The aim of the workshop is to gather researchers from different areas related to the development of quantum algorithms. Topics include but are not limited to open quantum systems, eigenvalue problems, eigenvalue transformation, differential equations, linear systems of equations, matrix input models, and learning theory.
Organizers
Speakers
Semi-plenary speakers
Harvard University
Invited speakers
Peking University
ETH Zurich
University of Warwick
University of California, Irvine
University of Michigan
Leiden University
Alfréd Rényi Institute of Mathematics
EPFL
Caltech
TU Munich
University of Copenhagen
Thursday, 16 July
![[HS 08 – 1st Floor]](https://focm2026.univie.ac.at/wp-content/uploads/2026/06/HS08.png){kind=link}
14:00-15:00 semi-plenary talk
Barbara Kraus (TU Munich)
I will present a comparison of the performance of different algorithms for ground-state preparation in the presence of noise, focusing on cooling protocols as proposed in [1], adiabatic evolution, and the quantum approximate optimization algorithm (QAOA) [2]. The analytical approach explained here, together with numerical validation, establishes an extendable approach to benchmarking ground-state preparation algorithms.
[1] D. Molpeceres, S. Lu, J. I. Cirac, and B. Kraus, “Quantum algorithms for cooling: A simple case study,” Phys. Rev. Res. 7, 033162 (2025)
[2] D. Molpeceres, S. Lu, B. Kraus, and J. I. Cirac, in preparation
15:00-15:30
Zhiyan Ding (University of Michigan)
I will introduce our recent work on using a system-bath interaction framework to prepare the thermal or ground state of a target Hamiltonian. The proposed algorithm requires only a single ancilla qubit, forward Hamiltonian simulation, and partial tracing, which makes it particularly well suited for near-term and early fault-tolerant quantum hardware. I will begin by presenting the algorithm and its theoretical guarantees. I will then discuss two very recent progress that provide further improvements and new insights.
15:30-16:00 Social Time
16:00-16:30 Coffee Break
17:00-17:30
Andras Gilyen (Alfréd Rényi Institute of Mathematics)
We present a general protocol for estimating M observables from only O(\log (M)/\epsilon^2) copies of a Gibbs state, given access to its Hamiltonian. The protocol uses single-copy, nonadaptive measurements and a total Hamiltonian simulation time of ~O(\beta M/\epsilon^2); we show that the sample complexity is optimal in a black-box setting. The key idea is a new interpretation of quantum Gibbs samplers as detailed-balanced measurement channels: measurements that preserve the Gibbs state when outcomes are marginalized. Consequently, shadow tomography of thermal states admits a general efficient algorithm when the Hamiltonian is known, substantially lowering the readout cost in quantum thermal simulation.
17:30-18:00
Daniel Stilck França (University of Copenhagen)
Quantum algorithms for semidefinite programming, beginning with the breakthrough work of Brandão and Svore and refined in subsequent quantum SDP solvers by Gilyén and coauthors, obtain polynomial speedups by reducing SDP feasibility to the preparation of a sequence of Gibbs states. However, these methods inherit the slow precision dependence of matrix multiplicative weights and Hamiltonian Updates, and recent non-asymptotic benchmarks suggest that the resulting algorithms may be “galactic”: asymptotically faster, but practically advantageous only at extremely large problem sizes. In this talk, I will present a maximum-entropy reformulation of the quantum SDP feasibility oracle. The key observation is that SDP feasibility can be encoded in a smooth convex Gibbs-dual objective whose gradient is exactly the vector of constraint residuals. This reformulation preserves the central quantum primitive of previous algorithms (Gibbs-state preparation) while replacing the multiplicative-weights outer loop by a guardrailed convex-optimization framework. The guardrail is simple: at each iteration, one may propose a gradient, accelerated, Newton, quasi-Newton, or other curvature-aware update, but the step is accepted only if it satisfies a certified decrease condition; otherwise the algorithm falls back to a safe gradient step. This gives a worst-case guarantee matching the Hamiltonian-Update iteration scale without requiring strong convexity or a condition-number assumption. However, when the Gibbs covariance map is well conditioned, the same framework yields exponentially faster convergence rates, replacing the worst-case polynomial dependence on 1/\varepsilon by logarithmic dependence for first- and second-order methods. I will then explain how the guardrailed maximum-entropy approach can be implemented within the quantum SDP setting, including the corresponding quantum improvements to gradient, objective, and certificate estimation. Finally, I will present numerical evidence on structured SDP instances showing that quasi-Newton variants can reduce the number of Gibbs-state evaluations by orders of magnitude, suggesting a concrete route from asymptotic quantum SDP speedups toward more practical algorithms.
Friday, 17 July
14:00-14:30
Zoë Holmes (EPFL)
Quantum platforms can realize many-body dynamics beyond classical simulation yet complete readout remains intractable: extracting all the accessible information scales exponentially with system size. Classical shadows and Bell sampling offer scalable, multi-observable estimation from randomized, entanglement-assisted measurements. Here we aim to push these ideas beyond static snapshots to dynamical correlators, including OTOCs and two-point functions. In particular, we introduce the notion of the shadow of an operator, defined as the classical shadow of the vectorized time-evolved operator. Pauli operator-shadows enable simultaneous estimation of all local OTOCs, while Clifford operator-shadows enable simultaneous estimation of large families of two-point correlators. Alternatively, Bell sampling allows one to simultaneously compute all diagonal OTOCs. We also prove information-theoretic lower bounds for multi-OTOC estimation, yielding exponential separations that formalize when the vectorized approach provides measurement-efficiency advantages.
14:30-15:00
Matthias Caro (University of Warwick)
Property testing aims to develop super-fast algorithms that can approximately decide whether a high-dimensional object has a property of interest. In this talk, I will present recent developments in applying the mindset of property testing to quantum Hamiltonians when given access to the corresponding time evolution. Building on mathematical tools from the randomised measurement toolbox and from hypercontractivity, I will discuss highly efficient algorithms for testing Hamiltonian properties such as locality as well as for Hamiltonian certification.
15:00-15:30
Vedran Dunjko (Leiden University)
Recent advances in quantum machine learning (QML) have identified a range of formally characterized settings in which quantum models offer provable exponential learning advantages. However, these settings are necessarily contrived, and a key practical challenge remains: how can we assess the real-world, task-specific performance of QML models on general natural problems without access to large-scale quantum computers?
At first glance, this challenge may appear intractable.
In this talk, I briefly review what is known about potential QML advantages before turning to this more pragmatic yet fundamental question. Recent developments in so-called classically trainable, quantumly deployable models for generative tasks suggest an intriguing possibility: obtaining meaningful information about the performance of certain QML models without quantum hardware.
In particular, I discuss a series of works (arXiv:2602.11042, arXiv:2510.08476, arXiv:2603.11014) that build on these ideas to characterize the learning capacity and trainability of such “classically benchmarkable” QML models, while also addressing questions of provable quantum advantage. Together, these results point toward a possible approach for reliably assessing QML models in realistic settings, even in the absence of quantum computers.
15:30-16:00 Social Time
16:00-16:30 Coffee Break
16:30-17:30 semi-plenary talk
Sitan Chen (Harvard University)
Unlike in finite dimensions, quantum information in continuous-variable systems has the peculiar feature that without imposing physical constraints, the sample complexity of state tomography can be unbounded. Remarkably, this is even the case for state of the art protocols for learning Gaussian states, which have finite-dimensional descriptions: the best known rates scale with log log E, where E is the energy of the system. In this talk, I will show that this dependence is not merely an artifact of current techniques, but a fundamental limitation of Gaussian measurements themselves.
I will present new lower and upper bounds that clarify how energy, adaptivity, entanglement, and non-Gaussian resources shape the sample complexity of bosonic state tomography. We prove that any protocol using Gaussian measurements, even adaptive or entangled ones, must incur log log E energy dependence. We also identify a smooth tradeoff between the number of adaptive rounds and this energy dependence, with a matching protocol. Finally, we show that non-Gaussian measurements can remove the energy dependence entirely, achieving optimal O(n^2/eps^2) sample complexity for pure Gaussian states.
17:30-18:00
Chi-Fang (Anthony) Chen (University of California, Irvine)
Learning the Hamiltonian underlying a quantum many-body system in thermal equilibrium is a fundamental task in quantum learning theory and experimental sciences. We give a local and efficient measurement+post-processing for this task, which recovers the classical picture of learning from Gibbs distributions.
Saturday, 18 July
14:00-15:00 semi-plenary talk
Cambyse Rouzé (Télécom Paris)
Classical Langevin dynamics provides a fundamental route to Gibbs sampling and free energy estimation. For quantum systems described by Schrödinger operators, the analogous problem requires genuinely quantum Gibbs samplers and becomes particularly delicate in infinite dimension, where the Hamiltonians are unbounded and the interactions may be singular. In this talk, we introduce a dissipative approach to Gibbs sampling for such systems, including Coulomb Schrödinger operators arising from molecular models and interacting quantum gases. The generation theory relies on Dirichlet form methods from noncommutative potential theory to construct well-defined quantum Markov semigroups having the desired Gibbs state as their invariant state. We then describe how these dynamics lead to mixing guarantees and quantum algorithmic implementations for free energy estimation and Gibbs state preparation.
15:00-15:30
Rolando Somma (Google)
I will describe a recent nearly optimal quantum algorithm for solving linear matrix differential equations, which has applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes an entry of the solution matrix with query complexity that scales as L^2/ϵ, where L involves the time integral of the norm of the transition matrix and ϵ is the error. This L is linear in the evolution time t for unitary dynamics and can be bounded by a constant for dissipative dynamics. The result contrasts prior quantum approaches for differential equations that typically require exponential time for this problem due to the encoding in a quantum state, which can lead to exponentially small amplitudes. I will mention an end-to-end application, namely the simulation of dissipative dynamics for non-interacting fermions, which can also be extended to other systems. I will compare with state-of-the-art classical algorithms for this problem and give evidence of substantial polynomial quantum speedups for systems in a lattice, and better improvements for systems with long-range interactions. I will also provide a lower bound of L^2/ϵ for unitary or weakly dissipative dynamics that proves the quantum algorithm is optimal.
15:30-16:00 Social Time
16:00-16:30 Coffee Break
16:30-17:30 semi-plenary talk
Norbert Schuch (University of Vienna)
I will discuss how by combining techniques developed in quantum information, one can devise rigorous and accurate algorithms for problems in quantum many-body physics. Specifically, by combining convex relaxations with tensor networks, we arrive at new algorithms for rigorously bounding ground state energies as well as spectral gaps for quantum spin chains. If needed, these algorithms can be turned into computer assisted proofs.
17:30-18:00
Dong An (Peking University)
Simulating the time evolution of quantum systems remains one of the most promising applications of quantum computing. In this talk, we will present an efficient quantum algorithm designed to simulate slowly varying time-dependent Hamiltonians. By leveraging Floquet theory alongside a smooth extension of the Hamiltonians to periodic systems, our approach achieves near-optimal scaling, specifically, an almost linear and additive dependence on evolution time and error parameters. We will also discuss how to extend this algorithm to general slow non-unitary dynamics using the linear combination of Hamiltonian simulation technique.
Posters
![[PZ08 – 1st Floor]](https://focm2026.univie.ac.at/wp-content/uploads/2026/06/poster_zones_1-stock.png){kind=link}
Sebastian Egginger
(JKU Linz)
Encoding combinatorial optimization problems into physically meaningful Hamiltonians with tractable energy landscapes forms the foundation of quantum optimization. Numerous works have studied such efficient encodings for the class of Quadratic Unconstrained Binary Optimization (QUBO) problems. However, many real-world tasks are constrained, and handling equality and, in particular, inequality constraints on quantum computers remains a major challenge. We show that including inequality constraints is equivalent to solving a multi-objective optimization. This insight motivates the Multi-Objective Quantum Approximation (MOQA) framework, which approximates the maximum via smaller 𝑝𝑝-norms and comes with rigorous performance guarantees. MOQA operates directly at the Hamiltonian level and is compatible with, but not restricted to, ground-state solvers such as quantum adiabatic annealing, the Quantum Approximate Optimization Algorithm (QAOA), or imaginary-time evolution. Moreover, it is not limited to quadratic functions.
Andreas Sturm
(Fraunhofer IAO)
This poster presents two novel block encoding methods that improve quantum algorithm efficiency. First, we introduce an explicit and efficient approach for encoding discretizations of the Laplacian [1], achieving better circuit complexity and success probability compared to existing methods [2, 3]. Second, we present a stabilizer-based technique for encoding linear combinations of Pauli strings that transforms the Pauli strings into pairwise anti-commuting ones, enabling direct unitary implementation followed by an ancilla-based correction to recover the original operator. This method outperforms standard linear combination of unitaries (LCU) and offers flexible optimization across circuit depth, width, gate sets, connectivity, and fault-tolerance.
[1] A. Sturm and N. Schillo. Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian. arXiv:2509.02429. 2025.
[2] D. Camps, L. Lin, R. van Beeumen, and C. Yang. Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices. SIAM J. Matrix Anal. Appl. 2024.
[3] T. Kharazi, A. M. Alkadri, J.-P. Liu, K. K. Mandadapu, and K. B. Whaley. Explicit Block Encodings of Boundary Value Problems for Many-Body Elliptic Operators. Quantum. 2025.
[4] N. Schillo, A. Sturm, and R. Quay. Block Encoding Linear Combinations of Pauli Strings Using the Stabilizer Formalism. arXiv:2601.05740. 2025.
[5] A. Childs and N. Wiebe. Hamiltonian Simulation Using Linear Combinations of Unitary Operations. Quantum Information and Computation 12. 2012.