Measurement fidelity is how accurately you can read a qubit's state (0 or 1) after it collapses. Higher fidelity = fewer readout errors = more reliable quantum computation.
Imagine you have a special coin that spins really, really fast. While it's spinning, it's kind of heads AND tails at the same time.
When you shine a flashlight on it to see what it is, it stops and becomes just heads or just tails.
But here's the tricky part: sometimes your flashlight doesn't work perfectly. Maybe it's a little blurry, so you think you saw heads when it was actually tails.
Measurement fidelity is asking: "How often does your flashlight show you the right answer?"
If your flashlight is 99% good, that means out of 100 times, you get it right 99 times. That's really good! If it's only 90% good, you make 10 mistakes out of 100. Not great.
A qubit is the quantum version of a computer bit. Normal bits are either 0 or 1. A qubit can exist in a "superposition" — kind of like being 0 and 1 at the same time — until you measure it.
When you measure a qubit, it "collapses" to either 0 or 1. Measurement fidelity asks: if I prepared a qubit in state 0 and then measured it, how often do I actually read 0?
Why it matters: Quantum computers need to run many operations. If your measurement is only 90% accurate, errors pile up fast. After 10 measurements, you've probably made at least one mistake.
Modern quantum computers aim for 99%+ measurement fidelity. Some systems (like trapped ions) achieve 99.9%+.
Measurement fidelity is formally defined as the average probability of correctly identifying the prepared state:
Where P(0|0) is the probability of measuring 0 given the qubit was prepared in |0⟩.
How measurement actually works:
In superconducting qubits, measurement is typically "dispersive" — the qubit is coupled to a resonator, and the resonator's frequency shifts depending on whether the qubit is in |0⟩ or |1⟩. You send in a microwave pulse and measure the reflected signal.
In trapped ions, you use fluorescence — shine a laser, and if the ion is in one state it glows, if in the other it stays dark.
Error sources:
Assignment vs. discrimination fidelity: "Assignment fidelity" is the raw measurement accuracy. "Discrimination fidelity" accounts for known state preparation errors.
Dispersive readout mechanics:
The qubit-resonator system is described by the Jaynes-Cummings Hamiltonian. In the dispersive limit (qubit-resonator detuning >> coupling), the resonator acquires a qubit-state-dependent phase shift:
Where g is the coupling strength and Δ is the detuning. Larger χ means easier discrimination but also increases Purcell decay.
The measurement SNR problem:
Increasing photon number improves SNR but drives non-linear effects (AC Stark shift, measurement-induced transitions). Integration time is limited by T1.
Advanced techniques:
State-of-the-art numbers:
The SPAM problem: State Preparation And Measurement errors are entangled. A "measurement error" might actually be a preparation error. Separating them requires careful benchmarking protocols.
Quantum non-demolition (QND) measurement:
Ideal QND measurement projects the qubit onto an eigenstate without introducing additional disturbance. In practice, all measurements have some "demolition" — residual entanglement with the environment, heating of motional modes (ions), or state leakage to non-computational states.
For superconducting qubits, ionization to higher transmon levels during high-power readout is a significant issue. The |0⟩/|1⟩ confusion rate improves with power, but leakage to |2⟩ worsens.
Mid-circuit measurement challenges:
Error correction requires measuring ancilla qubits while preserving data qubits. This introduces:
Google's 2023 surface code experiments showed measurement-induced errors as a dominant noise source.
The threshold question:
Surface code fault tolerance requires total error rates below ~1%. This means:
Current debate: Is 99% measurement fidelity sufficient, or do correlated errors and non-Markovian effects raise the effective threshold?
Multiplexed readout:
Reading many qubits simultaneously is harder than reading one. Frequency crowding, amplifier bandwidth, and crosstalk all degrade fidelity. At 100+ qubits, this becomes a significant engineering challenge.
Active research frontiers:
The ultimate limit:
Quantum mechanics imposes no fundamental limit on measurement fidelity — in principle, arbitrary precision is achievable. In practice, the limit is engineering: how much you can suppress noise while maintaining the qubit's coherence. The current gap between theory and experiment (~0.1-1% infidelity) represents billions of dollars of unsolved engineering.