quant-phOct 13, 2026

Steering the Fidelity in State Preparation on Noisy Bosonic Systems with Risk-Seeking Optimization

Authors: Riccardo Piantoni, Riccardo Pellini, Maurizio Ferrari Dacrema, Paolo Cremonesi

Organizations: Politecnico di Milano, Italy

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

In order to execute quantum algorithms on bosonic quantum computers, it is necessary to encode their inputs into a desired target quantum state, with a process called state preparation. In real settings, state preparation methods operate in stochastic scenarios, where the prepared state is represented as a mixed state, that is a probabilistic ensemble of pure states. Therefore, existing state preparation methods optimize a variational ansatz by averaging over all possible sequences of photon loss events contained in the prepared ensemble, yielding an output state which approximates the desired target with a certain average fidelity. Such an approach, however, does not take into account directly the distribution of fidelities across states in the ensemble. In this work, we aim to maximize the fidelity of only a subset of pure states sampled from the prepared ensemble, at the cost of reducing the average fidelity overall. This trade-off is relevant when the goal is to obtain high-fidelity states with a certain probability, rather than maximizing the average fidelity of the prepared ensemble. We borrow and adapt objective functions from risk-sensitive optimization, a framework that optimizes specific characteristics of a distribution rather than only its expectation, and that has been successfully applied in Reinforcement Learning. In the considered experimental settings, our results show that the infidelities of some pure states in the prepared ensemble can be reduced by up to four orders of magnitude when using risk-seeking objectives, compared to those achieved using the standard optimization of the average fidelity. Furthermore, we show that it is possible to control the trade-off between the probability of obtaining high-fidelity states and the lowest infidelity threshold reached, providing the flexibility to select the operating point that best suits a certain application.

Figures & tables

Objective functionβ\betaAverage fidelityϵ\epsilon -probability for an infidelity ϵ\epsilon of:
   10−110^{-1}10−210^{-2}10−310^{-3}10−410^{-4}10−510^{-5}10−610^{-6}10−710^{-7}
Average         
fidelityN/A0.823921 ±\pm 0.0358750.793 ±\pm 0.041 (SR=86%)0.772 ±\pm 0.026 (SR=5%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)
Fidelity entropic risk100.795007 ±\pm 0.0793140.766 ±\pm 0.085 (SR=97%)0.766 ±\pm 0.049 (SR=86%)0.776 ±\pm 0.034 (SR=32%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)
 1000.728762 ±\pm 0.1391180.658 ±\pm 0.196 (SR=95%)0.726 ±\pm 0.095 (SR=77%)0.745 ±\pm 0.051 (SR=68%)0.760 ±\pm 0.039 (SR=39%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)
 10000.698329 ±\pm 0.1446920.602 ±\pm 0.204 (SR=97%)0.682 ±\pm 0.082 (SR=79%)0.694 ±\pm 0.042 (SR=74%)0.708 ±\pm 0.028 (SR=61%)0.713 ±\pm 0.027 (SR=24%)0.0 ±\pm 0.0 (SR=0%)0.0 ±\pm 0.0 (SR=0%)
Table 1: ϵ\epsilon -probabilities and success rates (SR) computed from the SD-ansatzes trained on the objective functions listed in Section 3.1 , for different values of the risk coefficient β\beta , if present. Each row reports the results of training the parameters of 100 repetitions of an SD-ansatz. For each objective function, the column ”Average fidelity” reports the mean average fidelity across all 100 repetitions, with its standard deviation. The group of columns under the ” ϵ\epsilon -probability for an infidelity ϵ\epsilon of:” label reports the evaluation using Monte Carlo sampling of noise trajectories, as explained in Section 4 . The mean probability estimates are computed using only the successful repetitions, which are also the same repetitions indicated by the SR. For each objective function and risk coefficient value, we highlight in bold the cell related to the lowest infidelity achieved by them. For each infidelity threshold instead, we underline the values related either to the highest probability estimate or the highest SR.
More in this topic

Quantum State Preparation

Quantum State Preparation develops circuits and control strategies for creating target quantum states with limited gates, noise, and hardware resources.

See all 27 papers

Explore similar work

CardsList
Aug 3, 2026

Adaptive Reconstruction of Bosonic Quantum States

Bosonic quantum systems provide a hardware-efficient platform for quantum information processing but remain challenging to characterise due to their large Hilbert space and the high measurement cost of state tomography. Existing approaches estimate the fidelity with respect to a single target state, making them unsuitable for applications in which physically equivalent states differ by phase space translations, rotations, or other transformations. Here, we introduce an adaptive reconstruction technique that estimates the fidelity with respect to a family of bosonic states while reconstructing the underlying Wigner function from a small number of measurements. The method combines a physics-informed parametric model with Bayesian inference, bootstrap, and active learning to iteratively select the most informative phase space sampling points. We implement the approach on a circuit quantum electrodynamics platform and benchmark it on Schrödinger cat states with amplitudes α∈[1,3]α\in[1,3]. The reconstruction yields reproducible fidelity estimates within a few minutes, remains robust to substantial displacements and rotations in phase space despite using a mismatched prior, and is sensitive to subtle state imperfections. We further compare the adaptive strategy with existing Wigner function sampling protocols experimentally, demonstrating the advantage of adaptive sampling for measurement-efficient fidelity estimation with respect to a family of cat states. Finally, we incorporate the reconstructed fidelity into the figure of merit used in a proof-of-principle closed-loop quantum optimal control experiment, demonstrating the applicability of the method to autonomous optimisation of bosonic quantum states.

Vasilisa Usova, Phila Rembold, Ian Yang +4

Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria · Institute for Experimental Physics, University of Innsbruck, 6020 Innsbruck, Austria · Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria +5

Quantum State Tomography
AskPDF
Jul 23, 2026

Approximate Quantum State Preparation Through Proximal Policy Optimization

In this work, a quantum architecture search framework for approximate quantum state preparation (QSP) is proposed. QSP is a challenging task, since the search space grows exponentially with the number of qubits, making the identification of the optimal circuit non-trivial. To address this problem, deep reinforcement learning is employed through an agent based on proximal policy optimization. The objective of the agent is to identify the best possible approximation of the target state while simultaneously minimizing the number of gates used. At each step, the agent appends a new gate to the circuit and recomputes the fidelity between the approximated state and the target states. Various experiments have been performed from 2 to 5 qubits. Both predefined states, such as Bell, GHZ, W, and Dicke states, and completely random states are considered. The proposed framework is able to achieve approximation errors of 10−1410^{-14}.

Marco Mordacci, Michele Amoretti

Quantum Software Laboratory, University of Parma, Parco Area delle Scienze, 181/A, Parma, 43124, Italy.

Quantum Architecture SearchQuantum State Preparation
AskPDF
Oct 15, 2026

Reducing the Cost of Qudit State Preparation by Learning a Sparse Structure for SNAP Gates

Preparing quantum states in bosonic qudits with SNAP--Displacement sequences requires both optimizing the gate parameters and deciding which Fock levels should be controlled by each SNAP gate. A fully parameterized ansatz assigns an independent phase to every Fock level in every gate, leading to a number of phases that grows steeply. This constitutes a problem for short to medium term systems as controlling many phases requires complex control pulses which are subject to increased control errors. Previous work reduced this cost by restricting the trainable phases to predefined sparse patterns, such as a diagonal or a grid, which however may not be optimal for a specific target state. In this work, we address this limitation by introducing a method that learns which phases are needed together with their values, using a differentiable mask. A sparsity penalty encourages the removal of unnecessary phases, while temperature annealing gradually turns the masks into binary decisions. We compare the proposed method with fully parameterized and predefined sparse ansatzes on Fourier and Haar-random target states. The evaluation considers both the minimum number of phases required to reach different infidelity thresholds and the overall trade-off between fidelity and phases required, measured through Pareto frontiers and hypervolume. The results show that learning the location of the phases together with their values provides competitive or improved fidelity--resource trade-offs, although the advantage depends on the target state and qudit dimension.

Marco Pennazio, Leonardo Ignazio Pagliochini, Riccardo Pellini +2

Politecnico di Milano, Milano, Italy

Quantum State PreparationVariational Quantum Circuits
AskPDF