29. Why Quantum Computers Fail
29.1Decoherence
Decoherence is the loss of definite phase relations between probability amplitudes, caused by the system becoming entangled with environmental degrees of freedom nobody observes. There is nothing mystical about it: the joint system-plus-environment evolves unitarily, and if you ignore the environment, your system's description degrades from a pure state into a mixture — Chapter 30 gives exactly the machinery for this. What is lost is interference, the computational resource of 1.2. The clock it sets is brutal: in a transmon, phase relations survive for tens of microseconds; in trapped ions, for seconds. Every quantum computation races this clock, and loses unless it finishes first.
29.2Relaxation
Energy relaxation is the decay of the excited state |1⟩ down to |0⟩, characterized by the time T1. It is irreversible dissipation — no unitary can restore what leaked away — and the channel that describes it is amplitude damping (31.7). In superconducting qubits the mechanisms are dielectric loss in amorphous oxides, Purcell decay through the readout resonator, and quasiparticle tunneling. The arithmetic to internalize: a qubit excited at t = 0 survives with probability exp(−t/T1). With T1 ≈ 100 µs and gates ≈ 20 ns, one gate loses about 2×10⁻⁴ to relaxation — negligible alone, meaningful multiplied over a thousand-gate circuit, fatal in a fault-tolerance cycle.
29.3Dephasing
Dephasing destroys relative phase without exchanging energy: populations stay fixed while the off-diagonal entries of the density matrix decay with the transverse time T2. The exact relation is 1/T2 = 1/(2·T1) + 1/Tφ, where Tφ is the pure dephasing time — hence T2 ≤ 2·T1 always. Dephasing is easy to underestimate because energy measurements see nothing: a superposition degrades into a classical mixture (30.2) while its energy statistics look perfectly healthy. Part of the noise is slow frequency wandering, which echo techniques (a mid-sequence π pulse, Hahn echo) can refocus — one of the few places noise is partially reversible.
29.4Gate errors
Every gate is a physical analog operation, and its error has two families. Coherent errors are systematic miscalibrations — over-rotation by a fixed angle, a wrong phase — which do not randomize the state but rotate it to the wrong state; their amplitudes add coherently over n gates, which can grow worse than the naive expectation. Stochastic errors are relaxation and dephasing during the gate plus control noise; their probabilities add. The standard metric is average gate fidelity from randomized benchmarking, which cleanly separates gate error from state-preparation and measurement error. Typical numbers: single-qubit gates 10⁻⁴–10⁻³, two-qubit gates 10⁻³–10⁻², against a surface-code threshold near 10⁻² (Part X).
29.5Measurement errors
Readout assigns the wrong bit: it reports 1 when the qubit was 0, or 0 when it was 1. The model is an asymmetric confusion matrix — the two error rates are generally different — and modern machines run 99–99.9% fidelity. Causes: a weak measurement signal before amplification, T1 decay during the 100 ns–1 µs readout itself, and discriminator drift (29.8). Readout error has a property no other error has: it acts after all quantum operations are done, so it can be corrected statistically in classical post-processing by inverting the confusion matrix — at the price of amplifying shot noise. This is the one error a software engineer can fully own, and the experiment below does exactly that.
29.6Leakage
Leakage is population escaping the computational subspace {|0⟩, |1⟩} into higher levels. Real qubits are not two-level systems: a transmon is a weakly anharmonic oscillator with |2⟩, |3⟩, ... sitting only ~200–300 MHz above |1⟩, and strong or misshapen pulses populate them. Leakage breaks the two-level channel models of Chapter 31 and is poison for error correction: a leaked qubit produces faulty syndromes and keeps doing so, since leakage does not randomize away. Mitigations: DRAG pulse shaping, leakage-reduction units between cycles, and leakage-aware compilation. Typical per-gate leakage is 10⁻⁴–10⁻³ — small, but it accumulates in long fault-tolerance computations.
29.7Crosstalk
Crosstalk is unintended drive of qubit j while you are addressing qubit i: shared microwave lines, a common resonator bus, and flux pulses bleeding through shared circuitry all do it. The measurable symptom: gates run simultaneously degrade in fidelity compared with isolated calibration, sometimes by several times. The structural damage is worse than the per-gate number suggests — crosstalk creates correlated errors between physical neighbors, and correlated errors violate the independence assumptions that error-correction thresholds are proven under (Part X). Countermeasures are classical engineering: frequency allocation, pulse shaping, dynamical decoupling on idle qubits, and simultaneous randomized benchmarking to quantify the damage. Nothing fundamental prevents engineering it down.
29.8Calibration drift
Device parameters move on hours-to-days timescales: qubit frequencies shift with flux noise and temperature, pulse amplitudes drift as electronics age, readout discriminators wander. A large machine is therefore never fully calibrated; it runs continuous automated recalibration, and vendors publish per-qubit, per-day error rates. Two consequences for working practice. First, fidelity is a time series, not a constant: a benchmark at 09:00 does not describe the machine at 21:00, and honest experiments sample over time. Second, calibration automation — scheduling what to recalibrate and when on a device with thousands of interacting parameters — is one of the most software-heavy jobs inside hardware companies.
29.9Thermal effects
A qubit arrives thermally excited unless the machine is colder than its own frequency: excited-state population is n = 1/(exp(hf/kT) − 1). A 5 GHz transmon needs T ≪ 240 mK, which is why dilution refrigerators run at 10–20 mK, giving n ~ 10⁻⁵. Warm wiring radiates blackbody photons into the chip, so attenuation and filtering are load-bearing components. Thermal effects differ per platform rather than disappearing: ions and neutral atoms escape cryogenics but pay in laser cooling and ultra-high vacuum; photonic detectors (SNSPDs) still need a cryostat. Every platform pays a thermal bill — the engineering question is where, and in what currency.
29.10Environmental noise
The environment is not an abstract bath; it has a spectrum you can measure and structures you can name. In superconducting chips: two-level-system defects in amorphous dielectrics, 1/f flux noise, charge noise, quasiparticles — and ionizing radiation, where cosmic rays or radioactive decay deposit energy bursts that flip or dephase hundreds of qubits at once, a documented correlated-error problem that directly threatens error correction (Part X). Mitigation is materials science, shielding, filtering, and layout discipline. The mindset is the one classical electronics engineers already have — grounding, EMI, noise budgets — raised to a much higher standard, because here the signal is a single quantum of energy.