## What quantum computers may tell us about quantum mechanics

**Carlo Paul P. Morente**

Even if quantum mechanics occupies a unique role in the course of history, its foundations are often questioned due to the difficulty of reconciling it with classical laws of physics. While today’s technology leads to the device being miniature towards atomic scale, quantum effects are beginning to confront this trend such as unnecessary quantum tunneling of electrons and large signal fluctuations. While many of these effects inhabit the continued miniaturization, another opportunities are arising such as **quantum information processing** which not only provide a way faster devices in terms of its performance but may also eclipse our existing technology. Instead of shrinking further the size of chip components, this new field takes advantage of different physical principles underlying these components.

Quantifying information began in mid century from the discovery of binary digit or bits by Claudde Shannon. Impressive growth in the technology of processing information speed and computing power is described exponentially where the chip components shrink in size. This is exponential growth is described in Moore’s law. New information sciences arise then as the limit of classical bits are meet, such as quantum information processing. Whereas Shannon’s bits can be 0 or 1, quantum bits, which is the simplest mechanical unit of information known as qubits, on the other hand can store superposition of 0 and 1. A single qubit is represented by the quantum state:

[eq]\psi = \alpha\left | 0 \right\rangle + \beta\left | 1 \right\rangle[/eq]

Where α and β are complex amplitudes of the superposition.

Hints of the power of quantum computing arise from the fact that in general for N qubits, it stores a superposition of *2 ^{N} *binary numbers.

*2*are possibilities of measurement, and according to quantum mechanics the measurement yields only one answer out of these possibilities which makes it hard in designing useful quantum computing algorithm. The trick behind a useful quantum computer is the phenomenon called quantum interference. As the complex amplitude evolves in the wave equation it is made to interfere with each other, and in the end these amplitudes will cancel out leaving only few or one answer. In some case this implies exponential speed up over what can be obtained classically.

^{N }In order to understand the nature of quantum computing or we need to be familiar with one of its major properties: quantum entanglement. Quantum entanglement is combination of two properties in quantum mechanics – superposition and measurement – that are themselves unremarkable, but taken together cause all the usual interpretative conundrums of quantum mechanics. Yet quantum entanglement seemed to be the most misunderstood concept in quantum mechanics. There are several definitions of quantum entangle with their own supporting assumptions.

The hunt for the way to measure or quantify how much entangled a given quantum state is leads to the formulation of two major definitions.

First: an entangled state is one that is not separable, where highly quantum-efficient measurements are performed on one constituent without affecting the others. This definition arises from the fact that there is a correlation between the subsystems of the entangled state, wherein one cannot measure the constituent state without affecting the others. Therefore when measuring the state there should be high detector quantum efficiency that reflects a measurement of any previously prepared quantum state. It is required that the probability distribution of measurement should results accurately reflect the amplitude of the original quantum states.

Second is a more strict definition of entanglement which is somehow derived from above definition having considered the bells inequality. It states that: An entangled state is one that is not separable, where highly quantum measurements are performed on one constituent without affecting the others and where the constituents are space-like separated during the measurement time. This would rule any possibility of interaction between constituents during a measurement requiring that the two subsystems must be separated by a space-like interval. In general, there is no known measure of how much entanglement a given quantum state has.

These definitions comprise the reference in building a quantum computer. One must have arbitrary and controlled unitary operators to launch a pure initial quantum state. This will require that the qubits must be very isolated from the environment and preserve the superposition character, yet it must interact strongly with one another in order to become entangled. On the other hand it also requires that there must be a strong interaction with the environment to be switch on at will in order to measure qubits, which confronts physicist with the problem of quantum measurement. This will require high quantum efficiency. Thus the most attractive physical candidate for quantum information processors are said to be “exotic” physical systems offering a high degree of quantum control.

Physicists today continue to probe the foundational aspects of quantum mechanics trying to meld it to quantum measurement. Theories like bohemian mechanics, many-worlds interpretations, transactional interpretation and the quantum decohernce theory, all attempts to meld quantum mechanics and quantum measurement with their supporting assumptions and theories yet non address the quantum measurement problems. There at least one alternative to quantum mechanics that is testable called “spontaneous wave function collapse”. This theory attempts to meld quantum measurement and quantum mechanics by adding nonlinear stochastic driving field to quantum mechanics that randomly localizes or collapses the wave function. What makes it remarkable is that this theory is testable, yet this is still far beyond the realization of a quantum processor.

This journey towards quantum computers yields at least three possible results, in which two are tantalizing: either a full blown large-scale quantum computer will be built, or the theory of quantum mechanics will be found incomplete. The third possibility would be that we can never reach to have the first possibility due to economic constraints.

*A summary of Christopher Monroe’s **“What Quantum Computers May Tell Us About Quantum Mechanics”**

Science and Ultimate Reality, eds. J. D. Barrow, P. C. W. Davies and C. L. Harper Jr. Published by Cambridge University Press. Cambridge University Press 2004.

**Carlo Paul P. Morente** is a graduate student in Physics of Mindanao State University-Iligan Institute of technology (MSU-IIT) Iligan City Philippines.

March 16th, 2010 at 8:59 am

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