Einstein and the Quantum Revolutions (The France Chicago Collection) - Tapa dura

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Alain Aspect is professor at Institut d’Optique-Université Paris-Saclay, professor at École Polytechnique, and CNRS senior scientist emeritus. Among his many awards, Aspect was a co-recipient of the 2022 Nobel Prize in Physics “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.” Teresa Lavender Fagan is a freelance translator living in Chicago; she has translated numerous books for the University of Chicago Press and other publishers.

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What is a difficult problem? For a computer scientist or a mathematician working in this field, a difficult problem is one that requires a calculation time that increases exponentially with the size of the object under consideration. For example, internet security uses a coding called RSA, after Ron Rivest, Adi Shamir, and Leonard Adleman, who described the algorithm in 1977. RSA security is based on the impossibility of factoring a sufficiently large number into prime factors. Factoring into prime factors means, for example, breaking down the number 60 into 3 multiplied by 4 multiplied by 5. Factoring a large number takes considerable time because you have to try all the prime numbers less than the square root of the number.

This calculation difficulty is the foundation of security. A few years ago, on the internet, coding was done on 64-bit numbers. But, with today’s more powerful computers, with great effort and networking, we can crack the code. The number of bits is then doubled, going to 128 bits, and we can rest easy for ten years. Going to 256, we enjoy another ten years, and so on. A number of theoretical physicists, applied mathematicians, and theoretical computer scientists have discovered that certain difficult problems, such as the one just described, would become easier to solve if there were a quantum computer. For example, what is called Shor’s algorithm, after mathematician Peter Shor, would enable the factorization of a number in a time that would no longer increase exponentially with size, but in a more reasonable way: a polynomial increase.

To implement Shor’s algorithm, one would need a perfect quantum computer. What does that entail? It would use quantum bits, qubits, entangled with each other. To give a vague idea of what this means, we must first ask ourselves what an ordinary “bit” is. In a classical computer system, a bit is a value that can be either 1 or 0, but never both. One traditional way to think of the two states is as a light switch, on or off. But we might equally think of the states as a photon which can go either to one side of the beam splitter or to the other.

In the quantum world, a bit can also be 1 or 0. But here is the interesting part: it can also at the same time be 1 and 0, like the photon that goes to both sides of the beam splitter at the same time in the interference experiment. So, a quantum bit or “qubit” is one that can be put in a state that is a superposition of 1 or 0. If we now take two quantum bits and entangle them, we have access to a great wealth of states because we can have 0–0, 0–1, 1–0, and 1–1, and all the combinations of these four possibilities. If we take three qubits, we have eight basic possibilities (0–0–0, 0–0–1, and so on) as well as the combinations of all those possibilities. If we entangle ten quantum bits, we obtain about a thousand basic possibilities. With twenty, we get one million basic possibilities . . . That’s exponential growth!