María Cea Fernández

State preparation compilers for quantum computers typically sit at two extremes: general-purpose routines that treat the target as an opaque amplitude vector, and bespoke constructions for a handful of well-known state families. We ask whether a compiler can instead accept simple, structure-aware specifications while providing predictable resource guarantees. We answer this by designing and implementing a quantum state-preparation compiler for regular language states (RLS): uniform superpositions over bitstrings accepted by a regular description, and their complements. Users describe the target state via (i) a finite set of bitstrings, (ii) a regular expression, or (iii) a deterministic finite automaton (DFA), optionally with a complement flag. By translating the input to a DFA, minimizing it, and mapping it to an optimal matrix product state (MPS), the compiler obtains an intermediate representation (IR) that exposes and compresses hidden structure. The efficient DFA representation and minimization offloads expensive linear algebra computation in exchange of simpler automata manipulations. The combination of the regular-language frontend and this IR gives concise specifications not only for RLS but also for their complements that might otherwise require exponentially large state descriptions. This enables state preparation of an RLS or its complement with the same asymptotic resources and compile time, which to our knowledge is not supported by existing compilers. We outline two hardware-aware backends: SeqRLSP, which yields linear-depth, ancilla-free circuits for linear nearest-neighbor architectures via sequential generation, and TreeRLSP, which achieves logarithmic depth on all-to-all connectivity via a tree tensor network. On the theory side, we prove circuit-depth and gate-count bounds that scale with the system size and the maximal Schmidt rank of the target state, and we give compile-time bounds that expose the benefit of the initial DFA representation. We implement the full pipeline and evaluate it on Dicke and W states, random uniform superpositions, and complement states, comparing against general-purpose, sparse-state, and specialized baselines.

Understanding the complexity of simulating out-of-equilibrium quantum many-body dynamics is a central challenge in quantum physics. In this work, we study this question in the kicked Ising model through two complementary diagnostics: temporal entanglement (TE), which controls the cost of transverse tensor-network contractions, and non-stabilizerness, quantified by the second stabilizer Rényi entropy. Focusing on the transverse boundary vectors generated in transverse light-cone contraction, we analyze how these quantities scale in proximity to classical limits, the dual-unitary point, and inside the generic non-integrable regimes. Although spatial and temporal entanglement are expected to scale linearly in generic non-integrable and dual unitary settings, our results present a multifaceted perspective. TE scaling is substantially more nuanced than the generic volume-law expectation. Although it vanishes at the classical points, it behaves quite differently around them, demonstrating sub-linear growth or area-law saturation depending on the classical point. It also vanishes at the dual-unitary point, but is restored to volume-law growth by infinitesimal detuning. By contrast, non-stabilizerness shows a much simpler pattern, growing linearly through most of the parameter space, with its main qualitative exception again at dual unitarity, where it also vanishes. Our results have implications for the potential efficiency of transverse folding methods in the kicked Ising model, while also underscoring that complexity is multifaceted and cannot be inferred from one notion alone.