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Measurement: The Price of Looking

A qubitThe basic unit of a quantum computer. Like a 'bit' in a normal computer, but instead of being only 0 or 1 it can be 0, 1, or a blend of both at once. can hold many possibilities at once. MeasurementReading a quantum system, which forces it out of its blend of possibilities into a single definite 0 or 1 and ends its quantum behaviour. is the act of looking, and looking lets only one answer out.

The one look

In an ordinary computer, reading a bit changes nothing; the value was always 0 or 1, and looking just reports it. A qubit is different. Before you look it holds a blend of possibilities together, and measurement forces that blend to resolve into a single definite outcome. Which outcome you get is left to chance: the Born ruleThe rule that sets the probability of each measurement outcome, given by the square of the state's amplitude for that outcome. fixes the probability of each answer from the qubit's state, so the same calculation can hand you different results on different runs.1

Reading an ordinary bit tells you what was already there. Reading a qubit decides it.

That resolving is called collapseThe instant a measurement forces a qubit from a blend of possibilities into one definite classical value., and it is not gentle. Measuring couples the qubit to the outside world, and that contact strips away its quantum behaviour; the superpositionThe quantum ability of a qubit to be in a combination of 0 and 1 simultaneously, which gives quantum computers their power. is gone the instant you read it.1 Measurement also disturbs whatever it touches, an effect called back-actionThe unavoidable disturbance a measurement inflicts on a quantum system simply by reading it., which is why you cannot quietly peek at a qubit mid-calculation to check on it without wrecking the very state you were computing with.2

The collapse. Before measurement a qubit is a blend of 0 and 1 at once; the act of measuring forces it into a single definite outcome chosen by chance, and the other possibility vanishes.
Figure 1: The collapse. Measuring forces a qubit’s blend of 0 and 1 into one definite answer, picked by chance under the Born rule; the superposition it had is gone.

Reading without breaking too much

So how do you read a qubitThe basic unit of a quantum computer. Like a 'bit' in a normal computer, but instead of being only 0 or 1 it can be 0, 1, or a blend of both at once. at all? On superconducting hardware the trick is to never touch it head-on. In dispersive readoutA way to read a superconducting qubit indirectly, by watching how it shifts the frequency of a microwave resonator coupled to it, rather than touching the qubit directly. the qubit is coupled to a tiny microwave resonator, and the machine watches how the qubit nudges the resonator's frequency; that shift reveals 0 or 1 without draining the qubit directly.3 The catch is that the signal is faint and easily buried in noise, so the number that matters is readout fidelityA score for how reliably the hardware can tell a qubit's 0 from its 1 when it measures it. Higher means fewer misreads., how reliably the hardware tells the two states apart. The best processors now push it above 99 percent.3

Every measurement spends a qubit to buy one classical bit.

Why it matters

Because one read gives only a single sample from a distribution, a quantum program has to be run again and again, the collapsed outcomes piled up until the underlying probabilities show through.1 Every run is a fresh preparation, evolution, and read, so a slow or unreliable measurementReading a quantum system, which forces it out of its blend of possibilities into a single definite 0 or 1 and ends its quantum behaviour. taxes each shot and can come to dominate how long a real calculation takes. Measurement is also the engine of error correctionTechniques that combine many shaky physical qubits into fewer reliable ones, so a long calculation stays correct., where the machine constantly measures helper qubits to catch errors without ever reading, and so collapsing, the protected data itself.

And in the strangest twist, measurement need not be the end of a computation at all. In one-way, or measurement-based, computing you first build one large entangled cluster stateA large, pre-entangled group of qubits used as a resource in photonic (measurement-based) quantum computing., then drive the whole calculation by measuring its qubits in a chosen order. There the measurements are not the exit. They are the program.4

Sources

  1. Schlosshauer, M. “Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics.” Reviews of Modern Physics 76, 1267–1305 (2004). DOI: 10.1103/RevModPhys.76.1267. Preprint: arXiv:quant-ph/0312059.
  2. Jacobs, K. & Steck, D. A. “A Straightforward Introduction to Continuous Quantum Measurement.” Contemporary Physics 47, 279–303 (2006). DOI: 10.1080/00107510601101934. Preprint: arXiv:quant-ph/0611067.
  3. Krantz, P., Kjaergaard, M., Yan, F., Orlando, T. P., Gustavsson, S. & Oliver, W. D. “A Quantum Engineer’s Guide to Superconducting Qubits.” Applied Physics Reviews 6, 021318 (2019). DOI: 10.1063/1.5089550. Preprint: arXiv:1904.06560.
  4. Raussendorf, R. & Briegel, H. J. “A One-Way Quantum Computer.” Physical Review Letters 86, 5188–5191 (2001). DOI: 10.1103/PhysRevLett.86.5188. Preprint: arXiv:quant-ph/0010033.