Crosstalk & Isolation
=====================

Checks for always-on ZZ, neighbour isolation, leakage, package modes, and unintended
                electromagnetic coupling.

.. list-table::
   :header-rows: 1

   * - #
     - VER ID
     - Parameter
     - Severity
     - Design Rule / Constraint
     - Ideal / Optimal Value
     - Acceptable Range
     - Good
     - Bad
     - Why It Matters
   * - 35
     - HFSS-C-001
     - ZZ Coupling ζ (idle)
     - Critical
     - ζ_ZZ/2π < 10 kHz between non-coupled pairs (idle)
     - < 1 kHz
     - 1 – 100 kHz
     - < 1 kHz: conditional phase < 0.01 rad in 10 µs; negligible idle ZZ
                        error
     - > 1 MHz: > 1 rad conditional phase per µs; circuit depth severely
                        limited
     - Always-on ZZ interaction from dispersive coupling. Even static ZZ causes
                        phase errors that accumulate, limiting circuit depth.
   * - 36
     - HFSS-C-002
     - Nearest Neighbour Isolation
     - High
     - S_ij (nearest neighbour) ≤ −40 dB
     - < −40 dB
     - −30 to −50 dB
     - < −40 dB: driven rotation on neighbour qubit < 10⁻⁴ rad during
                        single-qubit gate
     - > −20 dB: significant driven rotation on neighbours; simultaneous
                        single-qubit gates not independent
     - EM isolation between nearest-neighbour qubits. Insufficient isolation causes
                        unwanted rotations during single-qubit gates.
   * - 37
     - HFSS-C-003
     - Next-Nearest Isolation
     - High
     - S_ij (next-nearest) ≤ −60 dB
     - < −60 dB
     - −50 to −70 dB
     - < −60 dB: long-range crosstalk < 10⁻⁶ rad; 2D grid operation fully
                        independent
     - > −40 dB: long-range coupling; frequency collisions compound with
                        nearest-neighbour
     - Isolation beyond nearest neighbour. Critical for scalable multi-qubit
                        processors; long-range EM leakage compounds errors.
   * - 38
     - HFSS-C-004
     - Leakage to \|2⟩ (L₁)
     - Critical
     - L₁ < 0.01% per gate
     - < 0.01 %
     - 0.01 – 0.1 %
     - < 0.01%: seepage outside qubit subspace negligible; DRAG pulse sufficient
     - > 1%: leakage accumulates over circuit; error correction cannot track
                        non-qubit states
     - Population leaked to \|2⟩ non-computational state during gates. DRAG pulses
                        mitigate but require sufficient anharmonicity.
   * - 39
     - HFSS-C-005
     - Spurious Mode Gap Δf_spur
     - High
     - Δf_spur ≥ 1 GHz from nearest spurious EM mode
     - > 1 GHz gap
     - 0.5 – 2 GHz gap
     - > 1 GHz gap: no spurious mode within pulse bandwidth; gate calibration
                        stable
     - < 0.2 GHz: mode within pulse bandwidth; state leakage and parametric
                        drive of spurious modes
     - Frequency distance to nearest unintended EM mode. Modes within drive
                        bandwidth cause state leakage and gate calibration drift.
   * - 40
     - HFSS-C-006
     - Package Mode Density
     - Medium
     - < 1 spurious package mode per GHz near qubit band
     - < 0.5 modes/GHz
     - < 5 modes/GHz
     - < 0.5/GHz: low probability of accidental hybridisation across 64-qubit
                        chip
     - > 10/GHz: dense mode spectrum; unavoidable hybridisation; package must be
                        redesigned
     - Density of package/enclosure modes near qubit frequency. High density
                        increases probability of accidental mode hybridisation.