Quantam Computing Essays - Quantum Information Science,

Quantam Computing What is quantum computing? Quantum Computing is something that could have been thought up a long time ago - an idea whose time has come. For any physical theory one can ask: what sort of machines will do useful computation? or, what sort of processes will count as useful computational acts? Alan Turing thought about this in 1936 with regard (implicitly) to classical mechanics, and gave the world the paradigm classical computer: the Turing machine. But even in 1936 classical mechanics was known to be false. Work is now under way - mostly theoretical, but tentatively, hesitantly groping towards the practical - in seeing what quantum mechanics means for computers and computing. In a trivial sense, everything is a quantum computer. (A pebble is a quantum computer for calculating the constant-position function - you get the idea.) And of course, today's computers exploit quantum effects (like electrons tunneling through barriers) to help do the right thing and do it fast. For that matter, both the computer and the pebble exploit a quantum effect - the Pauli exclusion principle, which holds up ordinary matter against collapse by bringing about the kind of degeneracy we call chemistry - just to remain stable solid objects. But quantum computing is much more than that. The most exciting really new feature of quantum computing is quantum parallelism. A quantum system is in general not in one classical state, but in a quantum state consisting (crudely speaking) of a superposition of many classical or classical-like states. This superposition is not just a figure of speech, covering up our ignorance of which classical-like state it's really in. If that was all the superposition meant, you could drop all but one of the classical-like states (maybe only later, after you deduced retrospectively which one was the right one) and still get the time evolution right. But actually you need the whole superposition to get the time evolution right. The system really is in some sense in all the classical-like states at once! If the superposition can be protected from unwanted entanglement with its environment (known as decoherence), a quantum computer can output results dependent on details of all its classical-like states. This is quantum parallelism - parallelis m on a serial machine. And if that wasn't enough, machines that would already, in architectural terms, qualify as parallel can benefit from quantum parallelism too - at which point the mind begins to seriously boggle! Why is Quantam Computing an exciting prospect: Quantum computation is an exciting prospect, because a quantum computer (if it could be built) would be exponentially faster than a classical computer on some problems. For example, a quantum computer could find prime factors in polynomial time instead of the exponential time required by a classical computer, thereby breaking conventional cryptographic codes. The problem with building a quantum computer is that the quantum bits (called qubits) simultaneously need to be protected from the environment so that they retain their quantum phase, but they need to be coupled to the environment so that initial conditions can be loaded, the calculation applied, and the results read out. Because of these apparently contradictory constraints, it's taken a heroic experimental effort to make just a 2 bit quantum computer. This has been done in systems such as trapped ions, or cavity quantum electrodynamics, that carefully isolate the qubits and cool them to their ground state. Neil Gershenfeld and Isaac Chuang have developed an entirely new approach to quantum computation that promises to solve many of these problems. Instead of carefully isolating a small number of qubits, we use a large thermal ensemble (such as a cup of coffee). Such a system has ~10^23 degrees of freedom; by applying RF pulses that excite nuclear magnetic resonances, we can create a tiny deviation from equilibrium that acts just like a much smaller number of pure qubits. The nuclear spin is beautifully isolated from the environment; its spin coherence can last for thousands of seconds. By representing the effective computational qubits in such an ensemble, we get these very long coherence times permitting thousands of logical operations before coherence is lost. Further, because the bits are represented in an ensemble, it is possible to continuously read out the quantum state (somthing that is of course impossible for individual quantum degrees of freedom). Best