Describing the dynamics of open systems is essential for fault-tolerant quantum computation. Under Markovian assumptions, we can characterize dissipative dynamics via the Lindbladian. Using Bell sampling, we provide an efficient, ansatz-free Lindbladian learning algorithm with polynomial-time classical postprocessing. Motivated by the prevalence of state preparation and measurement (SPAM) noise on near-term devices, we also introduce the first efficient SPAM-robust protocol capable of learning the gauge-independent components of sparse Lindbladians to arbitrary precision in the presence of constant-order SPAM error. In doing so, we provide the first rigorous characterization of the gauge degrees of freedom in noisy Lindbladian learning, precisely identifying which components remain learnable under SPAM noise.
Senior Thesis for the Degree of Bachelor of Science, Computer Science and Physics. Defended May 29, 2026, California Institute of Technology. Supervised by Prof. Yu Tong and Prof. John Preskill. 81 pages, 5 figures
Describing the dynamics of open systems is essential for fault-tolerant quantum computation. Under Markovian assumptions, we can characterize dissipative dynamics via the Lindbladian. Using Bell sampling, we provide an efficient, ansatz-free Lindbladian learning algorithm with polynomial-time classical postprocessing. Motivated by the prevalence of state preparation and measurement (SPAM) noise on near-term devices, we also introduce the first efficient SPAM-robust protocol capable of learning the gauge-independent components of sparse Lindbladians to arbitrary precision in the presence of constant-order SPAM error. In doing so, we provide the first rigorous characterization of the gauge degrees of freedom in noisy Lindbladian learning, precisely identifying which components remain learnable under SPAM noise.
Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present a sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, admits provably stable coefficient reconstruction, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.
We study the problem of learning a local Lindbladian in the presence of state-preparation-and-measurement (SPAM) noise. Although recent work has developed scalable learning algorithms under idealized access assumptions, SPAM can make distinct Lindbladians experimentally indistinguishable, thus making part of the Lindbladian fundamentally unlearnable. We give a sharp characterization of this obstruction for bounded-degree local Lindbladians. We identify a family of locality-preserving gauge transformations that commutes with trusted single-qubit control, and use it to classify Lindbladian components. For the generically gauge dependent components, we construct Lindbladians to show that they can have Ω(1) uncertainty independent of system size, even after imposing complete positivity.
We complement this characterization with SPAM-robust algorithms for learning every universally gauge-invariant component. Our algorithms use only trusted single-qubit operations, require neither ancillas nor entangling control, and use O(ε−2log(N/δ)) experiments and total evolution time for constant locality and degree. Our guarantees allow global SPAM to become arbitrarily far from ideal as N grows, requiring only nonvanishing local visibility. We also establish sufficient conditions for boundary-induced gauge invariance of additional Hamiltonian coefficients under physical positivity constraints, though learning these additional parameters in general remains an open problem. More broadly, our gauge-aware framework and SPAM-cancellation techniques offer a practical toolkit for the scalable characterization of open quantum systems.
Quantum devices are open systems whose dynamics interleave coherent evolution with dissipation, and benchmarking, error mitigation, and error correction all rest on a faithful model of both. Existing characterization protocols either assume prior knowledge of the interaction and noise structure, or demand ancillas, entangled probes, or mid-circuit control, or capture only the Pauli-diagonal part of the noise. Here, we present a protocol that reconstructs an arbitrary sparse Markovian generator, including every Hamiltonian together with the jump operator coefficients, using only product Pauli state preparation, single uninterrupted forward evolutions, and product Pauli measurements. Given a sparsity budget M0 and a strength bound Γ of the Lindbladian, every coefficient is learned to precision ε from O(Γ2M02/ε4) experiments and O(ΓM02/ε2) total evolution time, with both supports identified from data without locality assumptions. The protocol runs at a logarithmic number of positive evolution times on a hardware clock lattice and is provably robust to calibrated state-preparation and measurement errors.
We study ansatz-free Lindbladian learning, the problem of reconstructing the generator of an open quantum system without prior knowledge of its Hamiltonian or dissipator structures. This problem exhibits two fundamental precision limits. Hamiltonian components not obscured by dissipation are Heisenberg-limited, while full Lindbladian reconstruction is subject to the quadratically worse standard quantum limit. This creates an apparent algorithmic impasse: achieving the Heisenberg-limited Hamiltonian learning requires suppressing unknown dissipation, which seemingly demands prior reconstruction of the noise and thereby incurs the standard-quantum-limit cost. In this work, we resolve this obstruction by giving an algorithm that learns the Hamiltonian disjoint from dissipator (HDD) at the Heisenberg limit without prior knowledge of either the Hamiltonian or dissipator supports. Our main technical ingredient is a randomized recursive stabilizer-code construction that progressively identifies and suppresses the dominant dissipative terms without reconstructing the full dissipator. Building on this framework, we also introduce an efficient end-to-end algorithm that learns the entire sparse Lindbladian at the standard quantum limit. Finally, we prove that in the ansatz-free setting, the HDD terms constitute the maximal set of Hamiltonian coefficients uniformly learnable at the Heisenberg limit. We show that every term outside HDD is fundamentally standard-quantum limited, extending prior no-go results to the ansatz-free setting. Together, our protocols provide a scalable framework for characterizing open quantum systems, with quantum error correction serving as a key learning primitive.
We study the problem of learning an unknown Markovian open-system generator from access to its physical time evolution. This generator, called a Lindbladian, contains Hamiltonian and dissipative coefficients indexed by an exponentially large family of possible Pauli terms. We propose an efficient algorithm that learns arbitrary Lindbladians from time evolution under minimal assumptions. For a Lindbladian of dynamical strength at most Λ, the algorithm estimates every coefficient to error ε using O(Λ2/ε2) experiments and O(Λ/ε2) total evolution time, together with polynomial classical running time. The algorithm consists of two nonadaptive, ancilla-free, and control-free stages: 1. The support-learning stage outputs a candidate support of size poly(Λ/η) that contains every Hamiltonian and dissipative coordinate of magnitude at least η, using O(Λ2/η2) experiments with preparations of product Pauli eigenstates and single-qubit Pauli measurements. 2.The coefficient-learning stage estimates all coefficients in any candidate support of size M to error ε, using O(Λ2logM/ε2) experiments with preparations of random stabilizer states and measurements in random Clifford bases. Composing the two stages identifies and estimates every coefficient of an arbitrary Lindbladian in polynomial time. The experiment-count and total-evolution-time scalings match the lower bounds up to logarithmic factors, so the algorithm is nearly optimal for learning arbitrary Lindbladians.
Characterizing the features of a Hamiltonian that governs a quantum system serves as a fundamental subroutine of quantum device calibration, signal sensing, and error correction. Recent works have proposed protocols achieving the optimal Heisenberg-limited scaling learning ansatz-free Hamiltonians from their real-time evolutions without fully specifying interaction structures. However, these protocols rely on both deep circuits with interleaving probes and control, and extremely short time resolution, making them difficult to implement on near- and intermediate-term in situ quantum experiments. In this work, we propose a computationally efficient, control-free, and ancilla-free algorithm that uses only Pauli product state preparation and measurement, and learns an ansatz-free Hamiltonian H with ∣∣H∣∣≤Λ in total evolution time of Θ(ε2Λlog(εΛ)). The evolution time cost of our algorithm is optimal for any control-free protocols as we further prove a lower bound of Ω(ε2Λlog(εΛ)). Technically, our method introduces a randomized-sampling framework that combines band-limited kernel-based time sampling with a displacement sieve for Hamiltonian structure learning. The characteristic probe time resolution depends only on Λ instead of ε, which makes our protocol especially appealing in the high-precision regime for sensing and calibration applications. We also show that the algorithm maintains the same asymptotic total evolution time in the presence of state-preparation-and-measurement (SPAM) noise when the Hamiltonian is local after calibration. Our results demonstrate the fundamental cost of experimentally friendly Hamiltonian learning and provide a practical route to rigorous in situ characterization of near-term quantum platforms.