Quantum Nondemolition Measurement
A quantum nondemolition measurement extracts information about an observable while leaving that observable's value undisturbed, allowing repeated readout.
The Idea
Every quantum measurement disturbs a system, but the disturbance need not fall on the quantity being measured. A quantum nondemolition, or QND, measurement is designed so that the measured observable is conserved by the measurement interaction. The unavoidable back-action is pushed onto a conjugate variable instead. As a result the same value can be read again and again, each measurement confirming the last.
The Formal Condition
For a measurement to be QND with respect to an observable A, the interaction Hamiltonian coupling the system to the meter must commute with A. Then A is a constant of the motion during measurement. In dispersive qubit readout the coupling depends on the qubit operator Z, and it commutes with Z, so the qubit's Z-basis populations are preserved even as the resonator, the meter, is disturbed. The back-action appears as dephasing in the X-Y plane, the conjugate degree of freedom.
- The interaction must commute with the measured observable.
- Repeated measurements yield the same result, up to real decay processes.
- Back-action is displaced onto the conjugate observable.
Why It Matters for Error Correction
Quantum error correction depends on measuring stabilizer operators repeatedly without collapsing the encoded logical information. This is only possible because stabilizer measurements are QND with respect to the code space: they reveal error syndromes while leaving the logical state intact. Without QND readout, the act of checking for errors would itself destroy the computation.
Limits in Practice
Real measurements are only approximately QND. Strong probe tones can drive unwanted transitions, and higher levels can be populated, effects sometimes called measurement-induced state transitions. Keeping readout genuinely QND means limiting probe power, filtering the environment, and designing the coupling carefully. The dispersive readout of transmons and the fluorescence readout of trapped ions are the canonical high-fidelity QND measurements in quantum hardware.