Through his career, Hilbert was interested in the ultimate limits of mathematical knowledge: what can humans know about mathematics, in principle, and what (if any) parts of mathematics are forever unknowable by humans? Roughly speaking, Hilbert’s 1928 problem asked whether there exists a general algorithm a mathematician can follow which would let them figure out whether any given mathematical statement is provable. Hilbert’s hoped-for algorithm would be a little like the paper-and-pencil algorithm for multiplying two numbers. Except instead of starting with two numbers, you’d start with a mathematical conjecture, and after going through the steps of the algorithm you’d know whether that conjecture was provable. The algorithm might be too time-consuming to use in practice, but if such an algorithm existed, then there would be a sense in which mathematics was knowable, at least in principle.
In 1928, the notion of an algorithm was pretty vague. Up to that point, algorithms were often carried out by human beings using paper and pencil, as in the multiplication algorithm just mentioned, or the long-division algorithm. Attacking Hilbert’s problem forced Turing to make precise exactly what was meant by an algorithm. To do this, Turing described what we now call a Turing machine: a single, universal programmable computing device that Turing argued could perform any algorithm whatsoever.
Today we’re used to the idea that computers can be programmed to do many different things. In Turing’s day, however, the idea of a universal programmable computer was remarkable. Turing was arguing that a single, fixed device could imitate any algorithmic process whatsoever, provided the right program was supplied. It was an amazing leap of imagination, and the foundation of modern computing.
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There’s a wrinkle in this story. Deutsch is a physicist with a background in quantum mechanics. And in trying to answer his question, Deutsch observed that ordinary, everyday computers based on Turing’s model have a lot of trouble simulating quantum mechanical systemsResearchers such as Yu Manin and Richard Feynman had previously observed this, and as a result had speculated about computers based on quantum mechanics.. In particular, they seem to be extraordinarily slow and inefficient at doing such simulations. To answer his question affirmatively, Deutsch was forced to invent a new type of computing system, a quantum computer. Those quantum computers can do everything conventional computers can do, but are also capable of efficiently simulating quantum-mechanical processes. And so they are arguably a more natural computing model than conventional computers. If we ever meet aliens, my bet is that they’ll use quantum computers (or, perhaps, will have quantum computing brains). After all, it’s likely that aliens will be far more technologically advanced than current human civilization. And so they’ll use the computers natural for any technologically advanced society.
This essay explains how quantum computers work. It’s not a survey essay, or a popularization based on hand-wavy analogies. We’re going to dig down deep so you understand the details of quantum computing. Along the way, we’ll also learn the basic principles of quantum mechanics, since those are required to understand quantum computation.
Learning this material is challenging. Quantum computing and quantum mechanics are famously “hard” subjects, often presented as mysterious and forbidding. If this were a conventional essay, chances are that you’d rapidly forget the material. But the essay is also an experiment in the essay form. As I’ll explain in detail below the essay incorporates new user interface ideas to help you remember what you read. That may sound surprising, but uses a well-validated idea from cognitive science known as spaced-repetition testing. More detail on how it works below. The upshot is that anyone who is curious and determined can understand quantum computing deeply and for the long term.
- Quantum Computing for the Very Curious
In 1928, the notion of an algorithm was pretty vague. Up to that point, algorithms were often carried out by human beings using paper and pencil, as in the multiplication algorithm just mentioned, or the long-division algorithm. Attacking Hilbert’s problem forced Turing to make precise exactly what was meant by an algorithm. To do this, Turing described what we now call a Turing machine: a single, universal programmable computing device that Turing argued could perform any algorithm whatsoever.
Today we’re used to the idea that computers can be programmed to do many different things. In Turing’s day, however, the idea of a universal programmable computer was remarkable. Turing was arguing that a single, fixed device could imitate any algorithmic process whatsoever, provided the right program was supplied. It was an amazing leap of imagination, and the foundation of modern computing.
[---]
There’s a wrinkle in this story. Deutsch is a physicist with a background in quantum mechanics. And in trying to answer his question, Deutsch observed that ordinary, everyday computers based on Turing’s model have a lot of trouble simulating quantum mechanical systemsResearchers such as Yu Manin and Richard Feynman had previously observed this, and as a result had speculated about computers based on quantum mechanics.. In particular, they seem to be extraordinarily slow and inefficient at doing such simulations. To answer his question affirmatively, Deutsch was forced to invent a new type of computing system, a quantum computer. Those quantum computers can do everything conventional computers can do, but are also capable of efficiently simulating quantum-mechanical processes. And so they are arguably a more natural computing model than conventional computers. If we ever meet aliens, my bet is that they’ll use quantum computers (or, perhaps, will have quantum computing brains). After all, it’s likely that aliens will be far more technologically advanced than current human civilization. And so they’ll use the computers natural for any technologically advanced society.
This essay explains how quantum computers work. It’s not a survey essay, or a popularization based on hand-wavy analogies. We’re going to dig down deep so you understand the details of quantum computing. Along the way, we’ll also learn the basic principles of quantum mechanics, since those are required to understand quantum computation.
Learning this material is challenging. Quantum computing and quantum mechanics are famously “hard” subjects, often presented as mysterious and forbidding. If this were a conventional essay, chances are that you’d rapidly forget the material. But the essay is also an experiment in the essay form. As I’ll explain in detail below the essay incorporates new user interface ideas to help you remember what you read. That may sound surprising, but uses a well-validated idea from cognitive science known as spaced-repetition testing. More detail on how it works below. The upshot is that anyone who is curious and determined can understand quantum computing deeply and for the long term.
- Quantum Computing for the Very Curious
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