Seminar

Tensor Methods for Quantum Systems and Beyond

Edgar Solomonik, University of Illinois at Urbana-Champaign

Tensors are an effective numerical representation for both computation with and analysis of multidimensional datasets and operators. In this talk, we review and motivate how tensor rank, decompositions, and eigenvalues can be used for computational simulation and for hardness measures, such as bilinear complexity and quantum entanglement. We then survey algorithms for computing low-rank decompositions of tensors.

From quantum circuit complexity to quantum information thermodynamics

Philippe Faist, Freie Universität Berlin

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. My talk will focus on two approaches to understand the behavior and the operational significance of quantum complexity in a many-body physical quantum system. First, I'll consider a simple model on n quantum bits: We create a random quantum circuit by randomly sampling the gates that compose it.

Interactive Proofs for Synthesizing Quantum States and Unitaries

Gregory Rosenthal, University of Toronto

Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations such as constructing quantum states or performing unitary transformations.

Communication networks are an essential part of our world today, used in transactions from banking to education, global business exchanges to defence. What happens when our private information is no longer private? Powerful quantum computers will have the ability to crack the encryption of public keys that we currently use to secure our data, putting our privacy at risk.

Universal efficient compilation: Solovay-Kitaev without inverses

Tudor Giurgica-Tiron, Stanford University

The Solovay-Kitaev algorithm is a fundamental result in quantum computation. It gives an algorithm for efficiently compiling arbitrary unitaries using universal gate sets: any unitary can be approximated by short gates sequences, whose length scales merely poly-logarithmically with accuracy. As a consequence, the choice of gate set is typically unimportant in quantum computing. However, the Solovay-Kitaev algorithm requires the gate set to be inverse-closed.

Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture

Sevag Gharibian, Paderborn University

The Quantum Singular Value Transformation (QSVT) is a recent technique that gives a unified framework to describe most quantum algorithms discovered so far, and may lead to the development of novel quantum algorithms. In this paper we investigate the hardness of classically simulating the QSVT.

Local-dimension-invariant stabilizer codes

Protection of quantum information is a central challenge in building a quantum computer. Quantum error-correcting codes can correct for logical errors that occur in the system. A particularly well-studied category is stabilizer codes, such as the 9-qubit Shor code, as these are the quantum analogue of classical additive codes. Qudits (particles with local-dimension greater than 2) have more computational basis states per particle than qubits and retain this feature in stabilizer codes.

Post-quantum security of the Even-Mansour cipher

Chen Bai, University of Maryland, College Park

The Even-Mansour cipher is a simple method for constructing a (keyed) pseudorandom permutation E from a public random permutation P: {0,1}^n ->{0,1}^n. It is a core ingredient in a wide array of symmetric-key constructions, including several lightweight cryptosystems presently under consideration for standardization by NIST.

Quantum sensors allow us to measure with incredible accuracy, precision and selectivity. Future quantum devices that achieve these ultimate sensing qualities by harnessing the complexities of atoms, photons and semiconductors will play a critical role in improving applications such as medical technology, radar, geological exploration, molecular imaging and more. 

Geometry of Banach spaces: a new route towards Position Based Cryptography

Aleksander Kubicki, University Complutense of Madrid

In this talk I will explain how some techniques coming from the local theory of Banach spaces can be used to obtain claims about the security of protocols for Position Based Cryptography.