# News

### Work on trapped ions in Nature Communications

Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, a regime in which coherences and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work published in Nature Communications , we report an experimental measurement of the genuine quantum correction to the classical work fluctuation-dissipation relation (FDR). We employ a single trapped ion qubit, realizing thermalization and coherent drive via laser pulses, to implement a quantum coherent work protocol. The results from a sequence of two-time work measurements display agreement with the recently proven quantum work FDR, violating the classical FDR by more than 10.9 standard deviations. We furthermore determine that our results are incompatible with any SPAM error-induced correction to the FDR by more than 10 standard deviations. Finally, we show that the quantum correction vanishes in the high-temperature limit, again in agreement with theoretical predictions. While this work is primarily located in the field of quantum thermodynamics, it develops tools of witnessing and benchmarking of quantum properties in a trapped ion quantum device - and is hence relevant for projects such as the Quantum Flagship project Millenion on trapped ion quantum computing.

Aug 20, 2024

### Maximilian Kramer wins the study award

Maximilian Kramer wins one of the 2024 study awards of the Berlin Physical Society . Congratulations! He is just starting his PhD in the team.

Jul 13, 2024

### Work on shallow shadows in the Physical Review Letters

We basically show that one can get away with logarithmically deep circuits when pursuing classical shadow estimation. We are happy to see this work out in the Physical Review Letters . We provide practical and powerful schemes for learning properties of a quantum state using a small number of measurements. Specifically, we present a randomized measurement scheme modulated by the depth of a random quantum circuit in one spatial dimension. This scheme interpolates between two known classical shadows schemes based on random Pauli measurements and random Clifford measurements. We focus on the regime where depth scales logarithmically in the system size and provide evidence that this retains the desirable sample complexity properties of both extremal schemes while also being experimentally feasible. We present methods for two key tasks; estimating expectation values of certain observables from generated classical shadows and, computing upper bounds on the depth-modulated shadow norm, thus providing rigorous guarantees on the accuracy of the output estimates. We achieve our findings by bringing together tools from shadow estimation, random circuits, and tensor networks.

Jul 10, 2024

### New DFG SPP initiated

We have initiated a new research initiative on quantum software in Germany: SPP2514 that will be dedicated to foundational aspects of “quantum software, algorithms and systems", funded by the Deutsche Forschungsgemeinschaft (DFG) - German Research Foundation . We had great fun discussing many aspects of the initative. Thanks for that. There will be a call for proposals later this year, aimed at bringing physics and computer science communities closer together to each other. This has been put together by Ina Schäfer , Robert Wille , Wolfgang Mauerer, Martin Schulz and Jens Eisert, and it will be coordinated by the spokesperson Ina Schäfer. Many thanks.

Jul 04, 2024

### Work on simulating non-equilibrium quantum dynamics in Nature Physics

Combining flow equations with scrambling techniques and error bounds, we present a new way to address the classical simulation of quantum dynamics for intermediate times. The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part reflecting complexity theoretic obstructions. In this work, published in Nature Physics , we present a new technique able to overcome this obstacle, by combining continuous unitary flow techniques with the newly developed method of scrambling transforms. We overcome the prejudice that approximately diagonalizing the Hamiltonian cannot lead to reliable predictions for relatively long times. To the contrary, we show that the method works well in both localized and delocalized phases, and makes reliable predictions for a number of quantities including infinite-temperature autocorrelation functions. We complement our findings with rigorous incremental bounds on the truncation error. This approach shows that in practice, the exploration of intermediate-scale time evolution may be more feasible than is commonly assumed, challenging near-term quantum simulators.

Jul 03, 2024

### Quant-ERA HQCC meeting in Berlin

We are hosting the meeting of the QuantERA project HQCC in Berlin, with a number of international speakers. This consortium involves Andris Ambainis (Latvijas Universitate, LV), Jens Eisert (Freie Universität Berlin, DE), Zoltán Zimborás (Wigner Research Centre for Physics, HU), Yasser Omar (Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, PT). The exciting programme can be found here, the local organizer is Johannes Meyer. Last week, we have been co-organizing the MATH+ workshop on quantum cryprography and quantum networks , with Nathan Walk being in the lead as a local organizer, jointly with Anna Pappa from TU Berlin.

May 28, 2024

### It's a kind of magic

In work published in the Physical Review Letters , we introduce ensembles of quantum states arising in quantum computing and many-body theory that, despite featuring low nonstabilizerness and hence “magic”, are actually computationally indistinguishable from those with high nonstabilizerness. Notions of nonstabilizerness, or “magic,” quantify how nonclassical quantum states are in a precise sense: states exhibiting low nonstabilizerness preclude quantum advantage. We introduce “pseudomagic” ensembles of quantum states that, despite low nonstabilizerness, are computationally indistinguishable from those with high nonstabilizerness. Previously, such computational indistinguishability has been studied with respect to entanglement, introducing the concept of pseudo-entanglement. However, we demonstrate that pseudomagic neither follows from pseudoentanglement nor implies it. In terms of applications, the study of pseudomagic offers fresh insights into the theory of quantum scrambling: it uncovers states that, even though they originate from non-scrambling unitaries, remain indistinguishable from scrambled states to any physical observer. Additional applications include new lower bounds on state synthesis problems, property testing protocols, and implications for quantum cryptography. Our Letter is driven by the observation that only quantities measurable by a computationally bounded observer—intrinsically limited by finite-time computational constraints—hold physical significance. Ultimately, our findings suggest that nonstabilizerness is a “hide-able” characteristic of quantum states: some states are much more magical than is apparent to a computationally bounded observer. This work has been distinguished as an "editor's suggestion" with the Physical Review Letters.

May 28, 2024

### Work on optimization in Science Advances

Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of scientific and industrial contexts - has been identified as one of the core potential fields of applicability of quantum computers. It is still unclear, however, to what extent quantum algorithms can actually outperform classical algorithms for this type of problems. In this work, published in the Science Advances , by resorting to computational learning theory and cryptographic notions, we prove that quantum computers feature an in-principle super-polynomial advantage over classical computers in approximating solutions to combinatorial optimization problems. Specifically, building on seminal work by Kearns and Valiant and introducing a new reduction, we identify special types of problems that are hard for classical computers to approximate up to polynomial factors. At the same time, we give a quantum algorithm that can efficiently approximate the optimal solution within a polynomial factor. The core of the quantum advantage discovered in this work is ultimately borrowed from Shor's quantum algorithm for factoring. Concretely, we prove a super-polynomial advantage for approximating special instances of the so-called integer programming problem. In doing so, we provide an explicit end-to-end construction for advantage bearing instances. This result shows that quantum devices have, in principle, the power to approximate combinatorial optimization solutions beyond the reach of classical efficient algorithms. Our results also give clear guidance on how to construct such advantage-bearing problem instances. A press release can be found here .

Mar 16, 2024

### Work on generalization in Nature Communications

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work published in Nature Communications , through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the study of quantum models for machine learning tasks. A press release can be found here .

Mar 01, 2024

### Work on quantum machine learning in Nature Communications

Work being done in the group on quantum machine learning is published in the Nature Communications . Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as O(T^2 polylog(n)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

Jan 10, 2024

### Work on many-body localization in Communications Physics

Work being done in the group is published in the Nature group journal Communications Physics . Quasi-local integrals of motion are a key concept underpinning the modern understanding of many-body localisation, a phenomenon in which interactions and disorder come together. Despite the existence of several numerical ways to compute them—and in the light of the observation that much of the phenomenology of many properties can be derived from them—it is not obvious how to directly measure aspects of them in real quantum simulations; in fact, hard experimental evidence is still missing. In this work, we propose a way to extract the real-space properties of such quasi-local integrals of motion based on a spatially-resolved entanglement probe able to distinguish Anderson from many-body localisation from non-equilibrium dynamics. We complement these findings with a rigorous entanglement bound and compute the relevant quantities using tensor networks. We demonstrate that the entanglement gives rise to a well-defined length scale that can be measured in experiments.

Dec 20, 2023

### Mentioned among top 100 researchers of Berlin

The Tagesspiegel , the leading newspaper of Berlin, has made a survey of the "100 most important minds in Berlin science 2023".

Oct 01, 2023

### Benchmarking quantum computers

How can one calibrate quantum computers to extremely high precision? Our work published in Nature Communications shows that one feasible kind of data from randomized benchmarking is sufficient to obtain a wealth of diagnostic information, ranging from randomized benchmarking with no end gate over full noise characterization and cross talk tomography. That is, from one dataset, one can in a robust and sample-optimal fashion calibrate quantum circuits. For articles in the academic press, see these links. Berlin Tagesspiegel: Forschung zu Quantencomputern: Ein Tüv für die Zukunftsrechner PhysOrg: Physicists develop series of quality control tests for quantum computers ProPhysik: Ein Qualitätstests für Quantencomputer Informationsdienst Wissenschaft: Quantencomputer: Gewissheit aus dem Zufall ziehen ScienMag: Quantum computing: Benchmarking performance by random data

Sep 01, 2023

### Quantum simulation with light

How can one think of pursuing quantum simulations of non-Gaussian states with light? Our new work in Nature Communications addresses this question. It shows how the emergence of properties of statistical physics in quantum theory can be reconciled and empirically probed. The significance of this work may not only stem from the actual application in quantum simulation, but from nitty gritty method development on how one can certify and witness certain quantum properties in integrated optical devices, with applications in optical quantum computing in mind. For articles in the academic press, see these links. PhysOrg, "Photonics experiment resolves quantum paradox " Photonics World, "Twente photonics experiment resolves longstanding quantum paradox" Yahoo, "Paradox, Solved: Thermodynamics and quantum mechanics CAN be true at the same time" SciTech Daily, "Time reversal photonics experiment resolves quantum paradox" NewsBeezer, "Time-reversal photonics experiment solves quantum paradox"

Jul 10, 2023

### Probing curved light cones on an analog quantum simulator

How can the non-equilibrium dynamics of a quantum field featuring curved light cones be simulated with an analog quantum simulato r ? We show this based on two tunneling-coupled superfluids in one-dimensional traps. We are happy to see this work in the Proceedings of the National Academy of Sciences . A press release can be found here .

May 16, 2023

### A comprehensive review on quantum advantages with quantum random sampling

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article , we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling. This work is in press with the Reviews of Modern Physics .

Mar 10, 2023

### Our team wins the best poster award at QIP

The team of Marcel Hinsche , Marios Ioannou , Alexander Nietner , Jonas Haferkamp , Yihui Quek , Dominik Hangleiter , Jean-Pierre Seifert , Jens Eisert , Ryan Sweke wins the best poster award at QIP 2023 .

Feb 02, 2023

### Talk at QIP 2023

We will present a talk at QIP 2023 on limitations of quantum error mitigation of even log-log-deep quantum circuits, based on arXiv:2210.11505 .

Jan 01, 2023

### Deutsche Welle interview on quantum computing

The international German public television broadcaster Deutsche Welle interviews Rainer Blatt and Jens Eisert on the perspectives of quantum computing .

Dec 21, 2022

### Work on a super-polynomial quantum advantage in combinatorial optimization

Combinatorial optimization - a field of research addressing problems that feature strongly in a wealth of practical and industrial contexts - has been identified as one of the core potential fields of applicability of near-term quantum computers. It is still unclear, however, to what extent variational quantum algorithms can actually outperform classical algorithms for this type of problems. In this work , by resorting to computational learning theory and cryptographic notions, we prove that fault-tolerant quantum computers feature a super-polynomial advantage over classical computers in approximating solutions to combinatorial optimization problems. Specifically, building on seminal work of Kearns and Valiant, we construct special instances of the integer programming problem (which in its most general form is NP-complete) that we prove to be hard-to-approximate classically but give an efficient quantum algorithm to approximate the optimal solution of those instances, hence showing a super-polynomial quantum advantage. This result shows that quantum devices have the power to approximate combinatorial optimization solutions beyond the reach of classical efficient algorithms.

Dec 20, 2022