This chapter discusses which applications are best fit to order the massive number crunching required and how best to move from an analog to digital economy. So….

**What’s Next?**

*Atoms Instead of Chips*

- One possibility for the future is the quantum computer, which takes advantage of the quantum nature of subatomic particles to perform the memory and processing tasks of a classical computer. Quantum “processors” could possibly one day replace silicon chips, just as the transistor replaced the vacuum tube.

*The Qubit and the Principle of Superposition*

- Quantum computers are based on the principles of quantum mechanics – mainly on the principle of superposition, which states that a particle does not exist in any single state but is an amalgamation of all its energy states.

- Quantum computers work by manipulating quantum bits, or qubits. Qubits are the counterpart to the computer bit we know today, where the transistor in the “on” or “off” state gives a value of “1” or “0.” Just as bits are the basic unit or building block of classical computing, qubits are the basic unit for quantum computers and have two basic

- Given the principle of superposition, one qubit can be in both the “1” or “0” states simultaneously. With two qubits, you can have a superposition of four states “00”, “01”, “10”, and “11”. This means that four calculations can be performed at once. Adding more and more qubits, the number of simultaneous calculations grows dramatically. In fact the number of calculations scales exponentially with each added qubit – 2
^{N}, where N is the number of qubits. Compare this with the linear scaling of a classical computer, where each bit is a “1” or “0.” Quantum computers could therefore theoretically perform certain types of computations much faster than any computer of today.

*Qubits and the Principle of Entanglement*

- Another quantum principle for quantum computing is called entanglement, which states that two particles that have interacted at some point can become correlated so that whatever happens to one particle would immediately affect the other. The two particles will predictably interact with each other regardless of how far apart they might be, as long as they remain in isolation. Einstein called this “spooky action at a distance.”

- Quantum mechanics show that, whereas a particle can be in two states simultaneously, – as with the qubit – it settles into either one state or the other one the particle is measured. At the instant one entangled particle settles into a particular state, the other particle instantly locks into the opposite. So, the measurement on any one particle will provide information on the state of its mate – it will be the opposite.

- Some scientists believe that this phenomenon and quantum superposition can create greatly enhanced computing capabilities.

**Quantum Computing Applications**

- Early interest in quantum computers involves solving problems that seem intractable with traditional models of computation.

- In 1994, Peter Shor, a scientist in AT&T research labs, developed a quantum computer algorithm to factor large numbers – on the order of 10
^{200}digits. A major application for this algorithm is encryption. With the Shor algorithm, a quantum computer would be able to crack codes much more quickly than a classical computer could. Public key cryptosystems, such as RSA, rely on the difficulty of factoring very large numbers into their primes and would become obsolete if the Shor algorithm were implemented. In quantum cryptography, protocols using quantum key exchanges could take advantage of the phenomenon of entanglement to ensure that only the sender and the intended recipient could read a message.

- In 1996, Luv Grover developed a quantum algorithm that, theoretically, could dramatically speed up a database search. The number of steps need in the Glover algorithm is defined by the square root of the number of items in the database. Using this algorithm, a quantum computer could search an unsorted database to locate a specific entry much more efficiently than a conventional computer can.

- Quantum computers could also be useful for simulations of quantum mechanical effects in physics, chemistry, biology and other fields.

My third and final chapter in this series explores how quantum computers are being built for the future and other forms defining quantum computing in the 21^{st} century.

Dr. Eslambolchi

[1] Qubits can exist in a superposition that is simultaneously both 1 and 0 or somewhere in between.