Seminars

The Hitchhiker’s Guide to QSP pre-processing, arXiv:2501.05977

Although discrete optimization has inspired much quantum algorithmic work, exponential advantages for conventional discrete optimization have remained largely elusive. Why? I’ll offer my perspective on this question using the Max Cut problem as a running example. I’ll talk about approximating Quantum Max Cut, which has very recently has resulted in a new sharp bound for the ground energy of the antiferromagnetic Heisenberg model relating to matchings in the interaction graph. Next, I’ll give an example of an exponential space advantage for approximating the Maximum Directed Cut problem. Finally, I’ll point out some limitations of the recent Decoded Quantum Interferometry (DQI) algorithm for approximating Max Cut.

Symmetries play a fundamental role in describing quantum systems. They are represented by the operators that stay constant over time, which happens when they commute with the Hamiltonian of the system. However, when the Hamiltonian is slightly perturbed, not all symmetries behave the same way. Some remain nearly conserved throughout the evolution: these are called robust symmetries. Others, instead, drift significantly from their original values for sufficiently long times: these are known as fragile symmetries. Our goal is to provide a precise characterization of both robust and fragile symmetries.

Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to exponential scaling with system size, posing an even harder problem than ground-state calculations. We present a quantum algorithm for estimating eigenvalues and singular values of parameterized matrix families, including solving generalized eigenvalue problems that frequently arise in quantum simulations. Our method uses quantum amplitude amplification, connected to Grover’s algorithm, and phase estimation to identify matrix eigenvalues by locating minima in the singular value spectrum. We demonstrate our algorithm by proposing a quantum-computing formulation of the pseudospectral collocation method for the Schrödinger equation. We estimate fault-tolerant quantum resource requirements for the quantum collocation method, showing favorable scaling in the size of the problem N (up to O(√N)) compared to classical implementations with O(N²), for certain well-behaved potentials. Additionally, unlike the standard collocation method, which results in a generalized eigenvalue problem requiring matrix inversion, our algorithm circumvents the associated numerical instability by scanning a parameterized matrix family and detecting eigenvalues through singular value minimization. This approach is particularly effective when multiple eigenvalues are needed or when the generalized eigenvalue problem involves a high condition number. In the fault-tolerant era, our method may thus be useful for simulating high-dimensional molecular systems with dense spectra involving highly excited states, such as those encountered in molecular photodynamics or quasi-continuum regimes in many-body and solid-state systems.

Arxiv link: arXiv:2506.13534

Bio:
Grzegorz is a physicist specializing in quantum information, in particular, entanglement and quantum channels. He started the journey with this branch of physics doing Bachelor and Master under supervision of Andrzej Dragan at University of Warsaw, studying properties of quantum protocols in the vicinity of black holes. Then, he moved on to a more applied branch of quantum science while doing PhD at Centre for Theoretical PAS, guided by Karol Życzkowski. During his PhD, he solved several problems related to multipartite quantum entanglement and quantum designs. One of those solutions, dubbed as entangled officers of Euler, was awarded a golden prize by National Quantum Information Centre (KCIK). Subsequently, also the entire thesis was recognized as the best PhD thesis in quantum information, defended in Poland in years 2021/22, awarded by the same institution. After the defense, he moved on to ICFO in Barcelona, joining the Quantum Optics Theory group of Maciej Lewenstein. He spent there two years, responsible for the branch of the group devoted to advancing the research on experimentally-motived quantum technologies. On coming back to Poland he joined newly created Quantum Computing group at NASK PIB. In October 2024, he became part of BEIT, and is exploring topics at the cross-section of quantum algorithms in chemistry and quantum information.

The development of quantum networks across distant locations is crucial for facilitating quantum key distribution and cloud quantum computing. Although such networks are currently being established, the relationship between network performance and specific configurations remains little understood.
In this study, I explore enhancements to simple quantum networks by equipping quantum repeaters with multiple quantum memory units. I present an analysis of average waiting times for quantum repeaters based on different memory distributions across all repeater stations. I provide numerical simulations alongside theoretical bounds for the waiting times of quantum repeaters in various scenarios involving memory buffers and discuss which configurations lead to the best results.

Sequential models of classical or quantum computation, such as Turing machines and circuits, describe computation as state changes over time. In contrast, higher-order models like the Lambda calculus operate on functions themselves—an idea that extends naturally to Higher-Order Quantum Theory (HOQT), where quantum channels become inputs to “second-order” transformations, which extend recursively to form a hierarchy of higher-order maps (HOMs).

I will present an axiomatic framework for HOQT, analogous to Kraus’ axiomatization of quantum operations, characterizing admissible HOMs via their Choi-Jamiołkowski operators. Some HOMs correspond to circuits with open slots, while others (e.g., the quantum switch) feature indefinite causal order. I will show how to relate each map’s functional description to its causal structure through no-signaling relations. Finally I will present a how to generalize the higher-order framework to Operational Probabilistic Theories (OPTs).

The quantum Schur transform has become a foundational quantum algorithm, yet even after two decades since the seminal 2005 paper by Bacon, Chuang, and Harrow (BCH), some aspects of the transform remain insufficiently understood. Moreover, an alternative approach proposed by Krovi in 2018 was recently found to contain a crucial error. In this talk, I present a corrected version of Krovi’s algorithm along with a detailed treatment of the high-dimensional version of the BCH Schur transform. This high-dimensional focus makes the two versions of the transform practical for regimes where the number of qudits n is smaller than the local dimension d, with Krovi’s algorithm scaling as Õ(n⁴) and BCH as Õ(min(n⁵,nd⁴)). As an application, I will show how high-dimensional Clebsch-Gordan transforms used in the BCH algorithm can efficiently simulate Haar random unitaries.

In higher-order quantum computing (HOQC), one typically considers the universal transformation of unknown quantum operations, treated as blackboxes. It is also implicitly assumed that the resulting operation must act on arbitrary—and thus unknown—input states. In this work, we explore a variant of this framework in which the operation remains unknown, but the input state is fixed and known. We argue that this assumption is well-motivated in certain practical contexts, such as unitary programming, and show that classical knowledge of the input state can significantly enhance performance. Moreover, this assumption allows us to distinguish protocols designed for pure, bipartite, and mixed states, which enabled us to identify the class of mixed states for which deterministic and exact implementation becomes possible.

arXiv:2510.20530 [quant-ph]

Quantum networks with multiple sources allow the observation of quantum nonlocality without inputs. Consequently, the incompatibility of measurements is not a necessity for observing quantum nonlocality when one has access to multiple quantum sources. In this talk, I will present the minimal input-free network where such correlations arise: a two-party, two-source configuration in which nonlocality appears as a new form of quantum steering, which we call swap-steering. Remarkably, this effect occurs even when the sources may be classically correlated, as long as one party is trusted to perform a fixed, known measurement. Interestingly, one cannot observe Bell-type correlations in this scenario; thus, a scenario exists where quantum steering can be observed but Bell non-locality cannot. I will introduce a simple linear witness to detect swap-steering and show that every entangled state and every entangled measurement gives rise to swap-steerable correlations—demonstrating that all entangled resources are fundamentally “non-classical” in the sense that they can steer a far-away system without signalling. As an application to practical problems, one of the proposed witnesses enables self-testing of the quantum states generated by the sources and the local measurement of the untrusted party. This, in turn, allows certifying two bits of randomness that can be obtained from the measurement outcomes of the untrusted device without the requirement of initially feeding the device with randomness. This is the first example of a scheme where secure randomness can be extracted without feeding in initial randomness into the scheme.
For curiosity, refer to arXiv:2307.08797, arXiv:2406.11994, arXiv:2502.06986.