Online Seminars on Quantum Information in Poland. Warsaw time zone.

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What is nonclassical about uncertainty relations?

Date: Wednesday, August 3, 2022
Time: 14:15
Passcode: 743020

Speaker: Lorenzo Catani (TU Berlin)

Abstract Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this view is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli X and Pauli Z observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that it has a quadratic tradeoff between these predictabilities is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements. Based on

Quantum value for a family of I3322-like Bell functionals

Date: Wednesday, July 27, 2022
Time: 14:15
Passcode: 743020

Speaker: Nicolás Gigena (University of Warsaw)

Abstract In this work, we study a three-parameter family of Bell functionals in a bipartite scenario with 3 measurement settings per party and 2 outcomes per measurement. The members of this family can be thought of as variations of the well-known I3322 functional, the only one in this scenario corresponding to a tight Bell inequality if we take aside the CHSH inequality. An analysis of their largest value achievable by quantum realisations (quantum value) naturally splits the set into two branches, and for the first of them, we show that this value is given by a simple function of the parameters defining the functionals. In this case we completely characterise the realisations attaining the optimal value and show that these functionals can be used to self-test any partially entangled state of two qubits. The optimal measurements, however, are not unique and form a one-parameter family of qubit measurements. Within the second branch, the quantum value presents a more complex dependence on the parameters defining the functionals and is studied numerically, identifying first the regions in parameter space where two-qubit systems suffice to approach the quantum value. The remainder of the branch includes the I3322 functional, for which a particular sequence of finite-dimensional realisations introduced by K. Pál and T. Vértesi is known to numerically attain the quantum value in the limit of infinite local dimension. We study the performance of these special strategies beyond the I3322 case and analyse the optimal solutions in those cases where they succeed in approaching the quantum value.

Strongly coupled quantum Otto cycle with single qubit bath

Date: Wednesday, July 20, 2022
Time: 14:15

Speaker: Sagnik Chakraborty (Nicolaus Copernicus University, Torun)

Abstract We discuss a model of a unitary evolution of two-qubits where the joint Hamiltonian is so chosen that one of the qubits acts as a bath and thermalizes the other qubit which is acting as the system. The corresponding master equation for the system, for a specific choice of parameters, takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite bath including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for heat engine regime (refrigerator regime) for different modifications of the joint Hamiltonian. Ref: arXiv:2206.14751v1

Quantum Singular Value Transformation – A Unifying framework of quantum algorithms

Date: Wednesday, July 6, 2022
Time: 16:00
Host: Team-Net Quantum Computing Colloquium
Passcode: teamnet

Speaker: András Gilyén (Alfréd Rényi Institute of Mathematics)

Abstract An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2^n-dimensional, Hilbert space, which is a major source of quantum speed-ups. We show how Quantum Singular Value Transformation can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singular values of a block of a unitary operator. The transformations are realized by quantum circuits with a very simple structure – typically using only a constant number of ancilla qubits – leading to optimal algorithms with appealing constant factors. We show that this framework allows describing and unifying many quantum algorithms on a high level, and enables remarkably concise proofs for many prominent quantum algorithms, ranging from optimal Hamiltonian simulation to quantum linear equation solving (i.e., the HHL algorithm) and advanced amplitude amplification techniques. Finally, we also prove a quantum lower bound on spectral transformations.

Gaussian states, Kähler structures and an entanglement duality

Date: Wednesday, July 6, 2022
Time: 14:15
Host: room 45, ICTQT

Speaker: Robert H. Jonsson (Wallenberg Initiative on Networks and Quantum Information, Nordita (Stockholm)

Abstract Gaussian quantum states play a central role in many branches of physics – from quantum optics, to condensed matter and quantum field theory. In this talk, I aim to showcase the strength of the Kähler structure formalism for Gaussian states by discussing a recent result on the entanglement structure of supersymmetric (SUSY) bosonic and fermionic Gaussian states [1]. Mathematically, Gaussian states can be defined in terms of Kähler structures on classical phase space. In fact, this approach has proven to be very powerful: It yields a formalism which is both practical for applications, clearly captures the structure and geometry of Gaussian states, adapts to discrete and continuous settings and, moreover, can treat bosons and fermions simultaneously. To exemplify this, we will consider the basic example of a free SUSY system. This is a pair of one bosonic and one fermionic quadratic hamiltonian which is generated by a supercharge and, therefore, is isospectral. Not only does the Kähler structure formalism parallelly capture the Gaussian ground states and their entanglement structure of both the bosonic and the fermionic part. Moreover, it allows us to derive an appealing entanglement duality between bosonic and fermionic subsystems [1], and to interpret it in terms of phase space geometry and its physical implications. Time permitting, as a special application, we consider topological insulators and superconductors and their SUSY partners, discussing the recently derived classification of supercharges in this context [2]. [1] Jonsson, Robert H., Lucas Hackl, and Krishanu Roychowdhury. “Entanglement Dualities in Supersymmetry.” Physical Review Research 3, no. 2 (June 16, 2021): 023213. [2] Gong, Zongping, Robert H. Jonsson, and Daniel Malz. “Supersymmetric Free Fermions and Bosons: Locality, Symmetry, and Topology.” Physical Review B 105, no. 8 (February 24, 2022): 085423.

Nonlocal games and operator algebras: solution spaces and robust self-testing in the quantum commuting model

Date: Wednesday, June 29, 2022
Time: 15:15
Host: Quantum Information and Quantum Computing Working Group (CTP PAS)
Passcode: nisq

Speaker: Alexander Frei (University of Copenhagen)

Abstract We begin by recalling quantum strategies in the context of nonlocal games, and their description in terms of the state space on the full group algebra of certain free groups. With this description at hand, we then examine the quantum value and quantum strategies for the following prominent classes of games: 1) The tilted CHSH game. We showcase here how to compute the quantum value at first for the classical CHSH game using some basic operator algebraic techniques. For the more general tilted CHSH game, we then invoke some more elaborate classification of representations which then allows us to reduce the quantum value to an optimisation problem. These allow us moreover to deduce the solution space of optimal states and their uniqueness, in the sense that there will be only a single optimal state giving rise to the optimal quantum value, and which in particular entails the usual self-testing result. We moreover find previously unknown phase transitions on the uniqueness of optimal states when varying the parameters for the tilted CHSH game. 2) The Mermin-Peres magic square and magic pentagram game. As before, we also note here uniqueness of optimal states, which in these two examples is a basically familiar result. Based on uniqueness of optimal states as entire states on full group algebras, we then discuss robust self-testing in the quantum commuting model in the context of above discussed games. We do so by building upon ideas found in work by Mancinska, Prakash and Schafhauser. We then demonstrate this on the classes (1) and (2) above, and so find a first robust self-testing result in the quantum commuting model. The talk is based on joint work with Azin Shahiri.

Spectral Metric and Einstein Functionals

Date: Friday, June 17, 2022
Time: 12:15
Host: IFTIA Seminar (room 361)
Passcode: 78pA05

Speaker: Andrzej Sitarz

Abstract I’ll review the concept of expressing the two basic notions of Riemannian geometry using spectral methods and Wodzicki residue over the algebra of pseudodifferential operators. This approach admits generalizations to the framework of noncommutative geometry. Based on joint work with L.Dabrowski and P.Zalecki.

Algebraic Bethe Circuits

Date: Wednesday, June 15, 2022
Time: 15:15
Host: Quantum Information and Quantum Computing Working Group (CTP PAS)
Passcode: nisq

Speaker: Diego García-Martín (TII, Abu Dhabi, UAE)

Abstract The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA to unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method in the spin- 1 2 XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run numerical simulations, preparing eigenstates of the XXZ model for systems of up to 24 qubits and 12 magnons. Furthermore, we run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models in 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.

Application of probabilistic quantum error correction for general noise

Date: Monday, June 13, 2022
Time: 14:15
Host: Quantum Chaos and Quantum Information (Jagiellonian University)
Passcode: subspace

Speaker: Ryszard Kukulski (IITiS PAN, Gliwice)

Abstract Probabilistic quantum error correction (pQEC) is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this talk, I will show an application of pQEC for various types of noise channels, e.g. Schur channels, channels with bounded Choi rank and random channels. I will present how to correct errors caused by an arbitrary unitary interaction with an auxiliary qubit system. Finally, I will discuss the optimization problem related with pQEC procedure.

Quantum software in 2022 : patterns and problems

Date: Friday, June 10, 2022
Time: 12:00
Host: ICTQT seminar
Passcode: 46veyQ

Speaker: Ross Duncan (Cambridge Quantum)

Abstract Quantum computers are based on the laws of quantum mechanics rather than Boolean logic; this implies very different algorithmic capabilities and, perhaps more surprisingly, very different issues across the board from software architecture to formal methods. In this talk I’ll give a broad overview of the current state of the art in 2022 and focus on some issues of current interest.