Contributed Session: Quantum Estimation
Paper ID: 23
Authors: Salma K. Elsokkary and Ian R. Petersen
Title: Predicting IBM quantum computer calibration parameters using different time series methods
Abstract: Execution of large quantum algorithms requires allocating the quantum circuit to more reliable qubits and gates. For IBM quantum computers, calibration parameters such as T1, T2, RO and CZ are important metrics to compare qubit and gate reliabilities. As these parameters change continuously, predicting them over the near future helps in both, preprocessing and postprocessing quantum error mitigation (QEM) schemes. For preprocessing QEM, allocation algorithms need to compare different components as a part of the algorithm. Currently, this is done by using the reported calibration data published on the IBM website. However, this may not yield good results as the data is continuously changing but is only reported daily. If the algorithm is executed a number of hours after the calibration data is reported, the data will already be obsolete. Also, for long algorithms, the parameters may change significantly during the execution of the algorithm. Hence, in qubit and gate allocation, we are motivated to predict the near future behaviour of the qubits and gates. In this paper, we develop a ’score’ metric, which enables us to understand how the order of qubits/gates in terms of calibration data, can be improved by using model predictions as compared to simply relying on the reported data.
Paper ID: 64
Authors: Tommaso Grigoletto, Marco Peruzzo and Francesco Ticozzi
Title: Reconstructing quantum states and expectations via dynamical tomography
Abstract: When the dynamics of a quantum system of interest is known, an informationally complete set of observables is not needed for state reconstruction via tomographic techniques: letting the system evolve before performing the measurement allows one to effectively extend the available ways to probe the system. This idea leads to dynamical quantum tomography, whose feasibility we characterize for general quantum dynamics using Krylov-based methods. Specializing in Markovian ones, we also provide deterministic tests and randomized ones to effectively assess parametric dynamics. The limits of the methods are explored by comparing unitary and open dynamics when a single observable is available, and the set of observables whose expectation can be reconstructed from the available ones characterized. The framework is illustrated with applications to a spin chain (with or without dissipation) and an electron-nuclear system.
Paper ID: 84
Authors: Mael Bompais
Title: Exponential purification of quantum trajectories and stability of quantum filters
Abstract: Quantum trajectories are stochastic processes describing the evolution of a quantum system under repeated indirect measurements. Starting from an arbitrary mixed state, a fundamental question is whether — and how fast — the accumulated measurement record reveals the true state of the system. This talk addresses both the qualitative and quantitative aspects of this question. Under a structural condition known as the absence of dark subspaces — subspaces on which the Kraus operators act isometrically, rendering the measurement uninformative — Kümmerer and Maassen established that quantum trajectories almost surely purify: the purity tr(rho_n^2) converges to 1 almost surely. We first present a short alternative proof of this result based on Lyapunov techniques, using the impurity function V(rho) = sqrt(1 - tr(rho^2)) as a supermartingale. The main contribution of this talk is to strengthen this asymptotic result to an exponential rate. We show that the expected impurity decreases exponentially fast, at an explicit rate expressed in terms of the contraction of two-dimensional volumes induced by the Kraus operators. This geometric interpretation connects the rate directly to how strongly the measurement channel distorts two-dimensional subspaces of the Hilbert space. A central theme of the talk is the intimate connection between purification and state estimation. When the true initial state is unknown, one constructs an estimated trajectory by propagating an arbitrary initial guess under the same measurement record. The stability of this quantum filter — the convergence of the estimated trajectory to the true one — is precisely what purification enables. We show that the infidelity between the true and estimated trajectories also decreases exponentially fast in expectation, establishing exponential stability of the quantum filter. This result quantifies the rate at which the measurement record erases all memory of the initial estimate, and provides an operational meaning to the purification rate: it governs the speed at which information about the current quantum state becomes accessible from observations alone. We illustrate the theory on a monitored spin-chain model consisting of four qubits with Ising interactions, subject to repeated local measurements at one end. Numerical simulations are consistent with the theoretical predictions and confirm the exponential decay of the impurity. This talk is based on the preprint arXiv:2601.14023.