Automatic Design of Quantum State Preparation Circuits for Resource-Efficient Initial Conditions in QLBM Software Frameworks

To address this gap, we propose HEASP (Hybrid Evolutionary Algorithm for State Preparation), a multi-objective QSP framework that simultaneously optimizes fidelity, circuit depth, and total gate count. HEASP combines an NSGA-II-based global search with a simulated-annealing local polishing stage. Relative to prior fidelity-centered approaches, HEASP introduces a structured multi-length initial population, inheritance of optimized parent angles, structural mutation that can change circuit length, adaptive fidelity thresholds, and stagnation-aware recovery based on polishing representative Pareto solutions. Therefore, HEASP formulates quantum state preparation as a Pareto optimization problem and returns a set of circuits that explicitly capture trade-offs between fidelity, circuit depth, and gate count.

In the joint research between TU Delft and Fujitsu Limited, we position HEASP as a complementary technology to the QLBM software frameworks. QLBM and QLBM-based quantum search are forward-looking workflows whose main algorithmic value lies in coherent fluid evolution, quantity evaluation, amplitude estimation, and search. HEASP instead targets the front end of that workflow: the offline synthesis of resource-efficient initial-state circuits. The intended use case is therefore not real-time generation of arbitrary states, but pre-compilation of a limited set of scientifically meaningful initial states that are known in advance and reused across repeated simulations or search runs. Since QLBM's initial conditions are defined through amplitude-based encoding of particle density over basis states, any valid initial condition corresponds to a well-defined quantum state. Therefore, HEASP can, in principle, synthesize the corresponding preparation circuit for any such initial condition. It is worth noting that since QLBM initial states are typically represented by real-valued amplitude distributions rather than fully generic complex-valued quantum states, additional reductions in circuit complexity may be achievable by introducing QLBM-specific constraints into the HEASP search space. Furthermore, since the present HEASP implementation repeatedly evaluates state vectors and classical angle optimization inside the loop, its classical design-time cost grows rapidly with problem size, which makes target initial states of small to medium scale the currently feasible and attractive candidates for practical applications.

We benchmark HEASP on representative QSP tasks based on 4–6 qubit Gaussian states and W states. The table below lists the comparative results between Qiskit's exact initialization routine, GASP and our method HEASP, where the results of HEASP are the solutions with over 99% fidelity at the Pareto front and the minimum circuit depth and total gate count. Across these benchmarks, HEASP consistently exhibits the behavior required for the intended QLBM role: it offers high-fidelity solutions together with shallower and lower-gate alternatives on the same Pareto front. In our experimental results, representative HEASP circuits achieve up to approximately 90% reduction in circuit depth and approximately 80% reduction in total gate count relative to Qiskit's exact initialization routine; compared with GASP, HEASP reduces depth by 47.7% and total gate count by 52.4% on average, while shortening search time by about a factor of five. The figure below also shows the quantum circuits for preparing 5-qubit Gaussian states generated by Qiskit, GASP, and HEASP, which can more intuitively show the differences in performance between the three methods.

Table: Comparative results for preparing 4--6 qubit Gaussian states and W states

Figure: Sample solutions (circuits) for 5-qubit Gaussian state target

These results support the use of HEASP as an offline compilation tool, where the cost of classical optimization is amortized over repeated executions of the same initial state. Furthermore, these results support the claim that our method HEASP, which employs explicit multi-objective optimization is practically valuable whenever state preparation competes for circuit budget with a much larger downstream algorithm.

For QLBM and QLBM-based quantum search, this contribution should be understood as a resource-efficient initial-state compiler for amplitude-based QLBM software frameworks. For instance, current superposed-configuration QLBM quantum search workflow has already supported efficient structured initialization, including uniformly distributed initial conditions, and then devote most of the algorithmic budget to coherent time evolution, quantity accumulation or mapping, amplitude estimation, and minimum finding. In this setting, HEASP offers two concrete advantages: first, it can extend initialization from simple structured states to arbitrary prescribed non-uniform states; second, it can reduce the initialization overhead of search workflows in which the later QLBM and search blocks are already resource-intensive.

It is especially attractive when the same initial states must be reused many times, for example in parameter studies, repeated evaluations of the same candidate class, or quantum search workflows over multiple lattice configurations. Since the QLBM quantum search can vary candidate systems through initial conditions or boundary conditions, a lighter and more flexible initialization layer can broaden the practically accessible design space. More generally, the ability to compile arbitrary prescribed non-uniform initial states would extend QLBM beyond its currently simple initialization patterns and provide a concrete bridge between NISQ-era state-preparation research and future quantum CFD applications aimed at optimization and design-space exploration.