News
Work on near-term quantum algorithms in the Physical Review Letters
This improvement of the important primitive of the Hadamard test in quantum algorithms is in press in the Physical Review Letters . This work combines the usually unused output with techniques of shadow estimation. The Hadamard test is naturally suited for the intermediate regime between the current era of noisy quantum devices and complete fault tolerance. Its applications use measurements of the auxiliary qubit to extract information, but disregard the system register completely. Separate advances in classical representations of quantum states via classical shadows allow the implementation of even global classical shadows with shallow circuits. This work combines the Hadamard test on a single auxiliary readout qubit with classical shadows on the remaining n-qubit work register. We argue that this combination inherits the best of both worlds and discuss statistical phase estimation as a vignette application. There, we can use the Hadamard test to estimate eigenvalues on the auxiliary qubit, while classical shadows on the remaining n qubits provide access to additional features such as, (i) fidelity with certain pure quantum states, (ii) the initial state's energy and (iii) how pure and how close the initial state is to an eigenstate of the Hamiltonian. Finally, we also discuss how anti-controlled unitaries can further augment this framework. Warm thanks to the dream team of Paul K. Faehrmann and Richard Kueng for this - once again - wonderful collaboration.
Oct 13, 2025
Public panel discussion with the federal minister for research
During a public panel discussion during the Q-Shift 2040 conference, a high level board discussed the future of research on quantum technologies and artificial intelligence in Germany. This panel took a forward-looking attitude, but also an honest and accurate one. Dorothee Bär , German Federal Minister for Research, Technology and Space ( BMFTR ). Alexandra-Gwyn Paetz , Head of Technological Sovereignty and Innovation at BMFTR . Heyo Kroemer , Head of the Charite Berlin . Miriam Meckel , Professor in St Gallen and Executive Chairwoman of ADA . Carsten Polenz , Head of the Quantum Team at SAP . Jens Eisert , professor at Freie Universität Berlin . The panel has been wonderfully moderated by Janosch Delcker of the Deutschlandfunk .
Oct 09, 2025
Work on quantum error correction in Nature Communications
Quantum low density parity check (QLDPC) codes offer a new paradigm within quantum error correction . A bottleneck, however, has been to find good decoders for such codes. This bottleneck has been address in new work published in Nature Communications . Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination , to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.
Sep 03, 2025
Work on thermalization in Communications Physics
New work on thermalization in weakly perturbed quantum many-body systems has been published in Communications Physics of the Nature group . Proving thermalization from the unitary evolution of closed quantum systems is one of the oldest questions that is still only partially resolved. Efforts led to various versions of the eigenstate thermalization hypothesis (ETH), which implies thermalization under certain conditions. Whether the ETH holds in specific systems is however difficult to verify from the microscopic description of the system. In this work, we focus on thermalization under local Hamiltonians of low-entanglement initial states, which are operationally accessible in many natural physical settings, including schemes for testing thermalization in experiments and quantum simulators. We prove thermalization of these states under precise conditions that have operational significance. More specifically, motivated by arguments of unavoidable finite resolution, we define a random energy smoothing on local Hamiltonians that leads to local thermalization when the initial state has low entanglement. Finally we show that this transformation affects neither the Gibbs state locally nor, under generic smoothness conditions on the spectrum, the short-time dynamics.
Jul 19, 2025
Work on a quantum many-body Landauer principle in Nature Physics
New work on a quantum many-body version of Landauer's principle in quantum statistical mechanics and thermodynamics has been published in Nature Physics. Landauer’s principle bridges information theory and thermodynamics by linking the entropy change of a system during a process to the average energy dissipated to its environment. Although typically discussed in the context of erasing a single bit of information, Landauer’s principle can be generalized to characterize irreversibility in out-of-equilibrium processes, such as those involving complex quantum many-body systems. Specifically, the relation between the entropy change of a system and the energy dissipated to its environment can be decomposed into changes in quantum mutual information and a difference in the relative entropies of the environment. Here, we experimentally probe Landauer’s principle in the quantum many-body regime using a quantum field simulator of ultracold Bose gases. Employing a dynamical tomographic reconstruction scheme, we track the temporal evolution of the quantum field following a global mass quench from a massive to a massless Klein–Gordon model and analyse the thermodynamic and information-theoretic contributions to a generalized entropy production for various system–environment partitions of the composite system. Our results verify the quantum field theoretical calculations, interpreted using a semi-classical quasiparticle picture. Our work demonstrates the ability of ultracold atom-based quantum field simulators to experimentally investigate quantum thermodynamics. This work has been covered in PhysOrg here and here , in SciTechDaily , at the press office Vienna , and elsewhere.
Jun 05, 2025
Three publications in a row in PRX Quantum
Three group publications have been published in a row in PRX Quantum , in topics of quantum error correction and fault tolerance, quantum learning and quantum complexity. XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime PRX Quantum 6, 010360 (2025) Analyzing and developing new quantum error-correcting schemes is one of the most prominent tasks in quantum computing research. In such efforts, introducing time dynamics explicitly in both analysis and design of error-correcting protocols constitutes an important cornerstone. In this work, we present a graphical formalism based on tensor networks to capture the logical action and error-correcting capabilities of any Clifford circuit with Pauli measurements. We showcase the formalism on new Floquet codes derived from topological subsystem codes, which we call XYZ ruby codes. Based on the projective symmetries of the building blocks of the tensor network we develop a framework of Pauli flows. Pauli flows allow for a graphical understanding of all quantities entering an error correction analysis of a circuit, including different types of QEC experiments, such as memory and stability experiments. We lay out how to derive a well-defined decoding problem from the tensor network representation of a protocol and its Pauli flows alone, independent of any stabilizer code or fixed circuit. Importantly, this framework applies to all Clifford protocols and encompasses both measurement- and circuit-based approaches to fault tolerance. We apply our method to our new family of dynamical codes which are in the same topological phase as the 2+1d color code, making them a promising candidate for low-overhead logical gates. In contrast to its static counterpart, the dynamical protocol applies a Z3 automorphism to the logical Pauli group every three timesteps. We highlight some of its topological properties and comment on the anyon physics behind a planar layout. Lastly, we benchmark the performance of the XYZ ruby code on a torus by performing both memory and stability experiments and find competitive circuit-level noise thresholds of 0.18%, comparable with other Floquet codes and 2+1d color codes. Complexity-constrained quantum thermodynamics PRX Quantum 6, 010346 (2025) Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process’s complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an 𝑛-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state in our model, via a complexity-constrained process, is quantified by the state’s complexity entropy . The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy . The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer’s ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy. In a random circuit—a simple model for quantum chaotic dynamics—the complexity entropy transitions from zero to its maximal value around the time corresponding to the observer’s computational-power limit. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy , which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time , as quantified by complexity . This work has been covered in PRX Quantum and in Quantum Frontiers . Tomography of parametrized quantum states PRX Quantum 6, 020346 (2025) Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum states that are being prepared in practice often involve families of quantum states characterized by continuous parameters, such as the time evolution of a quantum state. In this work, we extend the foundations of quantum state tomography to parametrized quantum states. We introduce a framework that unifies different notions of tomography and use it to establish a natural figure of merit for tomography of parametrized quantum states. Building on this, we provide an explicit algorithm that combines signal processing techniques with a tomography scheme to recover an approximation to the parametrized quantum state equipped with explicit guarantees. Our algorithm uses techniques from compressed sensing to exploit structure in the parameter dependence and operates with a plug and play nature, using the underlying tomography scheme as a black box. In an analogous fashion, we derive a figure of merit that applies to parametrized quantum channels. Substituting the state tomography scheme with a scheme for process tomography in our algorithm, we then obtain a protocol for tomography of parametrized quantum channels. We showcase our algorithm with two examples of shadow tomography of states time-evolved under an NMR Hamiltonian and a free fermionic Hamiltonian.
Mar 28, 2025
Work on verifiable quantum advantages in Nature Communications
New work on verifiable measurement-based quantum random sampling with trapped ions has been published in Nature Communications. Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create and sample from random cluster states, which are at the heart of measurement-based computing, up to a size of 4 × 4 qubits. By exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states—in single instances and on average—and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage. This work is joint work within the Quantum Flagship project Millenion and has been covered by PhysOrg and others.
Jan 02, 2025
Work on Hamiltonian learning in Nature Communications
New work on Hamiltonian learning has been published in Nature Communications . The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. The key to solving these issues are precise means of characterizing analog quantum simulators. Here, we robustly estimate the free Hamiltonian parameters of bosonic excitations in a superconducting-qubit analog quantum simulator from measured time-series of single-mode canonical coordinates. We achieve high levels of precision in estimating the Hamiltonian parameters by exploiting a priori knowledge, making it robust against noise and state-preparation and measurement (SPAM) errors. Importantly, we are also able to obtain tomographic information about those SPAM errors from the same data, crucial for the experimental applicability of Hamiltonian learning in dynamical quantum-quench experiments. Our learning algorithm is scalable both in terms of the required amounts of data and post-processing. To achieve this, we develop a new super-resolution technique coined tensorESPRIT for frequency extraction from matrix time-series. The algorithm then combines tensorESPRIT with constrained manifold optimization for the eigenspace reconstruction with pre- and post-processing stages. For up to 14 coupled superconducting qubits on two Sycamore processors, we identify the Hamiltonian parameters -- verifying the implementation on one of them up to sub-MHz precision -- and construct a spatial implementation error map for a grid of 27 qubits. Our results constitute an accurate implementation of a dynamical quantum simulation that is characterized using a new diagnostic toolkit for understanding, calibrating, and improving analog quantum processors. This work has been covered by PhysOrg , Tagesspiegel , Spektrum der Wissenschaft , and many others.
Nov 10, 2024
Work on quantum error correction in the Physical Review Letters
Quantum computing will scalably work only if appropriate methods of quantum error correction and fault tolerance are being made use of. In new work published in the Physical Review Letters , we introduce the domain wall color code, a new variant of the quantum error-correcting color code that exhibits exceptionally high code-capacity error thresholds for qubits subject to biased noise. In the infinite bias regime, a two-dimensional color code decouples into a series of repetition codes, resulting in an error-correcting threshold of 50%. Interestingly, at finite bias, our color code demonstrates thresholds identical to those of the noise-tailored XZZX surface code for all single-qubit Pauli noise channels. The design principle of the code is that it introduces domain walls which permute the code's excitations upon domain crossing. For practical implementation, we supplement the domain wall code with a scalable restriction decoder based on a matching algorithm. The proposed code is identified as a comparably resource-efficient quantum error-correcting code highly suitable for realistic noise.
Sep 22, 2024
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
Work on quantum error mitigation in Nature Physics
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault-tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In new work published in Nature Physics , however, we identify strong limitations to the degree to which quantum noise can be effectively ‘undone’ for larger system sizes. Our framework rigorously captures large classes of error-mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to those of current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. Noise also impacts other near-term applications by constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian. A good press release can be found in PhysOrg .
Jul 05, 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
