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# Seminaria

### A random matrix model for random approximate t-designs

#### Speaker: Adam Sawicki (Centre for Theoretical Physics, Polish Academy of Sciences)

## Abstract

For a Haar random set $\mathcal{S}\subset U(d)$ of quantum gates we consider the uniform measure $\nu_\mc{S}$ whose support is given by $\mathcal{S}$. The measure $\nu_\mc{S}$ can be regarded as a $\delta(\nu_\mc{S},t)$-approximate $t$-design, $t\in\mathbb{Z}_+$. We propose a random matrix model that aims to describe the probability distribution of $\delta(\nu_\mathcal{S},t)$ for any $t$. Our model is given by a block diagonal matrix whose blocks are independent, given by Gaussian or Ginibre ensembles, and their number, size and type is determined by $t$. We prove that, the operator norm of this matrix, $\delta({t})$, is the random variable to which $\sqrt{|\mathcal{S}|}\delta(\nu_\mc{S},t)$ converges in distribution when the number of elements in $\mc{S}$ grows to infinity. Moreover, we characterize our model giving explicit bounds on the tail probabilities $\mathbb{P}(\delta(t)>2+\epsilon)$, for any $\epsilon>0$. We also show that our model satisfies the so-called spectral gap conjecture, i.e. we prove that with the probability $1$ there is $t\in\mathbb{Z}_+$ such that $\sup_{k\in\mathbb{Z}_{+}}\delta(k)=\delta(t)$. Numerical simulations give convincing evidence that the proposed model is actually almost exact for any cardinality of $\mc{S}$. The heuristic explanation of this phenomenon, that we provide, leads us to conjecture that the tail probabilities $\mathbb{P}(\sqrt{\mathcal{S}}\delta(\nu_\mathcal{S},t)>2+\epsilon)$ are bounded from above by the tail probabilities $\mathbb{P}(\delta(t)>2+\epsilon)$ of our random matrix model. In particular our conjecture implies that a Haar random set $\mathcal{S}\subset U(d)$ satisfies the spectral gap conjecture with the probability $1$.
### Quantum algorithms for search and optimization

#### Speaker: Andris Ambainis (Center for Quantum Computer Science, Faculty of Computing, University of Latvia)

## Abstract

Quantum algorithms are useful for a variety of problems in search and optimization. This line of work started with Grover’s quantum search algorithm which achieved a quadratic speedup over naive exhaustive search but has now developed far beyond it. In this talk, we describe three recent results in this area: (i) We show that, for any classical algorithm that uses a random walk to find an object with some property (by walking until the random walker reaches such an object), there is an almost quadratically faster quantum algorithm (arxiv:1903.07493). (ii) We show that the best-known exponential time algorithms for solving several NP-complete problems (such as Travelling Salesman Problem or TSP) can be improved quantumly (arxiv:1807.05209). For example, for the TSP, the best-known classical algorithm needs time O(2^n) but our quantum algorithm solves the problem in time O(1.728…^n). (iii) We show an almost quadratic quantum speedup for a number of geometric problems such as finding three points that are on the same line (arxiv:2004.08949).
About the speaker
Andris Ambainis is a professor of computer science at the University of Latvia. He has invented widely used methods for constructing quantum algorithms and has constructed record-breaking examples of quantum advantage for quantum computers. Andris Ambainis’ work has been recognized by an Advanced Grant from the European Research Council (2012) and the Grand Medal of the Latvian Academy of Sciences (2013).
### Quantum correlations from the post-quantum perspective: When can we have security against a super-quantum adversary ?

#### Speaker: Marcin Wiesniak (Gdansk University)

### Random approximate t-designs

#### Speaker: Adam Sawicki (CTP PAS)

## Abstract

Approximate t-design are ensembles of unitaries that (approximately) recover Haar averages of polynomials in entries of unitaries up to the order t. As such, they find numerous applications throughout quantum information, including randomized benchmarking , efficient estimation of properties of quantum states, decoupling, information transmission and quantum state discrimination. In this talk I will characterize how finite random gate-sets mimic the Haar measure.
The talk will be based on the joint word with Piotr Dulian.
arXiv:2210.07872
### Modes and states of light in Gaussian quantum metrology

#### Speaker: Giacomo Sorelli (Fraunhofer Institute for Optotronics, System Technology and Image Exploitation)

## Abstract

Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply it to the transverse localisation of a Gaussian beam, and to the temporal separation between two pulses. In both cases, we will show which are the relevant modes where to deploy quantum resources, i.e. squeezing, to achieve a sensitivity enhancement.
### Shallow shadows: expectation estimation using low-depth random Clifford circuits

#### Speaker: Christian Bertoni (Dahlem Center for Complex Quantum Systems, Freie Universitat Berlin, Germany)

## Abstract

Classical shadows have recently emerged as an efficient method to extract expectation values of observables using randomized measurements. In particular, two schemes have been proven to be able to efficiently perform this task for certain classes of observables: random single-qubit Clifford measurements, and random global Clifford measurements. In this talk, I will present a new scheme in which measurements in the computational basis are performed after the application of a brickwork circuit of random two-qubit gates of an arbitrary depth. This interpolates between the two known cases, which correspond to either 0 or linear depth. At a depth scaling logarithmically in the number of qubits and for an average state, this scheme has the same sample efficiency as the global Clifford measurements scheme, while retaining some of the favorable characteristics of the single-qubit Clifford measurements scheme. This provides strong evidence that logarithmically deep Clifford circuits, which are experimentally feasible to implement, can be used in place of global Clifford gates for classical shadows.
### Lindblad Master Equation and the Quantum Brachistochrone

#### Speaker: Bartosz Grygielski (Faculty of Physics, UJ)

### Device-independent extraction of min-entropy sources against quantum adversaries using few devices

#### Speaker: Ravishankar Ramanathan (Hong Kong)

## Abstract

Abstract: It is well known that classical tools do not allow the extraction of randomness from a single random source. On the other hand, quantum theory allows for such extraction even within the device-independent framework. While practically feasible protocols have been proposed for randomness sources that possess a specific Santha-Vazirani structure, it has remained an open problem to derive a finite-device protocol for extraction from an arbitrary min-entropy source. In this talk, we will present and outline the security of such a device-independent protocol with the following features: (1) robust amplification of an arbitrary min-entropy source, (2) usage of a device with a constant number of components, (3) security in the presence of a quantum adversary.
### How to check universality of quantum gates?

#### Speaker: Adam Sawicki (CFT PAN, Warsaw)

## Abstract

Universal quantum gates play a central role in quantum computing. It is well known that in order to construct a universal set of gates for many qudits it is enough to take a universal set for one qudit and extend it by a two-qudit entangling gate. On the other hand, it is a great challenge to find a time efficient procedure that enables deciding if a given set of one-qudit gates is universal. In this talk I will connect the universality problem with the theory of t-designs and provide a universality checking procedure whose complexity scales polynomially with the dimension of the qudit. The talk will be based on: A. Sawicki, L. Mattioli, Z. Zimboras Phys. Rev. A 105, 052602, 2022
### Speed limits: from thermodynamics to annealing

#### Speaker: Luis Pedro Garcia Pintos (Joint Quantum Institute and QuICS, University of Maryland)

## Abstract

I will give an overview of recent bounds on the speed with which observables can evolve in quantum and classical systems. The bounds typically take the form of uncertainty relations that connect the maximum rate of change of an observable to its standard deviation. Surprisingly, these general bounds are saturated in a range of disciplines. I will illustrate this with an application of these techniques to quantum annealing.

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Tu znajdziesz listę organizowanych w Polsce spotkań, seminariów i konferencji związanych z zagadnieniami informacji kwantowej

Date: środa, 25 stycznia, 2023

Time: 14:00

Host: ICTQT, room 319

Passcode: 3SM3fW

Date: środa, 25 stycznia, 2023

Time: 11:00

Host: Quantum Computing Colloquium

Zoom link: https://us06web.zoom.us/j/81247873600

Passcode: teamnet

Date: poniedziałek, 23 stycznia, 2023

Time: 14:15

Host: Quantum Chaos and Quantum Information (Jagiellonian University)

Zoom link: https://us05web.zoom.us/j/89601291160?

Passcode: please contact albertrico23 at gmail.com

Date: środa, 18 stycznia, 2023

Time: 14:30

Host: Quantum Information and Quantum Computing Working Group

Zoom link: https://us06web.zoom.us/j/88571566818

Passcode: nisq

Date: wtorek, 17 stycznia, 2023

Time: 12:00

Host: UG, Room 411 of New Rektorat (Floor IV)

Date: środa, 11 stycznia, 2023

Time: 15:15

Host: Quantum Information and Quantum Computing Working Group

Zoom link: https://us06web.zoom.us/j/88571566818

Passcode: nisq

Date: poniedziałek, 9 stycznia, 2023

Time: 14:15

Host: Quantum Chaos and Quantum Information (Jagiellonian University)

Zoom link: https://us05web.zoom.us/j/89601291160?

Passcode: please contact albertrico23 at gmail.com

Date: czwartek, 22 grudnia, 2022

Time: 14:00

Host: ICTQT, room 319

Passcode: 3SM3fW

Date: poniedziałek, 19 grudnia, 2022

Time: 14:15

Host: Quantum Chaos and Quantum Information (Jagiellonian University)

Zoom link: https://us05web.zoom.us/j/89601291160?

Passcode: please contact albertrico23 at gmail.com

Date: środa, 14 grudnia, 2022

Time: 16:00

Host: ICTQT, room 319

Passcode: 3SM3fW