Below you will find a list of seminars organised by ICTQT. For comprehensive list of quantum events in other institutions please see the KCIK website.
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.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.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.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.