Resonance is how you talk to a qubit. Drive at the right frequency and energy transfers; miss it and nothing happens. This page explores the frequency-domain physics that underpins Rabi oscillations, qubit readout, and selective addressing on real hardware.
A qubit has two energy levels separated by a gap ΔE = hω₀. Send in a microwave pulse at exactly ω₀ and the qubit absorbs energy, transitioning from |0⟩ to |1⟩. Detune the drive and the response drops off as a Lorentzian peak.
The swing metaphor captures the core idea — frequency matching — but hides critical differences. A classical oscillator absorbs energy continuously and its amplitude grows without bound. A qubit has only two levels: it absorbs one photon, flips to |1⟩, then re-emits and flips back. This Rabi cycling is fundamentally quantum.
| Property | Classical | Quantum |
|---|---|---|
| Energy levels | Continuous — any amplitude allowed | Discrete — only |0⟩ and |1⟩ (for a qubit) |
| On-resonance response | Amplitude grows without bound (until nonlinear) | Rabi oscillation: cycles between |0⟩ and |1⟩ |
| Energy absorption | Continuous — proportional to drive time | Quantized — absorbs exactly one photon hω₀ |
| Steady state | Fixed amplitude set by drive and damping | No steady state — coherent cycling (or decays to mixed state) |
| Measurement | Non-invasive — read amplitude anytime | Destructive — collapses to |0⟩ or |1⟩ |
| Frequency matching | ✓ Maximum energy transfer at ω₀ | ✓ Maximum transition probability at ω₀ |
| Linewidth | ✓ Set by damping γ | ✓ Set by decoherence 1/(πT₂) |
| Detuning response | ✓ Lorentzian falloff | ✓ Lorentzian falloff (same shape!) |
Sweep the drive frequency and measure P(|1⟩) at each point. The peak reveals the qubit frequency. Adjust the drive amplitude (Ω) and coherence time (T₂) to see how they shape the spectral line. Hover the plot for exact values.
Drive amplitude: stronger drive → taller peak
Coherence time: longer T₂ → narrower peak
Sound sweeps through the Lorentzian: loud at resonance, quiet off-resonance.
Three qubits with T₂ = 5, 20, and 100 μs, all at the same frequency. Longer coherence means a narrower spectral line and higher Q factor. The current drive amplitude (Ω = 2.0 MHz) is shared with the spectroscopy plot above.
When a qubit couples to a cavity (or another qubit), their energy levels can't simply cross. Instead they repel, creating an avoided crossing (anticrossing). The gap at Δ = 0 equals twice the coupling strength. Hover to see how the state character changes from pure qubit/cavity to maximally mixed dressed states.
Coupling strength: larger g → bigger gap between dressed states
Two tones (L/R stereo) sweep through the avoided crossing. At Δ=0 the gap is widest.
Resonance isn't just a calibration detail — it's the mechanism behind every operation in a quantum computer. Every gate, every entangling interaction, and every measurement depends on resonance. Here's how the pieces fit together.
These two phenomena are the computational engine of a quantum computer. Entanglement creates correlations that no classical system can replicate. Interference amplifies correct answers and suppresses wrong ones. Both are enabled by resonant interactions.
Resonant pulses create superposition. A π/2 microwave pulse at ω₀ puts a qubit into (|0⟩+|1⟩)/√2. Off-resonance? The pulse does almost nothing. This selectivity is why resonance matters.
Resonant coupling creates entanglement. When two qubits are brought into resonance (same frequency), they exchange energy via the avoided crossing. This interaction produces two-qubit gates (iSWAP, CZ) that generate entanglement. On tunable-frequency chips (like transmons), you literally tune the qubit frequency to create the gate.
Gate sequences create interference. Quantum algorithms are sequences of resonant pulses arranged so that the probability amplitudes for wrong answers cancel (destructive interference) and correct answers reinforce (constructive interference). This is the quantum speedup — exploring many paths simultaneously and having them interfere to concentrate probability on the right answer.
Dispersive resonance enables measurement. To read the result, a microwave probe hits the readout cavity at its resonant frequency. The qubit state shifts that frequency by ±g²/Δ (from the avoided crossing above), letting you distinguish |0⟩ from |1⟩ without directly touching the qubit.
A single qubit has one resonance peak. A chip with many qubits has many peaks — and they must not overlap. When peaks collide (“spectral crowding”), qubits exchange energy uncontrollably, destroying information. This is the frequency planning problem every chip designer must solve.
When a qubit couples to a readout cavity (or another qubit), the coupling creates a state-dependent frequency shift. The cavity's resonant frequency moves left or right depending on whether the qubit is in |0⟩ or |1⟩. This dispersive shift χ = g²/Δ is how measurement works — you probe the cavity and the frequency you see tells you the qubit state.
Coupling shifts frequencies. Two coupled systems can't have independent resonance frequencies — they become dressed states with shifted energies (the avoided crossing from Section 4).
Entanglement makes shifts state-dependent. If qubit A is entangled with qubit B, measuring A collapses B into a definite state — which shifts B's frequency. The stronger the entanglement, the larger the shift. This is the always-on ZZ interaction that limits fidelity on fixed-frequency transmons.
Topology determines which qubits couple. Only physically connected qubits have significant coupling. The chip's wiring layout determines which pairs can interact directly — all other interactions require SWAP chains, each adding ~1% error.
Here's Tuna-9's actual topology with measured Bell-state fidelity on each edge. The fidelity varies from 85.8% to 93.5% — this variation reflects different frequency separations, coupling strengths, and local noise environments at each pair. Routing matters: GHZ states on q[2,4,6] (high-fidelity path) beat q[0,1,2] (weak links) by 5.8 percentage points.
Each qubit on a chip is tuned to a slightly different frequency, allowing selective addressing via frequency-multiplexed microwave pulses. Here are representative qubit frequencies across our three platforms. The spread within each chip is deliberate — it prevents unwanted crosstalk between neighboring qubits.
Note: frequencies are representative (real calibration data is proprietary). The principle — each qubit at a distinct frequency — is accurate.
See the full glossary for more definitions.
The condition where a driving frequency matches a system’s natural frequency, enabling maximum energy transfer. For a qubit: ω_drive = ω₀.
The difference between the drive frequency and the qubit frequency: Δ = ω_drive - ω₀. Zero detuning means perfect resonance.
Sweeping a drive frequency across a range and measuring the response. The peak reveals the qubit’s transition frequency. First step in any calibration workflow.
The characteristic frequency response P(Δ) = Ω²/(Ω² + Δ² + γ²) of a resonance peak. Natural for systems with exponential decay (T₂ decoherence).
Full Width at Half Maximum — the frequency span where the response exceeds half its peak value. Related to coherence: FWHM = 1/(π T₂).
Quality factor = ω₀/FWHM. Measures how many oscillations a system completes before losing energy. Superconducting qubits: Q ~ 10⁶. Higher Q means better frequency selectivity.
The timescale over which a qubit loses phase information. Determines linewidth: longer T₂ → narrower peak → sharper frequency selectivity.
When two coupled quantum systems have nearby energies, their levels repel rather than crossing. The minimum gap equals 2g, where g is the coupling strength.
Eigenstates of the coupled qubit-cavity system. At Δ = 0, they are equal superpositions of |qubit⟩ and |cavity⟩. At large Δ, they return to bare states.
Reading a qubit by measuring cavity frequency shift χ = g²/Δ. In the dispersive regime (Δ ≫ g), |0⟩ and |1⟩ shift the cavity in opposite directions.
The rate at which a resonant drive rotates the qubit state. Proportional to the microwave amplitude. Determines spectroscopy peak height and Rabi oscillation speed.
A charge qubit with reduced charge sensitivity (E_J/E_C ~ 50–100). The dominant superconducting qubit architecture. Used in Tuna-9, Garnet, and Torino.
P. Krantz, M. Kjaergaard, F. Yan, T.P. Orlando, S. Gustavsson, W.D. Oliver, “A Quantum Engineer’s Guide to Superconducting Qubits,” Appl. Phys. Rev. 6, 021318 (2019).
arXiv:1904.06560 ↗A. Blais, A.L. Grimsmo, S.M. Girvin, A. Wallraff, “Circuit quantum electrodynamics,” Rev. Mod. Phys. 93, 025005 (2021).
arXiv:2005.12667 ↗Rabi Oscillations — Time-domain view of qubit control — chevron patterns, detuning effects, Bloch sphere dynamics.
Visit page →Hamiltonians Explorer — How molecular Hamiltonians are built and compressed. What gets measured in VQE.
Visit page →Time-domain qubit control: chevron heatmaps, pulse sequences, Bloch sphere
Molecular Hamiltonians, Pauli decomposition, bond stretching
Circuit architectures from 4 papers, mapped to 3 quantum processors
37 terms across 7 categories with clear definitions
Superconducting qubits are controlled by microwave pulses tuned to their resonance frequency, typically 4–6 GHz. When the drive frequency matches the qubit's energy splitting, the qubit absorbs energy and transitions between states — this is the physical mechanism behind every quantum gate.
The resonance line shape is a Lorentzian peak whose width is set by the qubit's coherence time. When a qubit couples to a resonator cavity, their energy levels undergo an avoided crossing: the bare frequencies repel, creating "dressed states" that are hybridizations of qubit and cavity. This dispersive coupling is how superconducting qubits are read out without destroying their state.
This interactive shows real frequency data from Quantum Inspire Tuna-9, IQM Garnet, and IBM processors, alongside the physics of Lorentzian peaks, Q-factors, and cavity-qubit coupling.