move in lockstep, even at a distance.

Harnessing this capability could enable completely secure communications, because tampering with one particle will destroy the communications value of its partner. This is crucial, since quantum computers would be capable of breaking any cryptological code now used.

Granted, changing the spin of an electron is a long way from building a circuit out of the same, and history is littered with promising technologies that didn't pan out. Intel CEO Paul Otellini is one major quantum skeptic, increasingly reluctant to fund R&D for it. Reports of the death of silicon have been greatly exaggerated, he says.

But quantum computing scientists are surprisingly bullish, for scientists. "This is the most exciting time of my life, and I'm not young," says Eli Yablonovitch, professor of electrical engineering at UCLA. "We're looking forward to a direct impact on everybody in the world."

Quantum computing "is tantalizingly possible, just on the edge of being too difficult, with remarkable progress every year," says Harvard's Charles Marcus. "As time goes by we'll be saying to ourselves, 'I can't believe this was so hard.' We'll have undergraduates doing it. That's just the nature of science."

Ask scientists to predict how quantum technology will change the world over the next 20 years or so, and their imaginations go wild.

Computers everywhere Their most common prediction is that we will see - or rather, we won't see - computers everywhere, painted onto walls, in chairs, in your body, communicating with one another constantly and requiring no more power than that which they can glean from radio frequencies in the air.

'I won't have to remember anything' Exponentially smarter computers also raise the possibility of achieving a couple of computer science's long-held goals: a human-brain-imitating neural network and true (or near-true) artificial intelligence. "This is going to be my mental prosthesis," says UCLA's Yablonovitch. "Everything I want to know, I can look up. Everything I can forget, I can find. I'm going to get old, but it won't matter. I won't have to remember anything."

Computers in your headband Of all the scientists' visions of the quantum future, Wolf's may be the most out-there. "The vision is that we don't have a laptop anymore," Wolf says. "We don't have a cellphone. We wear it. It's a headband. And instead of having a screen, we have direct coupling into the right side of the brain."

Recent experiments suggest it's actually quite easy to send information to the brain in a precisely targeted manner using ultrasound. Sony filed a patent earlier this year for ultrasonic technology that will beam videogames into our brains.

But these won't be like any videogames we know today. Having your brain surrounded by a thin band of ultrasonic transducers controlled by hypersmart quantum computers, all linked up to a global network with infinite bandwidth, means that any sense can be stimulated in any way. You can be made to see, hear, touch, taste, or smell anything.

Getting instructions back from the brain - mind-reading computers, in other words - is harder but not impossible (neuroscientists have already developed communication devices for the disabled that read brain waves).

Wolf anticipates that within 20 years, instead of cellphone conversations we will have "network-enabled telepathy." Imagine you're on a busy street, and a small percentage of the people in the crowd around you have decided to let their headbands transmit their field of vision - you could literally see around corners. A vehicle could be driven by thought. Dreams could be recorded and passed around online as easily as we share photos on Flickr.

Yes, some people will find it unsettling, which happens with almost every new technology. But while the contours of how quantum computing will apply to society are unclear, the map for how we get there isn't.

"The amazing thing is there's nothing I can see as a big roadblock to this," says Wolf. It's a question of when, not if; exactly when (and where) will be determined by the amount of research dollars available. The U.S. certainly isn't alone in this race; the Europeans and Japanese are funding huge research efforts. India and China are getting onboard as well.

Beyond the actual creation of a quantum computer, our chief limitations are the imaginations of software engineers. This will be the major challenge of the Google geniuses of tomorrow: to take computing and networking power that is effectively infinite and create interfaces that are simple enough for mere mortals to understand.

But what about that headband? Won't it creep us out? "What people will not like is having it implanted," Wolf believes. "But if you're just wearing it and it's ultrasonically connected, I mean, you could always take it off."

As with all previous disruptive technologies - radio, television, the Internet - it will probably take a new generation raised to think of quantum headbands as normal for its potential to be truly realized. Sharon Oja, born in 2006, will barely realize the good fortune she, and the world, have inherited.

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Scenario planner and noted futurist Peter Schwartz is co-founder and chairman of Global Business Network. Rita Koselka is a San Francisco-area writer and consultant. Reporter Associate Christopher Tkaczyk; additional reporting by Chris Taylor