Hi there,
How do you measure a qubit in a specific basis ? And what does this even mean ?
If you ever looked at quantum error correction circuit schematics, there are so many gates and symbols popping up that it is hard to keep a clear head.
One thing that often goes unexplained is why we are measuring in a specific basis at a specific point in the circuit. Yet, the cool thing is that the choice of basis directly determines what type of error you can detect.
But let’s not get ahead of ourselves and unpack this story from the beginning.
Let's first look at how we perform a measurement for superconducting qubits, also called ‘readout':
Each qubit is coupled to its own readout resonator
You send a microwave probe tone into that resonator
The resonator's resonance frequency shifts slightly depending on whether the qubit is in |0⟩ (ground) or |1⟩ (excited)
You demodulate the reflected/transmitted signal (IQ plane) and discriminate: did the qubit have more or less energy?
That is by definition always a Z-basis measurement.
So how do you measure in a different basis ? X or Y?
You rotate the qubit first, then do the standard dispersive readout.
The X-basis states are |+⟩ = (|0⟩+|1⟩)/√2 and |−⟩ = (|0⟩−|1⟩)/√2. A rotation gate maps them onto the Z poles, so the standard readout can distinguish them perfectly.
On a transmon, this is just a microwave pulse: a 90° rotation around a specific axis on the Bloch sphere, implemented as a shaped pulse (typically Gaussian or DRAG) at the qubit's resonance frequency, with carefully calibrated amplitude and duration (typically ~20–40 ns). The phase of the microwave pulse determines the rotation axis (X vs Y).
So:
Z measurement: directly probe readout resonator
X measurement: R_y(π/2) pulse → probe readout resonator
Y measurement: R_x(−π/2) pulse → probe readout resonator
No hardware modification, just a gate prepended.
But why does the choice of basis matter in the first place?
Let’s look at quantum error correction. In a surface code, you run two types of stabilizer measurements in parallel, every single cycle:
Z-type stabilizers measure the Z parity of 2–4 neighboring data qubits. A bit-flip (X) error on any of those qubits flips the parity outcome, flagging the error. These require Z-basis measurements on the ancilla qubits.
X-type stabilizers measure the X parity of the same neighborhood. A phase-flip (Z) error flips their outcome instead. These require X-basis measurements: the ancilla gets a Hadamard before and after the interaction with the data qubits.
The two stabilizer types are blind to each other's errors by design. Z stabilizers can't see phase-flips; X stabilizers can't see bit-flips. Running both in parallel gives you full syndrome information, a complete picture of what went wrong and where. The fact that switching basis costs only ~30 ns and zero hardware changes is what makes running hundreds of these measurements per cycle practical.
In the Wallraff group's recent lattice surgery experiment, this plays out directly. The middle column of data qubits is measured in the Z basis at the moment of the split. Z stabilizers contained within each half survive and continue protecting against bit-flips. The X stabilizers that crossed the boundary, which protected against phase-flips, are destroyed. The result: two bit-flip repetition codes.
Measure those same qubits in X instead, and you cut the Z correlations rather than the X ones. The surviving structure is two phase-flip repetition codes. A different code, a different logical operation, from a single pulse choice.
Until next time,
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