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Quantum Superposition

Quantum superposition is one of those things that sound like esoteric nonsense after a third bottle of cognac. It is a basic feature of quantum physics, which underlies semiconductors, lasers and MRI. GPS also uses atomic clocks and relativistic corrections; these technologies do not all work through the same superposition trick. Nature behaves very strangely at this scale.

Most people imagine the world as a collection of objects with definite states. A light is either on or off. A server is either down or running. A patient is either alive or has reached the stage of “no further treatment required.” The quantum world works differently.

What is superposition?

Imagine a patient being given all these diagnoses at once:

In this analogy, the problem is neither an uncertain doctor nor missing test results. The patient represents a combination of states. It sounds as though the doctor needs a diagnosis. An electron, however, really can be in a superposition.

An electron does not follow a definite trajectory like a little ball. Before measurement, its state is described by a wave function, which may combine several possible states: \[\Psi = a|1\rangle + b|2\rangle + c|3\rangle + \cdots\]

Here the states form an orthonormal measurement basis and the state is normalized: \(|a|^2+|b|^2+|c|^2+\cdots=1\). The squared coefficients give probabilities for measurement in that basis, not for an arbitrary choice of overlapping states.

The coefficients are probability amplitudes. Their squared magnitudes determine the probabilities of the corresponding measurement outcomes. This is where our intuition short-circuits. We are used to a deterministic world, while quantum mechanics tells us that a measurement need not have a predetermined outcome.

It is a bit like a database physically containing every possible value, with a SQL query producing one particular record only when SELECT runs. Any CTO would start smoking nervously.

Classical bit versus qubit

An ordinary bit has one of two values:

0
or
1

A qubit can be in a superposition of 0 and 1. This is more than our simply not knowing which value it already has. That distinction matters enormously. An ordinary server with 64 bits stores one particular number out of 2^64 possibilities. A state of 64 qubits can have amplitudes for all those possibilities. We cannot read them all out in one measurement, but a suitable algorithm can use interference between amplitudes to find an answer efficiently.

That is why quantum computing attracts so much attention. It offers ways to work with enormous state spaces, even if marketers have spent a decade promising a “quantum laptop in two years.”

Why don't we see superposition around us?

Because of decoherence, one of the more merciless things in the universe. Quantum coherence is fragile: a stray photon, an air molecule or a thermal fluctuation can entangle a system with its surroundings and destroy the interference we wanted to observe.

It reminds me of intensive care: a patient is in a critical but reversible condition, and an orderly pulls out the power cable. For the quantum system, “the information died” is only a metaphor. Coherence becomes inaccessible locally as information spreads into correlations with the environment; decoherence does not by itself prove fundamental destruction of information.

Superconducting quantum processors can operate near 15 mK, far below the roughly 2.7 K cosmic microwave background. Different kinds of quantum hardware have different cooling requirements. Thermal excitations are one source of noise, and noise is sepsis for a quantum system.

The double-slit experiment

The double-slit experiment is another level of madness. Send electrons through two slits one at a time and record their arrival positions on a screen. Without a coherent relationship between the paths, the single-slit intensity distributions add. With coherence, an extra interference term produces alternating maxima and minima; even each single slit has its own diffraction envelope. The pattern builds up from individual detection events.

There need not be another electron around. A single electron interferes with itself. Nature seems to be saying: “Yes, I went everywhere at once. Any questions?”

If a detector or the environment retains fully distinguishable records of which slit was taken, interference between the paths disappears from the unconditioned screen distribution. Partial path information can reduce its visibility. A person need not read the record: the relevant change is the physical interaction, not human awareness. These predictions have repeatedly been tested.

Practical applications

Transistors

Modern processors rely on the quantum behaviour of electrons in semiconductors. Tunnelling is another effect of their wave nature; it matters in electronic devices and becomes a serious design constraint as components shrink. If the world were entirely classical, today's chips would not exist.

Lasers

Photons can be in superpositions of states. Lasers produce coherent light through stimulated emission, another quantum process. Fibre optics, the internet and data centres all depend on quantum physics, even if some crypto enthusiast thinks the internet runs on his NFT.

MRI and nuclear magnetic resonance

MRI uses the quantum spin properties of hydrogen nuclei. A huge medical industry is built on quantum mechanics. A patient can undergo a scan because protons behave like tiny quantum gyroscopes.

Quantum computers

Here superposition becomes a computational resource. A classical computer processes definite bit values and can use algorithms far better than brute-force enumeration. A quantum computer manipulates probability amplitudes; interference helps only when a suitable algorithm turns it into useful measurement statistics. An enormous state space alone does not guarantee a speedup.

This requires neither magic nor a commitment to parallel universes. Shor's algorithm, for example, factors integers in polynomial time, faster than the best known classical algorithms. Cryptographers have reason to pay attention, although large-scale attacks on RSA require much more capable quantum hardware.

What happens during measurement?

This is where physicists start arguing. There are several interpretations.

Copenhagen interpretation

A measurement gives a definite outcome from a state that may previously have been a superposition. In the usual textbook account, this is described as wave-function collapse.

Many-worlds interpretation

In this interpretation, outcomes with nonzero amplitudes remain in different decohered branches of the universal state. That is an interpretation, not an experimentally established catalogue of alternative biographies. “Somewhere you became a billionaire; elsewhere you deployed on Friday” is a joke about the picture, not a prediction of those particular lives.

Hidden-variable theories

Perhaps additional variables determine the outcomes. Experiments violating Bell inequalities rule out local hidden-variable explanations under the theorem's assumptions; they do not rule out every conceivable hidden-variable theory. Nature is still stranger than our everyday picture suggests.

Why should an engineer understand this?

Because we are running into physical limits. Fabrication processes are measured in nanometres, and we are designing devices in which quantum effects are part of the essential functionality. The next generation of technology will depend on controlling these states: quantum sensors, cryptography and networks, new materials and medicines, and new ways to model chemistry. Names such as “3 nm” are process-node labels, not a literal measurement of every transistor feature.

One of the most unsettling discoveries of the twentieth century is how little reality resembles our intuitive picture. The universe is no tidy relational database. It looks more like an enormously complicated distributed system with lazy evaluation, probabilistic states, data races and an observer whose query changes the result.

Any architect of heavily loaded systems looking at quantum mechanics would ask: “Who designed this thing?” Unfortunately, nobody has found the universe's support ticket form yet.

Quantum superposition