Qubits

Three hundred of them hold more amplitudes than there are atoms in the universe, and you can read out three hundred bits. Which is why the popular account of quantum computing — trying every answer at once — is not merely simplified but wrong.

1973 – today19 min

By the end you should be able to

Say what a qubit is and locate any state of one on the Bloch sphere
Explain why the phase is invisible to measurement and matters anyway
Say why quantum computers are not fast because they try everything in parallel

Something changed in the 1980s, and it changed the field completely. For fifty years the strangeness of quantum mechanics had been a problem — something to be interpreted, argued over, or set aside in favour of getting on with the calculation. Then people began asking a different question. Not what does this mean, but what is it good for. Not how to explain superposition away, but: given that it is real, thoroughly confirmed, and not going anywhere — what can be built with it? Nothing in the foundations was resolved. The measurement problem sits exactly where Act 6 left it. What changed was that the strangeness became a resource rather than an embarrassment.

IBM Quantum System One: a chandelier of gold-coloured wiring stages suspended inside a glass case. — What a handful of qubits costs. Almost everything visible here is refrigeration and wiring: the processor is a chip at the very bottom, held near 15 millikelvin, and the gold cascade above it is the plumbing needed to get signals down without carrying heat with them. The reason for all of it is the subject of the last lesson in this act.

What a qubit is

A classical bit is any system with two distinguishable states. Call them 0 and 1. A qubit is a quantum system with two states — and therefore, unavoidably, any superposition of them: |ψ⟩ = α|0⟩ + β|1⟩, with |α|² + |β|² = 1 That normalisation condition means the state is fixed by just two real numbers, so every possible state of a qubit corresponds to a point on the surface of a sphere. The north pole is |0⟩, the south pole is |1⟩, and everything else is a superposition. Written out with the angles: |ψ⟩ = cos(θ/2)|0⟩ + e^(iφ) sin(θ/2)|1⟩ Note the θ/2. That is the same half-angle from the Stern–Gerlach lesson, and it is not a coincidence — a qubit is a spin-½, mathematically, whatever it happens to be made of. A superconducting circuit, a trapped ion, a photon's polarisation and a nuclear spin are the same object wearing different clothes.

Drag θ and watch the probabilities move. Then drag φ and watch them not move.

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Every pure state of a qubit is one point on this sphere. Latitude (θ) sets the odds; longitude (φ) sets the phase. Both are genuine physical parameters, and only one of them shows up in a measurement.

The phase is invisible, and does all the work

Move φ and the point travels round the sphere — a genuinely different state. And the probability bars do not move. Not slightly, not subtly. P(0) = cos²(θ/2) contains no φ at all, so the phase is completely invisible to a measurement in this basis. So we have a real, physical difference between two states that no single measurement can detect. It is tempting to conclude that the phase is therefore meaningless — a bookkeeping artefact. That conclusion is exactly backwards. The phase is where the entire advantage lives. It is the quantity that interferes; it is what a quantum algorithm manipulates; and it is the thing decoherence destroys first. Everything interesting a qubit does, it does with the parameter you cannot see by looking at it. The way to see it is to rotate first — change the basis, so a phase difference becomes an amplitude difference — and then measure. That is what a Hadamard gate is for.

Try H, then H again. Then try Z and watch the probabilities refuse to change.

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Gates are rotations of the sphere. H takes a pole to the equator, making an equal superposition — and applying it twice returns you exactly to where you started, which no random process could do. Z moves the point half a turn about the axis and leaves both probabilities untouched.

You might think

A qubit in superposition is like a coin spinning in the air — it is really 0 or 1, we just do not know which yet.

Actually

The H gate settles this in one move. Take |0⟩, apply H, and you have a 50/50 state. Apply H again and you get |0⟩ back with certainty, every time. If the first H had produced a genuine random 0 or 1 that you merely did not know, the second could not undo it — randomising twice gives you more randomness, not less. What is being manipulated is an amplitude, which can be reversed and can cancel. The double-Hadamard is the single-qubit version of the double-slit result from Act 6: adding a second operation can make an outcome go away entirely, and no ignorance-based account permits that.

Measure, then measure again. Notice how little you learn the second time.

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Two continuous real parameters go in. One bit comes out, the state collapses to a pole, and θ and φ are gone. Measuring again returns the same answer indefinitely and tells you nothing new.

You might think

A quantum computer is fast because it tries all 2ⁿ possible answers simultaneously.

Actually

This is the standard popular account and it is wrong, not merely simplified — and you can see why from the Holevo bound above. Suppose the machine really did evaluate every possibility at once. You still have to read the answer out, and reading out gives you one of them, chosen at random by the Born rule. You would have performed an exponential amount of work to obtain a random guess, which you could have had for free. Parallelism without a way to select the right branch is worthless. What actually happens is interference: the algorithm arranges the phases so that amplitudes leading to wrong answers cancel and amplitudes leading to right answers reinforce. It is not a search of a large space — it is the construction of an interference pattern whose bright fringes are the answers you want. Shor’s algorithm is, at bottom, a very clever way of making the period of a function appear as a sharp peak, in much the same sense as a diffraction grating.

So what is it actually good for? Less than the coverage suggests, and it is worth being specific. Exponential speedup, for a short list of structured problems. Factoring large numbers (Shor, 1994), which is why the field is funded. And simulating quantum systems — chemistry, materials, catalysis — which is probably the application that will matter most, and which is the one Feynman proposed in 1981 on the straightforward grounds that if nature is quantum, a quantum machine is the natural thing to model it with. Quadratic speedup for unstructured search (Grover, 1996). Useful, and much less dramatic: it turns 10¹² operations into 10⁶, not into 40. Nothing at all, for most of what computers do. Word processing, databases, rendering, the overwhelming majority of ordinary computation gains nothing. A quantum computer is not a faster computer. It is a machine that is good at a peculiar and narrow class of problem, and the class happens to include two extremely valuable members.

The experiment

Making an electrical circuit behave as a single qubit

Yasunobu Nakamura, Yuri Pashkin and Jaw-Shen Tsai · 1999 · NEC Fundamental Research Laboratories, Tsukuba

The question: Superposition is established for photons, electrons and atoms. Can a manufactured, macroscopic object — a circuit built by lithography, containing billions of atoms — be made to behave as a single controllable two-level quantum system?
The apparatus: A "Cooper-pair box": a superconducting island connected through a Josephson junction, cooled to around 30 mK, so small that adding one Cooper pair changes its energy appreciably. The two charge states of the island play the roles of |0⟩ and |1⟩. Short voltage pulses drove transitions between them, and the resulting charge state was read out through a probe junction.

Theory predicted

If the circuit is genuinely a two-level quantum system, varying the pulse duration should produce coherent oscillation between the states — the population moving smoothly back and forth, rather than saturating at 50% as an incoherent process would.

They measured

Coherent oscillations, with the state cycling as a function of pulse length. The circuit was behaving as a single quantum object with a definite phase, not as a statistical ensemble of its billions of constituent atoms.

How sure could they be? Coherence lasted around 2 nanoseconds — enough to see a few oscillations and nothing more. That figure is the reason the result mattered and also why it looked, at the time, like a curiosity rather than a technology. Superconducting qubits now reach coherence times of order 100 microseconds, an improvement of roughly 10⁵.

Why it mattered

The birth of the solid-state qubit, and the ancestor of essentially every superconducting quantum processor built since. It also makes a point about scale: the object was fabricated, macroscopic, and made of ordinary metal — and it held a superposition. Whatever separates quantum behaviour from classical, it is evidently not size.

1973Holevo proves that n qubits can carry at most n classical bits.
1981Feynman proposes quantum computers for simulating quantum systems.
1985Deutsch defines the universal quantum computer.
1994Shor’s factoring algorithm. Funding follows.
1996Grover’s search algorithm — quadratic, not exponential.
1999Nakamura and colleagues demonstrate a superconducting qubit.
2019–Processors reach tens then hundreds of qubits; error correction remains the obstacle.

Where this leaves us

A qubit holds two continuous parameters and yields one bit. The phase is invisible to measurement and is where the whole advantage lives. And the exponential state space is real but not directly harvestable — what makes quantum algorithms work is interference, not parallel search. There is one more property of a qubit worth stating, and it is a prohibition. You cannot copy it. Not with better apparatus, not with a cleverer scheme, not in principle. There is a short proof — four lines, requiring nothing but the linearity of the Schrödinger equation — that no physical process whatsoever can duplicate an unknown quantum state. That sounds like a pure limitation, and for building a quantum computer it is a severe one: you cannot back up a qubit, and you cannot use the ordinary trick of copying a bit three times and taking a majority vote to correct errors. But it is also the reason an entire technology exists. If an unknown state cannot be copied, then an eavesdropper cannot copy it either — and a communication scheme built on that fact is secure not because breaking it is computationally hard, but because breaking it is physically impossible.