Imagine a computer whose memory is exponentially larger than its apparent physical size; a computer that can manipulate an exponential set of inputs simultaneously; a computer that computes in the twilight zone of space. You would be thinking of a quantum computer. Relatively few and simple concepts from quantum mechanics are needed to make quantum computers a possibility. The subtlety has been in learning to manipulate these concepts. Is such a computer an inevitability or will it be too difficult to build?
By the strange laws of quantum mechanics, Folger, a senior editor at Discover, notes that; an electron, proton, or other subatomic particle is “in more than one place at a time,” because individual particles behave like waves, these different places are different states that an atom can exist in simultaneously.
What’s the big deal about quantum computing? Imagine you were in a large office building and you had to retrieve a briefcase left on a desk picked at random in one of hundreds of offices. In the same way that you would have to walk through the building, opening doors one at a time to find the briefcase, an ordinary computer has to make it way through long strings of 1’s and 0’s until it arrives at the answer. But what if instead of having to search by yourself, you could instantly create as many copies of yourself as there were rooms in the building all the copies could simultaneously peek in all the offices, and the one that finds the briefcase becomes the real you, the rest just disappear. – (David Freeman, discover )
David Deutsch, a physicist at Oxford University, argued that it may be possible to build an extremely powerful computer based on this peculiar reality. In 1994, Peter Shor, a mathematician at AT&T Bell Laboratories in New Jersey, proved that, in theory at least, a full-blown quantum computer could factor even the largest numbers in seconds; an accomplishment impossible for even the fastest conventional computer. An outbreak of theories and discussions of the possibility of building a quantum computer now permeates itself though out the quantum fields of technology and research.
It’s roots can be traced back to 1981, when Richard Feynman noted that physicists always seem to run into computational problems when they try to simulate a system in which quantum mechanics would take place. The calculations involving the behavior of atoms, electrons, or photons, require an immense amount of time on today’s computers. In 1985 in Oxford England the first description of how a quantum computer might work surfaced with David Deutsch’s theories. The new device would not only be able to surpass today’s computers in speed, but also could perform some logical operations that conventional ones couldn’t.
This research began looking into actually constructing a device and with the go ahead and additional funding of AT&T Bell Laboratories in Murray Hill, New Jersey a new member of the team was added. Peter Shor made the discovery that quantum computation can greatly speed factoring of whole numbers. It’s more than just a step in micro-computing technology, it could offer insights into real world applications such as cryptography.
“There is a hope at the end of the tunnel that quantum computers may one day become a reality,” says Gilles Brassard of University of Montreal. Quantum Mechanics give an unexpected clarity in the description of the behavior of atoms, electrons, and photons on the microscopic levels. Although this information isn’t applicable in everyday household uses it does certainly apply to every interaction of matter that we can see, the real benefits of this knowledge are just beginning to show themselves.
In our computers, circuit boards are designed so that a 1 or a 0 is represented by differing amounts of electricity, the outcome of one possibility has no effect on the other. However, a problem arises when quantum theories are introduced, the outcomes come from a single piece of hardware existing in two separate realities and these realties overlap one another affecting both outcomes at once. These problems can become one of the greatest strengths of the new computer however, if it is possible to program the outcomes in such a way so that undesirable effects cancel themselves out while the positive ones reinforce each other.
This quantum system must be able to program the equation into it, verify it’s computation, and extract the results. Several possible systems have been looked at by researchers, one of which involves using electrons, atoms, or ions trapped inside of magnetic fields, intersecting lasers would then be used to excite the confined particles to the right wavelength and a second time to restore the particles to their ground state. A sequence of pulses could be used to array the particles into a pattern usable in our system of equations.
Another possibility by Seth Lloyd of MIT proposed using organic-metallic polymers (one dimensional molecules made of repeating atoms). The energy states of a given atom would be determined by it’s interaction with neighboring atoms in the chain. Laser pulses could be used to send signals down the polymer chain and the two ends would create two unique energy states.
A third proposal was to replace the organic molecules with crystals in which information would be stored in the crystals in specific frequencies that could be processed with additional pulses. The atomic nuclei, spinning in either of two states (clockwise or counterclockwise) could be programmed with a tip of a atomic microscope, either “reading” it’s surface or altering it, which of course would be “writing” part of information storage. “Repetitive motions of the tip, you could eventually write out any desired logic circuit, ” DiVincenzo said.
This power comes at a price however, in that these states would have to remain completely isolated from everything, including a stray photon. These outside influences would accumulate, causing the system to wander off track and it could even turn around and end up going backward causing frequent mistakes. To keep this from forming new theories have arisen to overcome this. One way is to keep the computations relatively short to reduce chances of error, another would be to restore redundant copies of the info on separate machines and take the average (mode) of the answers.
This would undoubtedly give up any advantages to the quantum computer, and so AT&T Bell Laboratories have invented an error correction method in which the quantum bit of data would be encoded in one of nine quantum bits. If one of the nine were lost it would then be possible to recover the data from what information did get through. This would be the protected position that the quantum state would enter before being transmitted. Also since the states of the atoms exist in two states, if one were to be corrupted the state of the atom could be determined simply by observing the opposite end of the atom since each side contains the exact opposite polarity.
The gates that would transmit the information is what is mainly focused on by researchers today, this single quantum logic gate and it’s arrangement of components to perform a particular operation. One such gate could control the switch from a 1 to a 0 and back, while another could take two bits and make the result 0 if both are the same, 1 if different.
These gates would be rows of ions held in a magnetic trap or single atoms passing through microwave cavities. This single gate could be constructed within the next year or two yet a logical computer must have the millions of gates to become practical. Tycho Sleator of NYU and Harald Weinfurter of UIA look at the quantum logic gates as simple steps towards making a quantum logic network.
These networks would be but rows of gates interacting with each other. Laser beams shining on ions cause a transition from one quantum state to another which can alter the type of collective motion possible in the array and so a specific frequencies of light could be used to control the interactions between the ions. One name given to these arrays has been named “quantum-dot arrays” in that the individual electrons would be confined to the quantum-dot structures, encoding information to perform mathematical operations from simple addition to the factoring of those whole numbers.
The “quantum-dot” structures would be built upon advances in the making of microscopic semiconductor boxes, whose walls keep the electrons confined to the small region of material, another way to control the way information is processed. Craig Lent, the main researcher of the project, base this on a unit consisting of five quantum dots, one in the center and four and at the ends of a square, electrons would be tunneled between any of the two sites.
Stringing these together would create the logic circuits that the new quantum computer would require. The distance would be sufficient to create “binary wires” made of rows of these units, flipping the state at one end causing a chain reaction to flip all the units states down along the wire, much like today’s dominoes transmit inertia. Speculation on the impact of such technology has been debated and dreamed about for years.
In the arguing points, the point that it’s potential harm could be that the computational speed would be able to thwart any attempts at security, especially the now NSA’s data encryption standard would be useless as the algorithm would be a trivial problem to such a machine. On the latter part, this dreamed reality first appeared in the TV show Quantum Leap, where this technology becomes readily apparent when Ziggy –the parallel hybrid computer that he has designed and programmed– is mentioned, the capabilities of a quantum computer mirror that of the show’s hybrid computer.
with components 
, where 
is the spin projection and 
defines a direction of spin projection measurement, 
. The ends of the vectors 
are on the sphere 
which is illustrated in the top-left corner. In general, 
is a probability distribution function of two discrete variables 
and 
, and 
determines a point on the five-simplex. If the directions 
are chosen with equal probability, then 
for all 
. In that case, a one-to-one correspondence can be established between all probability vectors 
and all points inside a cube 
, 
, which is illustrated in the top-right corner. In other words, any quantum state is associated with a probability vector of the form 
, 
is a cube in 
of side 
. 
is expressed through the probabilities 
by 
, 
is the identity operator, 
are Pauli operators, and the vectors 
form a dual basis with respect to the vectors 
: 
, 
, 
. 
. Using Sylvester's criterion, one obtains restrictions of the first and the second order (the blue and red surfaces inside the cube, respectively). In the probability space, the set of quantum states is an ellipsoid located between two planes. The set of qubit states is depicted in the top-right corner for any choice of directions 
. 
result in the reconstruction procedure above being erroneous. The error bar is directly proportional to the condition number 
of the Gram matrix 
, which is the ratio of the absolute values of the maximum to the minimum eigenvalue. The behavior of the condition number is shown at the bottom. 
