Diabatic State Preparation in Quantum Systems

• Diabatic state preparation is a set of techniques that exploit controlled non-adiabatic transitions to efficiently engineer tailored quantum states.
• It utilizes methods such as counterdiabatic driving and variational modulation to suppress unwanted transitions and achieve fast state transfer.
• These protocols provide practical solutions in systems with limited coherence times by optimizing Hamiltonian control for quantum metrology and simulation.

Diabatic state preparation refers to non-adiabatic protocols that deliberately generate, control, or exploit transitions away from instantaneous eigenstates during a time-dependent change of the system Hamiltonian, with the practical aim of efficiently preparing entangled, excited, or otherwise tailored quantum states. In contrast to adiabatic protocols—which rely on slow evolution to suppress transitions out of the target manifold—diabatic state preparation leverages engineered couplings, counterdiabatic driving, variational modulation, or controlled ramps to achieve fast, high-fidelity state transfer, ground-state targeting, or the creation of desired excitation distributions. Diabatic preparation is essential in contexts where coherence times are limited, gaps close (e.g., at quantum critical points), or access to thermal distributions or non-equilibrium excited states is required.

1. Fundamentals of Diabatic State Preparation

Diabatic protocols are built around explicit violation or control of the adiabatic criterion, $\|\partial_t H\|/\Delta^2 \ll 1$ ($\Delta$ being the instantaneous gap). Landau–Zener theory quantifies the transition probability near avoided crossings: $P_{\rm exc} \approx \exp(-2\pi \Delta^2/\hbar v)$, with $v$ the sweep speed. Generic diabatic strategies include exponentially ramped fields (Lim et al., 2015), composite pulses, Floquet modulation (Duncan, 24 Jan 2025), Trotterized time evolution (Stenger et al., 4 Dec 2025), and constrained optimization over control parameters (He et al., 6 Aug 2024).

In quantum metrology and state engineering, the goal is often to transfer an initial simple state (e.g., spin-coherent) into a highly structured entangled state (e.g., Dicke, topological, charge-transfer manifold) within operational timescales dictated by decoherence or device bandwidth. Diabatic approaches enable this by encoding the desired final state in the structure of the time-dependent Hamiltonian and supplementing the main Hamiltonian trajectory with engineered compensating forces or control excursions that suppress or repurpose inevitable nonadiabatic transitions.

2. Counterdiabatic and Shortcut-to-Adiabaticity (STA) Protocols

Counterdiabatic (CD) driving is a central mechanism for diabatic state preparation. The Berry–Demirplak–Rice CD term,

$$H_{\rm CD}(t) = i\sum_m ( |\partial_t m\rangle \langle m| - \langle m| \partial_t m\rangle |m\rangle \langle m| ),$$

suppresses all unwanted transitions out of a chosen instantaneous eigenstate $|m(t)\rangle$. For ground-state targeting, only the ground-manifold term is required.

Implementable approximations rely on variational ansätze for the adiabatic gauge potential $A_\lambda$ (satisfying $H_{\rm CD}(t) = \dot{\lambda}(t) A_\lambda$), constructed from experimentally available few-body operators and optimized through minimization of $$\mathrm{Tr}\{\left( \partial_\lambda H_0 + i[A',H_0] \right)^2 \}$$ (Opatrný et al., 2015, Hartmann et al., 2021). For collective spin systems, efficient compensating operators include $L_1 = J_z J_y + J_y J_z$, $L_2 = J_z J_y J_x + J_x J_y J_z$, etc., reached by sequences of quadratic Hamiltonians or composite pulses (Opatrný et al., 2015).

In spin models and topologically ordered states, counterdiabatic terms can be locally constructed as, e.g., off-diagonal two-spin exchanges in the Kitaev model—allowing preparation of non-trivial topological order with high fidelity on short timescales (Kumar et al., 2021).

3. Variational and Modulated Diabatic Trajectories

Gap-agnostic variational approaches, such as modulated time evolution (He et al., 6 Aug 2024), dispense with explicit CD terms or gap knowledge. Instead, control fields (e.g., scaling $\lambda_j$ and transverse field $B_j$) are jointly optimized over the entire trajectory to ensure that diabatic amplitude, though permitted to leak out during evolution, is recovered in the desired state at the end. The cost function is typically the final energy in the target Hamiltonian, or equivalently, infidelity to the target ground-state. Joint optimization (e.g., via autodiff or Adam) results in dramatic reduction in required time or circuit steps: in example spin-glass systems, modulated evolution achieves fidelity $\epsilon < 10^{-3}$ in half the layers compared to QAOA (He et al., 6 Aug 2024).

CAFFEINE integrates counterdiabatic Floquet engineering with optimal control; time-dependent Floquet coefficients $\{\beta_k(\lambda)\}$ are variationally learned to stroboscopically approximate the exact gauge potential, bypassing the need for analytic CD construction (Duncan, 24 Jan 2025).

4. Diabatic State Preparation in Quantum Platforms

Diabatic protocols have been successfully implemented and characterized in trapped-ion Ising simulators (Yoshimura et al., 2014, Lim et al., 2015), cold-atom collective spin systems (Opatrný et al., 2015), superconducting qubit-cavity arrays (Cai et al., 19 Feb 2024), and gate-model quantum computers (Stenger et al., 4 Dec 2025, Wan et al., 2020). Performance metrics include fidelity to the instantaneous target state, squeezing parameter $\xi^2 = 4 \Delta J_z^2/N$, or excitation probability distributions.

In trapped-ion chains, intentional diabatic sweep (exponential ramp of field) can prepare low-lying excitation spectra, facilitate compressive-sensing-based spectroscopy, and generate nearly thermal energy distributions with effective inverse temperature $$\beta_{\rm eff} \sim 2\pi \Delta^2/(\hbar v \Delta E)$$ when the spectrum is dominated by a single crossing (Lim et al., 2015).

Gate-model algorithms (digital adiabatic via quasi-adiabatic continuation) attain diabatic error $\leq \epsilon$ with complexity $$O(\alpha^2/\gamma^2 \mathrm{polylog}(\alpha/(\gamma\epsilon)))$$ where $\alpha \geq \max\{\|H_0\|, \|H_1\|\}$ and $\gamma$ is the minimum gap (Wan et al., 2020); ground-state guiding via diabatic circuits also enables chemical-accuracy VQE–CVQE hybrid algorithms on current NISQ devices (Stenger et al., 4 Dec 2025).

5. Diabatic State Construction in Molecular and Charge-Transfer Systems

In electronic structure, diabatic labeling is crucial for charge-transfer, non-adiabatic transitions, and excited-state dynamics. Methods such as constrained charge equilibration (CQEq) directly compute diabatic state energies and couplings via electrostatic functionals and linear constraints on atomic charges, providing a low-cost alternative to CDFT with excellent agreement for realistic benchmarks (Kundu et al., 7 Nov 2024).

Recently, the Direct Diabatic States Construction (DDSC) protocol constructs valence and Rydberg diabatic states by assembling fragment-localized, state-consistent molecular orbitals into configuration-state functions (CSFs), forming each diabatic state via a small block-diagonal CI within a non-orthogonal CSF basis. Diabatic couplings and non-adiabatic coupling (NAC) vectors follow by standard contraction and differentiation (Jin et al., 16 May 2025). DDSC is particularly effective for systems with clear fragment partitions and weak inter-fragment interactions.

6. Error Scaling, Performance, and Physical Limitations

Diabatic error and fidelity scale sharply with the details of the CD protocol and regime. For collective spin transfer (N=30, T=2/$\chi_{\rm max}$), the use of progressively more compensating operators boosts fidelity from 19% (no compensation) to $1 - 2\times 10^{-7}$ (four compensators) (Opatrný et al., 2015). Squeezing parameters reach $-65$ dB below shot noise in the same context. In Ising chains, runtime scaling drops from $T_{\rm ad} \sim N^2$ (adiabatic) to $T_{\rm CD} \sim N$ (CD), and fidelity decay exponent improves by 3–5$\times$ (Hartmann et al., 2021).

Noise resilience depends on locality and the symmetry of CD corrections. In circuit QED lattices, CD driving remains robust to 15% control errors and environmental decoherence rates up to $5 \times 10^{-4}$, preserving fidelity $>0.97$ (Cai et al., 19 Feb 2024). For chemistry-inspired algorithms, short (diabatic) circuits optimize the trade-off between fidelity and noise in NISQ devices, reliably achieving chemical accuracy in ground-state energies (Stenger et al., 4 Dec 2025).

Physical limitations arise in the implementation of multi-body or nonlocal compensating terms, bandwidth for Floquet modulation, and parameter-inference for variational approaches. Most protocols rely on smooth ramp profiles (e.g., cos$^3$/sin$^3$), piecewise-constant approximations, and modular operator decompositions to maximally leverage available hardware controls.

7. Practical Guidelines and Experimental Recommendations

For laboratory realization of diabatic state preparation:

• Time-dependent Hamiltonians should be smoothly ramped to ensure boundary conditions $\partial_t H_0(0)=\partial_t H_0(T)=0$, avoiding quench-induced errors (Opatrný et al., 2015).
• CD Hamiltonian approximations should be limited to 3–4 few-body operators for practical fidelity, with coefficients determined by efficient linear algebra and weighted by atom-number probability if population fluctuates.
• Fast sequences and composite pulses enable realization of higher-order operator commutators; Rydberg blockade or cavity-QED hardware can greatly facilitate multi-spin control.
• Measurement observables such as squeezing, fidelity, correlators, and diagonal population statistics allow real-time verification of diabatic suppression and state purity.
• For charge-transfer and molecular systems, CQEq and DDSC provide scalable, computationally efficient protocols for generating diabatic surfaces and couplings, apt for embedding in machine learning force fields and molecular dynamics workflows.

Diabatic state preparation forms a rapidly evolving toolkit for high-speed, high-fidelity quantum control applicable in metrology, quantum information, molecular simulation, and condensed-matter platforms, enabling access to regimes and final states unattainable by strict adiabatic passage.