Sparse Phase Ansatzes for Resource-Efficient Qudit State Preparation via the SNAP-Displacement Protocol

Abstract

Efficient preparation of nonclassical bosonic states is a central requirement for quantum computing, simulation, and precision metrology. We study resource-efficient quantum state preparation in bosonic qudit systems using the SNAP-displacement (SD) protocol. Existing SD-based approaches typically require a large number of gates and SNAP phases, resulting in complex control pulses, increasing the ansatz duration, and amplifying the impact of photon-loss and control errors. In this work, we focus on the near- to medium-term regime, in which noisy quantum devices impose trade-offs on the fidelity that can be achieved, which must be taken into account. Specifically, we propose to optimize only a subset of the SNAP phases and introduce three progressively more general sparse ansatzes. To provide fine-grained control and identify the most suitable ansatz for a given target fidelity, we further employ a scalarized multi-objective optimization that trades off fidelity against either the number of phases or the duration of the ansatz. Numerical results for several target states and qudit dimensions up to $d=64$ show that these sparse ansatzes achieve favorable trade-offs compared to the fully parameterized SD protocol in both ideal and noisy settings, consistently reducing the number of required phases and suggesting a practical route to more efficient near- and medium-term bosonic state preparation.

Figures (10)

• Figure 1: Absolute values of the learned SNAP phase angles and of the Fock state population after each displacement gate, for each block of a Full ansatz, preparing a Haar random state with $d=16$.
• Figure 2: Location of the learnable SNAP phases on matrix $\Theta$ ($B\times d$), arranged on the block-Fock grid $(b,k)$, for a qudit of $d=8$ and $B=8$ blocks. Learnable phases are highlighted in black.
• Figure 3: Infidelity and number of non-zero phase angles for the best hyperparameter configuration $h$ obtained when penalizing the number of phases, for each penalty coefficient $\beta$.
• Figure 4: Infidelity and duration of the ansatz for the best hyperparameter configuration $h$ obtained when penalizing the duration of the ansatz, for each penalty coefficient $\beta$.
• Figure 5: Pareto frontiers showing the trade-off between the infidelity of the prepared state and the number of non-zero phase angles when optimizing the hyperparameters penalizing the number of phases. Each faded point represents a hyperparameter configuration, while solid lines connect the configurations that achieve the best trade-off (Pareto-optimal points) for each ansatz.