Scientific Method —

The cost of quantum error correction

Researchers take a look at one of the hidden costs of quantum computing.

In many articles, we have discussed the possible applications for quantum computers. These articles have usually been related to some advance in the science and technology behind quantum computing. However, we have neglected one critical area of quantum computing: error correction. In normal communications and computing, error correction means providing a certain amount of redundancy so that errors in the message can be detected and, within certain limits, corrected. For instance, a microwave communications link might devote up to 20 percent of its signal bandwidth to providing sufficient redundancy to ensure a robust link.

Error correction is also an important concept in computation and it goes right alongside reversibility: the ability for any logic operation to be undone. In classical computers this is relatively trivial because reversibility of logic does not imply a physically reversible process. On the other hand, quantum computation stores its information in the physical states of quantum objects and, as such, logical operation reversibility also requires that the operation be physically reversible.

In this case, the environmental noise doesn't reduce the signal to noise in the same sense of a classical computer, but rather it changes the probability of a subsequent measurement receiving a logical one or zero. It also makes reversibility difficult because the quantum state is not the one set by the logical operation, so the undo isn't accurate. This makes the correction of errors, the amount of redundancy and the entropy of quantum computing very important to understand.

Experimental investigation of these issues is very difficult because these problems scale with the complexity of the computer, and there are no scalable quantum computer architectures yet. However, a recent Physical Review Letter has partially answered the question by looking at how error correction and entropy interact in a generic reversible quantum system.

The paper looks at the increase in entropy due to a generic quantum operation, the amount of work required to extract the entropy, and the amount of redundancy required to reduce the entropy. The main conclusion is that the entropy increases with the square of the number of quantum operations per second.

What does this mean? Well on the surface this is not too surprising since the power dissipated by a normal gate also scales with the clock speed squared. However, the heat dissipation of a normal logic gate does not change the signal fidelity very much because it only contributes a leakage current that degrades the logic zero state. In quantum logic, the heat is introduced directly into the quantum bit state, altering the relative probabilities. That means that scientists and designers are going to have to either remove the heat and restore the original quantum state, or provide lots of redundancy. In reality, this makes for a difficult situation, where speed is desirable but the number of qubits required to compensate for the noise scales as the square of the speed. This raises the spectre that the equipment requirements may scale too fast for a usable quantum computer to become feasible.

Physical Review Letters, 2007, DOI: 10.1103/PhysRevLett.99.110502

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