Team-Net Quantum Computing Colloquium – CFT PAN – Centrum Fizyki Teoretycznej Polskiej Akademii Nauk

An optimal LCU-based quantum linear system solver

dev — Fri, 27 Dec 2024 12:19:37 +0000

Abstract
In this talk, I will first give an overview of recent techniques such as taking linear combinations of unitaries (LCU) and the quantum singular value transformation framework (QSVT). These techniques allow one to reduce many quantum algorithmic problems to questions about finding good / the best polynomial approximations to certain functions. We study one such function: the inverse. In other words, we consider the problem of solving linear systems of equations. Prior work has shown that an asymptotically optimal approximation to the inverse can be evaluated using LCU and/or QSVT. We show the same for the optimal approximating polynomial, thus achieving constant factor improvements.

This is based on https://arxiv.org/abs/2109.04248 which is joint work with Daniel Szilagyi and Iordanis Kerenidis.

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About the speaker
Sander Gribling’s research focuses on the interaction between optimization and quantum information theory / quantum computing. He is also interested in the many uses of polynomials in quantum information theory: polynomial optimization, quantum query complexity, and quantum algorithms.

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Webpage of the project: nisq.pl

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Limitations of optimization algorithms on noisy quantum devices

dev — Fri, 27 Dec 2024 12:19:37 +0000

Whether current and next generation quantum computers solve relevant problems that are unachievable to our traditional devices remains an open question. A central question is whether the imperfections present in quantum computers can be overcome or it fundamentally restricts quantum computers. In this talk, I will present a way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that consist of minimizing a cost function, such as in optimization problems. I will then discuss the capability of current and next-generations quantum computer to solve relevant optimization problems.

The talk will be based on joint work with Daniel Stilck Franca
Reference: Nature Physics 17, 1221–1227 (2021), https://arxiv.org/abs/2009.05532
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About
The purpose of the Team-Net Quantum Computing Colloquium series is to expose Polish and international researchers, as well as interested peers, to the most important recent achievements and trends in the field of quantum computing. Seminars will be taking place on a monthly basis, on Wednesdays at 16:00 CET. Topics of the colloquium include, but are not limited to:

Near-term quantum algorithms
Quantum supremacy experiments
Resource-theoretic approaches to quantum computing
Quantum machine learning
Practical quantum error correction and error mitigation
Mathematical aspects of quantum computing and many-body physics

Webpage of the project: www.nisq.pl

Kind regards,

Susane Calegari

Felix Huber
Kamil Korzekwa

Marek Kuś
Michał Oszmaniec
Zbigniew Puchała
Karol Życzkowski

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Zoom meeting details

Topic: Quantum Computing Colloquium
Time: Wednesday, 02.03.2022, 16:00 Warsaw (CET)

Join Zoom Meeting
https://tinyurl.com/QCcolloquium

Meeting ID: 830 8179 4965
Passcode: Qcomputing

If you encounter any problems with connecting to the Zoom meeting, please email calegari@cft.edu.pl.

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Optimal programming of quantum gates

dev — Fri, 27 Dec 2024 12:19:37 +0000

Abstract

A universal quantum processor is a device that can approximately implement any desired quantum gate on a given system. The specification of the desired gate is provided by a program, which in most implementations of quantum computing consists of classical data. From the foundational point of view, however, it is interesting to explore the more general scenario where the program is itself a quantum system. In the past two decades, a major open question has been to determine how the size of the smallest quantum program scales with the required accuracy in the implementation of the desired gate. Here we answer the question, by proving a bound on the size of the program and designing a concrete protocol that attains the bound in the asymptotic limit. Our result is based on the representation theory of the special unitary group. It provides improved bounds on the estimation of unitary gates, and on the implementation of quantum protocols subject to conservation laws.

About
The purpose of the Team-Net Quantum Computing Colloquium series is to expose Polish and international researchers, as well as interested peers, to the most important recent achievements and trends in the field of quantum computing. Seminars will be taking place on a monthly basis, on Wednesdays at 16:00 CET. Topics of the colloquium include, but are not limited to:

Near-term quantum algorithms
Quantum supremacy experiments
Resource-theoretic approaches to quantum computing
Quantum machine learning
Practical quantum error correction and error mitigation
Mathematical aspects of quantum computing and many-body physics

Webpage of the project: nisq.pl

Quantum advantage with noisy shallow circuits

dev — Fri, 27 Dec 2024 12:19:37 +0000

Abstract

As increasingly sophisticated prototypes of quantum computers are being developed, a pressing challenge is to find computational problems that can be solved by an intermediate-scale quantum computer, but are beyond the capabilities of existing classical computers. Here we explore computational problems that can be solved with certainty by noisy quantum circuits of depth independent of the input size (so-called ‘shallow’ circuits) but cannot be solved with high probability by any (noise free) shallow classical circuit.

The talk will be based on a paper coauthored by Marco arxiv:904.01502 published in Nature Physics.

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Zoom meeting room (zoom link, passcode: teamnet)

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Near-term quantum algorithms
Quantum supremacy experiments
Resource-theoretic approaches to quantum computing
Quantum machine learning
Practical quantum error correction and error mitigation
Mathematical aspects of quantum computing and many-body physics

Webpage of the project: nisq.pl

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Quantum Complexity of Experiments

dev — Fri, 27 Dec 2024 12:19:37 +0000

Abstract
We introduce a theoretical framework to study experimental physics using quantum complexity theory. This allows us to address: what is the computational complexity of an experiment? For several 'model’ experiments, we prove that there is an exponential savings in resources if the experimentalist can entangle apparatuses with experimental samples. A novel example is the experimental task of determining the symmetry class of a time evolution operator for a quantum many-body system. Some of our complexity advantages have been realized on Google’s Sycamore processor, demonstrating a real-world advantage for learning algorithms with a quantum memory.

References: ArXiv:2111.05881 ArXiv:2111.05874 ArXiv:2112.00778

Near-term quantum algorithms
Quantum supremacy experiments
Resource-theoretic approaches to quantum computing
Quantum machine learning
Practical quantum error correction and error mitigation
Mathematical aspects of quantum computing and many-body physics

Webpage of the project: nisq.pl

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Zoom details

Link: https://us06web.zoom.us/j/83081794965

Passcode: teamnet

Quantum Error Correction with Superconducting Transmon Qubits

dev — Fri, 27 Dec 2024 12:19:37 +0000

‍Abstract
We review the goals of quantum error correction, in particular the use of the surface code. We discuss some of the results and challenges in experimental quantum error correction, in particular with respect to qubit leakage.

About the speaker
Barbara Terhal has been working as a theorist in quantum computing research since her PhD in 1999 (University of Amsterdam). She has a long-standing interest and track-record in quantum error correction and fault-tolerance, and she has also worked extensively on quantum complexity, quantum algorithms, and the theory of quantum entanglement. After spending time in the US during and after her PhD she returned to Europe in 2010 to become a professor at RWTH Aachen University, moving to the Delft University of Technology in 2017. She is a fellow of the American Physical Society, a distinguished visiting research chair at Perimeter Institute in Canada, and a member of the Royal Netherlands Academy of Arts and Sciences since 2020.

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Link: https://us06web.zoom.us/j/81247873600

Meeting ID: 812 4787 3600

Passcode: teamnet

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Webpage of the project: nisq.pl

Quantum Singular Value Transformation – A Unifying framework of quantum algorithms

dev — Fri, 27 Dec 2024 12:19:37 +0000

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.

Near-term quantum algorithms
Quantum supremacy experiments
Resource-theoretic approaches to quantum computing
Quantum machine learning
Practical quantum error correction and error mitigation
Mathematical aspects of quantum computing and many-body physics

Webpage of the project: nisq.pl

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