Coherent Quantum Crosstalk Noise

• Coherent quantum crosstalk noise is a deterministic, phase-preserving error mechanism arising from unintended couplings between qubits, inducing neighbor-dependent phase accumulation.
• It manifests across quantum platforms such as superconducting, trapped-ion, and neutral-atom systems, each with specific interaction models like ZZ couplings and cross-resonance spillover.
• Mitigation techniques including pulse shaping, dynamical decoupling, and quantum optimal control are employed to suppress these coherent interactions and improve circuit performance.

Coherent quantum crosstalk noise is a phase-preserving, deterministic error channel in which unintended couplings between qubits or quantum modes produce neighbor-dependent phase accumulation or spectator rotations during idling, driving, or entangling operations. In contemporary quantum devices it is widely considered one of the major problems that must be solved for operation beyond one or two qubits, because its unitary character allows errors to interfere constructively or destructively across parallel gates, deep circuits, and repeated syndrome-extraction rounds (Gicev et al., 26 May 2026). In superconducting processors the dominant low-order manifestation is often static or gate-induced $ZZ$ coupling, but related coherent crosstalk mechanisms also arise from cross-resonance spillover, trapped-ion spectator interactions, Rydberg blockade shifts, and bosonic mode mixing (Goldschmidt et al., 16 Mar 2026).

1. Definition and formal distinction from incoherent crosstalk

Coherent crosstalk is the deterministic unitary component of unwanted inter-qubit or inter-mode coupling. A generic two-qubit model is

$$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$

which generates neighbor-dependent rotations or conditional phase accumulation. By contrast, incoherent crosstalk corresponds to stochastic population or phase shifts, commonly modeled as correlated Lindblad channels or Pauli channels, and therefore cannot be undone by unitary refocusing alone (Gicev et al., 26 May 2026).

In fixed-coupler superconducting architectures, a common specialization is the always-on parasitic interaction

$$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$

For transmons, the coupling strength can be written as

$$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$

with $J$ the fixed capacitive coupling, $\alpha_k$ the qubit anharmonicities, and $\Delta_{ij}=\omega_i-\omega_j$. In the rotating frame with ideal single-qubit drives $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$, the total Hamiltonian is $H(t)=H_C(t)+H_{XT}$, so parallel single-qubit gates acquire coherent phase errors from $H_{ZZ}$ (Goldschmidt et al., 16 Mar 2026).

A complementary gate-induced model treats crosstalk as a small unitary leakage on spectator qubits,

$$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$0

where the net rotation angle on qubit $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$1 is $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$2. This formulation is useful when the dominant effect is control spillover rather than residual two-qubit coupling (Kang et al., 20 Feb 2025).

The distinction is operationally important. A coherent $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$3 term preserves phase information and can therefore accumulate across circuit layers, whereas a Pauli-twirled approximation retains only the marginal stochastic error rate. This difference underlies both the enhanced sensitivity of coherent crosstalk to scheduling and the inadequacy of isolated single-gate calibration for predicting full-circuit performance (Gicev et al., 26 May 2026).

2. Microscopic mechanisms and platform-specific Hamiltonians

In superconducting transmons, coherent crosstalk typically originates from residual capacitance or inductance, fixed-frequency cross-resonance interactions, and imperfect isolation of microwave drives. The review literature describes always-on $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$4 couplings with $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$5, producing a residual phase $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$6 during idle time $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$7. Cross-resonance spillover is modeled by

$$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$8

where $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$9 is the “Rabi-ratio” characterizing pulse spillover onto a spectator (Gicev et al., 26 May 2026).

Idle-tomography measurements on IBM’s 27-qubit ibm_hanoi extracted a reduced H–S–A generator

$$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$0

with dominant coherent terms $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$1 of order $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$2 and local $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$3-shifts of order $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$4. In that dataset, coherent crosstalk contributed roughly $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$5 of the crosstalk-induced infidelity for qubits within one hop of the aggressor, while beyond two hops the coherent terms fell below $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$6 and incoherent rates dominated (Harper et al., 2024).

In trapped-ion processors, the intended Mølmer–Sørensen interaction on target ions is accompanied by spectator couplings induced by finite beam tails. One model writes the crosstalk unitary as

$$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$7

with $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$8 the residual-to-target Rabi-frequency ratio. A related effective form for individually addressed gates is $$H_{ZZ}=\sum_{\langle i,j\rangle}\zeta_{ZZ}^{(ij)}\,\sigma_Z^{(i)}\sigma_Z^{(j)}.$$9, where $$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$0 on the spectator (Parrado-Rodríguez et al., 2020). This is not merely a phenomenological correction: it arises microscopically from residual coupling in the state-dependent force and therefore scales with the same control parameters that determine entangling-gate speed (Fang et al., 2022).

Neutral-atom platforms exhibit coherent crosstalk through Rydberg blockade interactions,

$$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$1

so excitation of one atom shifts the levels of nearby atoms by $$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$2 and produces detuning-induced phase errors (Gicev et al., 26 May 2026).

Bosonic and communication settings admit an analogous description. In a two-mode multiplexed channel, coherent crosstalk can be represented by a beamsplitter-type unitary

$$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$3

which mixes quadratures and displacements across modes (Koudia et al., 26 Jun 2025). In multicore-fiber quantum links, leaked coherent fields from neighboring cores beat with the local oscillator and contribute excess noise proportional to total leaked power, so the crosstalk remains phase-sensitive rather than purely thermal or shot-noise-like (Eriksson et al., 2019).

3. Characterization, tomography, and direct detection

The characterization of coherent quantum crosstalk combines control-theoretic figures of merit with hardware-level spectroscopy and circuit-level benchmarks. For shaped single-qubit gates, one uses the unitary fidelity

$$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$4

and the crosstalk sensitivity

$$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$5

which measures the second-order infidelity contribution from an error Hamiltonian such as $$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$6 (Goldschmidt et al., 16 Mar 2026).

Experimental signatures include Ramsey spectroscopy on a qubit while continuously driving its neighbor, cross-resonance spectroscopy to estimate spillover amplitudes $$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$7, simultaneous randomized benchmarking in which increased error per Clifford under parallel driving indicates injected crosstalk, Quantum Instrumental RB for separating coherent $$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$8-type and stochastic measurement crosstalk, and idle tomography for reconstructing the small coherent generator of an idle channel as a function of neighbor operations (Gicev et al., 26 May 2026).

A particularly direct protocol for residual $$\zeta_{ZZ}^{(ij)}=-J^2\cdot \frac{2(\alpha_i+\alpha_j)}{(\alpha_i+\Delta_{ij})(\alpha_j-\Delta_{ij})},$$9 extraction is parallel XY4 dynamical decoupling. The measured ground-state return probability is fit by

$J$0

where $J$1 encodes residual $J$2 and $J$3 is the decay rate. In parallel multi-qubit RB, the per-Clifford decay parameter $J$4 defines an error per gate $J$5, and the increase in $J$6 under simultaneous driving serves as a crosstalk indicator (Goldschmidt et al., 16 Mar 2026).

Idle tomography on ibm_hanoi provided a quantitative coherent-versus-incoherent split. The extracted crosstalk channel could be written as

$J$7

with coherent Hamiltonian part $J$8, stochastic Pauli part $J$9, and small affine leakage part $\alpha_k$0. The same study reported a coherent error rate per CNOT of approximately $\alpha_k$1, an incoherent rate $\alpha_k$2, and a diamond-norm distance $\alpha_k$3 (Harper et al., 2024).

Direct single-shot detection has also been proposed. In the time-adaptive CSMQC protocol, a block of spectator qubits is prepared in a modified GHZ state, exposed to unknown crosstalk bursts, inverted, and measured so that the click probability on the final spectator qubit is

$\alpha_k$4

where $\alpha_k$5 is the number of crosstalk events. For IBM-noise simulations, the reported average detection success probability was $\alpha_k$6 under equally scaled noise channels and $\alpha_k$7 under asymmetrically scaled noise channels for $\alpha_k$8 to $\alpha_k$9 crosstalk counts (Kang et al., 20 Feb 2025).

4. Suppression conditions, pulse design, and circuit-level mitigation

A central analytical result is that leading-order static $\Delta_{ij}=\omega_i-\omega_j$0 crosstalk can be cancelled by forcing the pairwise toggling-frame overlap to vanish. In a cumulant-expansion treatment of

$\Delta_{ij}=\omega_i-\omega_j$1

the first cumulant contains only the static $\Delta_{ij}=\omega_i-\omega_j$2 contributions, and the cancellation condition is

$\Delta_{ij}=\omega_i-\omega_j$3

This is a hardware-agnostic design rule for first-order suppression of coherent crosstalk (Zhou et al., 2022).

That condition leads to explicit pulse-pattern constructions. In crosstalk-robust XY4, the device is divided into two sublattices, and the pulse pattern on one sublattice is shifted relative to the other so that nearest-neighbor overlap integrals vanish. In crosstalk-robust fixed-total-time pulse sequences, a “cosine” probe $\Delta_{ij}=\omega_i-\omega_j$4 is alternated with a “sine” probe $\Delta_{ij}=\omega_i-\omega_j$5 to enforce $\Delta_{ij}=\omega_i-\omega_j$6 on neighboring qubits (Zhou et al., 2022).

A more general approach uses quantum optimal control to synthesize crosstalk-robust gate sets. The scalable formulation assigns a control trajectory $\Delta_{ij}=\omega_i-\omega_j$7 to each colored vertex of the device graph and solves

$\Delta_{ij}=\omega_i-\omega_j$8

subject to high-fidelity constraints $\Delta_{ij}=\omega_i-\omega_j$9 with $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$0, dynamical constraints, and amplitude/curvature bounds $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$1, $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$2. With a two-coloring of the heavy-hex lattice, the problem scales as $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$3 rather than exponentially. In the Magnus picture, the objective is to shape $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$4 so that the relevant $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$5-frame integrals acquire orthogonal “Fourier components,” forcing the net $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$6 overlap to zero (Goldschmidt et al., 16 Mar 2026).

Echoing remains a platform-independent mitigation primitive when the desired interaction commutes with the echo pulse while the crosstalk term anticommutes. For trapped ions, one can split an $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$7 gate into two halves and insert either spectator $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$8 pulses or target $H_C(t)=\sum_j a_j(t)\sigma_X^{(j)}/2$9 pulses, cancelling all first-order $H(t)=H_C(t)+H_{XT}$0 crosstalk while retaining the intended entangling phase (Fang et al., 2022). A related refocussing construction for MS gates uses

$H(t)=H_C(t)+H_{XT}$1

so that the spectator term changes sign between halves (Parrado-Rodríguez et al., 2020).

At the circuit level, coherent $H(t)=H_C(t)+H_{XT}$2 errors can be compensated rather than only averaged. In superconducting cross-resonance circuits, an unwanted

$H(t)=H_C(t)+H_{XT}$3

can be converted, through circuit identities, into a compensating single-qubit $H(t)=H_C(t)+H_{XT}$4 placed adjacent to the relevant CNOT. On noisier devices, a deliberately inserted stabilizer gate can contribute a coherent error of opposite sign and partially cancel the original crosstalk (Ahsan, 2021).

Randomization provides a distinct mitigation philosophy. Extended randomized compiling applies standard Pauli twirling to active qubits and additional $H(t)=H_C(t)+H_{XT}$5 rotations to neighboring spectators, converting coherent spillover into an effectively depolarizing channel on the neighbors. This allows subsequent noise-estimation techniques to treat the dominant crosstalk contribution as stochastic rather than phase-coherent (Perrin et al., 2023).

5. Experimental benchmarks and algorithmic consequences

Hardware benchmarks show that coherent crosstalk suppression affects not only calibration observables but also algorithmic output distributions. On IBM Quantum Platform devices, parallel XY4 experiments on $H(t)=H_C(t)+H_{XT}$6 qubits reported $H(t)=H_C(t)+H_{XT}$7 and $H(t)=H_C(t)+H_{XT}$8 for Gaussian gates of duration $H(t)=H_C(t)+H_{XT}$9, $H_{ZZ}$0 and $H_{ZZ}$1 for detuning-robust pulses, and $H_{ZZ}$2 with $H_{ZZ}$3 for a crosstalk-robust gate set, corresponding to a $H_{ZZ}$4 slower decay and the disappearance of the residual oscillation (Goldschmidt et al., 16 Mar 2026).

In simultaneous $H_{ZZ}$5-qubit randomized Clifford circuits, isolated single-qubit RB yielded $H_{ZZ}$6 for the crosstalk-robust gate set and $H_{ZZ}$7 for Gaussian gates, while simultaneous RB yielded $H_{ZZ}$8 and $H_{ZZ}$9, respectively, corresponding to an approximately $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$00 improvement in error per Clifford under crosstalk injection. The same study further reported that, in in-house single-qubit RB at durations $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$01, the crosstalk-robust gate-set performance was essentially independent of duration, even though cloud calibration forced $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$02 pulses on IBM hardware (Goldschmidt et al., 16 Mar 2026).

The first algorithm-level assessment of complete optimal-control gate sets used a four-qubit transverse-field Ising model with

$$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$03

and second-order Trotter step $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$04. Using the Kullback–Leibler divergence between measured and ideal output distributions, the reported IBM Brisbane result after one Trotter step was $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$05 for Gaussian gates, $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$06 for detuning-robust pulses, and $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$07 for the crosstalk-robust gate set, implying an approximately fourfold median improvement in algorithmic performance over the Gaussian baseline (Goldschmidt et al., 16 Mar 2026).

Related experiments on dynamical decoupling and trapped-ion entangling gates show comparable sensitivity to coherent crosstalk engineering.

Benchmark	Baseline	Crosstalk-aware result
IBM parallel XY4 on 8 qubits	Gaussian: $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$08, $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$09	CRGS: $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$10, $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$11
IBM simultaneous 4-qubit RB	Gaussian: $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$12	CRGS: $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$13
IBM Brisbane TFIM, $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$14 Trotter step	Gaussian: $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$15	CRGS: $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$16
IBM state preservation and QNS	Standard XY4 / FTTPS	CR-XY4 gives $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$17 longer $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$18; CR-FTTPS gives $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$19 reduction in reconstruction error
$$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$20 five-ion chain	Native repeated $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$21 gates	Echo suppression yields Bell-state fidelity $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$22; per-gate infidelity $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$23 for local suppression (Zhou et al., 2022)

The circuit-level consequences of coherent crosstalk also appear in encoded-state preparation. On IBMQ Melbourne, Casablanca, Jakarta, and Lagos, phase-sensitive tracing of $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$24 $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$25-state preparation showed that reordering commuting CNOTs changes the observed phase-flip profile and that targeted compensation can reduce infidelity by up to $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$26, with larger improvements in some hardware-specific settings (Ahsan, 2021). This suggests that the observable effect of coherent crosstalk is inseparable from circuit geometry and scheduling.

6. Fault tolerance, shared-use systems, and unresolved problems

Coherent crosstalk is a first-class concern for quantum error correction because it lowers thresholds modestly while increasing sub-threshold logical error rates substantially. In surface-code simulations with coherent nearest-neighbor $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$27 crosstalk modeled as

$$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$28

the baseline threshold was reported as $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$29 without crosstalk, $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$30 with Pauli-twirled crosstalk, and $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$31 with fully coherent crosstalk. At $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$32, coherent crosstalk raised the logical error-rate proxy by up to a factor of two compared with the Pauli-twirled approximation. The same study found that random-sign coherent crosstalk nearly coincides with the Pauli-twirled result, showing that the distribution of coherent phases matters, not only their marginal strength (Harper et al., 28 May 2026).

A complementary rotated-surface-code study distinguished gate-based and always-on crosstalk, as well as data–ancilla and data–data channels. The most damaging channel was gate-based nearest-neighbor data–ancilla crosstalk, which reduced the threshold from $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$33 to $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$34 and shrank the effective distance at $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$35 by approximately $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$36. Hardware-agnostic remedies based on redundant stabilizer checks and $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$37-flagged syndrome-measurement gadgets restored thresholds to above $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$38 and removed the additional time overhead in stability experiments (Zhou et al., 6 Mar 2025).

The logic-level implications are not limited to thresholds. In an $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$39 code, if the maximum physical crosstalk weight is $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$40, then no weight-$$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$41 physical correlated error can coincide with a logical operator, so no logical correlated Pauli error arises. Conversely, low-distance codes can map specific correlated physical crosstalk events into correlated logical errors, as illustrated by the $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$42 example in which a physical $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$43 error implements $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$44 (Zhou et al., 6 Mar 2025).

Shared quantum-computing environments add a security dimension. Crosstalk attacks benchmarked on IBM hardware showed that coherent crosstalk is a viable threat to computations on nearby qubits, motivating mitigation strategies such as circuit separation, qubit allocation optimization via reinforcement learning, and spectator qubits (Harper et al., 2024). The time-adaptive CSMQC detector extends this line of work by using dedicated GHZ-like spectator registers to flag sparse coherent crosstalk in a single shot, which is particularly relevant when the exact spatio-temporal gate distribution is hidden in multi-user systems (Kang et al., 20 Feb 2025).

Several open problems remain. The review literature identifies non-Markovian crosstalk, scaling to QEC lattices, and emerging platforms such as photonic switch networks, semiconductor quantum dots, and neutral-atom analog simulators as under-explored directions (Gicev et al., 26 May 2026). At the architecture level, quantum optimal-control studies indicate that crosstalk-robust gate sets can tolerate larger qubit–qubit coupling strengths and may halve two-qubit gate times, with simulated fidelities approaching the $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$45 limit for coupling increases of $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$46 or $$H_{\mathrm{ct}}=J_{ij}\,(\sigma_i^+ \sigma_j^-+\sigma_i^- \sigma_j^+) + \zeta_{ij}\,\sigma_i^Z\sigma_j^Z,$$47 in transverse-field Ising benchmarks (Goldschmidt et al., 16 Mar 2026). A plausible implication is that coherent crosstalk should not be viewed solely as an unwanted by-product of hardware scaling; once characterized at the Hamiltonian level, it becomes a target for hardware–software co-design spanning calibration, compilation, benchmarking, and fault-tolerant architecture.