Quantum Computing: Theoretical versus Practical Possibility

Quantum computing is a young discipline at the interface between computer science and quantum physics. It rests on the discovery that certain computational tasks, such as number factorization, period finding, and database search, could be speeded up if these problems are encoded in the states of systems called quantum bits (qubits) and in operations described by quantum mechanics. In a quantum processor, the qubit states can be superposed and entangled by sequences of externally controlled manipulations that result in unitary transformations (quantum gates). The effect of measurement on the qubits is described by the standard von Neumann projection postulate. 1 It is somewhat counterintuitive that more efficient processing of information can be obtained by using quantum mechanics. Should not exactly the opposite be the case? Objects in quantum mechanics in general do not have well-defined properties, so any information associated with such properties should be diffuse and, owing to the randomness of the measurement process, unreliable to recover. After all, does not the Heisenberg uncertainty relation set a fundamental limit to our knowledge of physical variables? And are there not several no-go theorems (no-cloning, 2 no-reflection, 3 no-deleting 4 ) indicating that some operations that are possible in a classical computer are forbidden in quantum mechanics? The clever trick of quantum computing is to bypass all of these objections by avoiding the encoding of classical bits of information directly into an observable or (as in classical Turing machines) into an "element of reality" of any type. A quantum processor is a just a system that is prepared in an initial state and evolves quantum mechanically under the application of a sequence of quantum gates; at the end of this evolution the state is measured. The result, which encodes the solution to a problem, is cast irreversibly--alea jacta est!--into the classical world. In other words, to perform a computation there does not have to be a one-to-one correspondence between the bit and the "it" at every step of the program: what matters are the correlations established in the final quantum state of the processor due to evolution 5 . As it turns out, quantum mechanics offers a way to produce stronger correlations --stronger than the correlations achievable by the above correspondence. This profound consequence follows because there cannot be any local realistic variables "hidden" behind the quantum formalism. The groundbreaking work of John Bell showed that no theory with such "hidden variables" will reproduce the predictions of quantum theory. The correlations between experimentally measured results (as predicted by quantum physics) are stronger than any theory of hidden variables satisfying conditions such as locality and realism, 6 which would be the classical-computing type of "it" to use for embedding the "bit." That is why, when examining the number of operations needed to solve a problem, a quantum computer could be more efficient than a classical one.

I shall not attempt to give a historical account of the many achievements in the field of quantum computing. Instead, I shall try to see if something can be learned about what could be expected in the future based upon analogies from the history of science. Theoretical attempts to design such a quantum-computing machine have led to important insights into the fundamentals of quantum physics, but experimental progress has not been so spectacular, at least when counting the number of qubits operated. What can we expect in the future? The simplest answer is that these difficulties are inherent in a long journey and just require persistence and courage to overcome them. However, there might be another answer, namely, that the laws of Nature have never been tested for systems of such complexity, and as a result we will simply face the unexpected. Ironically, therefore, the failure to build a quantum-computing machine might translate into the discovery of new physics. I speculate that there are two ways in which this physics could manifest itself: either the quantum many-qubit state would collapse above a certain level of complexity, or there could be a limiting principle–a situation in which increasing the computing power would require more and more classical resources. I characterize the first attitude as “strong emergentism” and the second as “weak emergentism.”

Quantum computers do not yet exist. The experimental effort to design them is already more than ten years old, during which time the field has clearly advanced. Many physical systems have been studied as candidates for the magic qubit, including trapped ions, photons, superconducting circuits, and atomic nuclei in certain materials. The most important quantum algorithms have been demonstrated for few-qubit systems (less than ten). This looks like solid progress, and one might wonder what exactly stops physicists from declaring the problem solved,

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