December 9, 2022

White Paper: Quantum Valuation

How can we measure Quantum Computing ‘power’ in comparison of Classical Computing? Does Moore’s Law apply to Quantum Computing? (The famous Moore’s Law is a empiric but foundation law of modern electronics and computers.)

Gordon Moore, a giant in the history of computing and co-founder of Fairchild and Intel, told in the 60s that the number of components (the famous transistors, basic elements of microprocessors) would double each year with equivalent area on the chip. 

One can also say that computing power would double each year at same equivalent cost. This is not really a demonstrable scientific law but rather a vision that has been true until today, despite all the technological issues researchers had to fix.

We can underline that this law, which is linear and impressive, does less well than other equivalent but exponential laws, such as the development of networks and mobile phones and genome sequencing technologies.

Currently, there is a theoretical limit to the evolution of Moore’s Law. Indeed, below 5 nm (nanometers), it is no longer possible to reduce the size of transistors due to quantum effect, precisely (tunneling)!

In 1973, Russian Soviet mathematician Alexander Holevo demonstrated a fundamental theorem of Quantum Computing (the now famous Holevo’s Theorem). This theorem establishes that n qubits cannot carry more than n conventional bits of information. It is very surprising since Quantum Computing is very often quoted as much better than Classical Computing. It’s not better, it’s different.

IBM has proposed a new interesting method of measuring the progress of Quantum Computing, a kind of equivalence of Moore’s Law, the Quantum Volume.

This measurement is defined by the number of qubits, the error rates and the connectivity between qubits.

Basically this definition means that it is not enough to add qubits to a quantum computer to improve its performance. A quantum computer is extremely sensitive to any disturbance (vibration, waves, temperature variations) which may lead to computation errors.

If this calculation method is applied to IBM’s own quantum systems, we find an evolution similar to Moore’s Law from 2017 to 2019 (respectively, 4, 8 and 16).

In 2019, the company ProteinQure, which is specialized in quantum computing and Machine Learning in the pharmaceutical field, introduced an interesting concept: Quantum Value. It proposed to balance two concepts:

  • The Quantum Value which improves how to solve a problem using a quantum computer (or a combination with a conventional computer) and to achieve better results than with a conventional solution. Improvement stands less in the speed of execution than in more convincing results.
  • The Quantum Advantage which allows to solve a problem with a quantum computer faster, cheaper or more efficiently than with a conventional computer.

The concept of Quantum Valuation is relevant because the technological (and probably financial) barrier to entry is much lower. It works when the error type of the quantum algorithm is different (uncorrelated) from the error type of the classical algorithm.

Another (surprising) way to express this concept is that the quantum algorithm does not necessarily have to be better. It just has to make mistakes (the famous rate of errors) differently than the classic algorithm. This means that the concept will be relevant only to certain classes of problems that match to this specificity.

Consider the following example which is a known problem in Artificial Intelligence, so-called classification.

Let’s take a set of 1 million so-cute dog pictures. Among these images, hundred nasty cats have infiltrated. Our mission is to sort these images and delete the images of cats.

In classical computer science, we would use an Artificial Intelligence algorithm of the Deep Learning Classifier type. Once we have applied the algorithm, although powerful, it would have only identified for example 90 images of cats. It has missed 10 cats, so-called false negatives. It is assumed that the algorithm did not take dogs for cats, which would be false positives.

Now let’s use a quantum algorithm. Imagine that this algorithm would only find 12 cats and that therefore seems less efficient, except that only 7 of these cats have already been found by the classical algorithm. This means that the quantum algorithm found 5 cats that the classical algorithm would never have found.

The use of the two algorithms makes it possible to find 95 cats and halve the false negative rate. That is Quantum Valuation!

Copyright ADVIXO 2019 / F. Franchin