Article
Optics
Dheeraj Peddireddy, Utkarsh Priyam, Vaneet Aggarwal
Summary: This research proposes an improved VQE algorithm by utilizing a classical gradient computation method that uses tensor-ring approximation. By truncating singular values and preserving the structure of the tensor ring, this method allows for faster evaluation of gradients on classical simulators, addressing the scalability challenge of VQE.
Article
Computer Science, Artificial Intelligence
Friederike Metz, Marin Bukov
Summary: Quantum many-body control is a key milestone in harnessing quantum technologies, and classically simulating these systems and designing optimal control protocols is challenging due to the exponential growth of the Hilbert space dimension. In this study, a framework combining reinforcement learning with matrix product states is proposed for efficient control of quantum many-body systems. The framework allows for control of larger systems than traditional neural network methods and retains the advantages of deep learning algorithms. The authors demonstrate that reinforcement learning agents can find universal controls, adapt control protocols, and learn to optimally steer previously unseen many-body states.
NATURE MACHINE INTELLIGENCE
(2023)
Article
Chemistry, Physical
Tobias Serwatka, Pierre-Nicholas Roy
Summary: In this study, a density matrix-based optimization procedure is used to generate customized basis functions for describing rotating water molecule chains at different intermolecular distances. The procedure provides a compact basis with a clear truncation criterion based on the population of single particle basis functions. For the water trimer, the convergence behavior of various properties is discussed and shown to be superior to an energy-based truncated basis. It is demonstrated that the optimized basis reduces the required number of basis functions by at least an order of magnitude. Finally, the optimization procedure is applied to larger chains of up to ten water molecules, investigating the formation of hydrogen bonds and their impact on the net polarization of the chain.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Daniel Azses, David F. Mross, Eran Sela
Summary: Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. We developed tensor-network methods to study the entanglement data of two-dimensional symmetry-protected topological states by constructing matrix product operators. We verified our approach using the Levin-Gu model and tracked the evolution of entanglement features and their symmetry resolution by using the cohomology formalism.
Article
Materials Science, Multidisciplinary
Philipp Schmoll, Augustine Kshetrimayum, Jan Naumann, Jens Eisert, Yasir Iqbal
Summary: We investigate the ground state of the spin S = 1/2 Heisenberg antiferromagnet on the shuriken lattice, and found that a valence bond crystal with resonances over length six loops emerges as the ground state, yielding the lowest reported estimate of the ground state energy for this model. We also study the model in the presence of an external magnetic field and find the emergence of 0, 1/3, and 2/3 magnetization plateaus, with the 1/3 and 2/3 plateau states respecting translation and point group symmetries and featuring loop-four plaquette resonances.
Article
Materials Science, Multidisciplinary
Song Cheng, Lei Wang, Pan Zhang
Summary: Tensor networks, originating from quantum physics, have been generalized in machine learning, with PEPS showing superior performance in image classification compared to treelike tensor networks. Furthermore, our model performs as well as multilayer perceptron classifiers with fewer parameters and increased stability.
Article
Materials Science, Multidisciplinary
Feng-Feng Song, Guang-Ming Zhang
Summary: Using tensor network representation, the phase diagram of a generalized two-dimensional XY spin model with topological vortex excitations has been accurately determined, revealing continuous topological phase transitions and transitions between different vortex binding phases. Additionally, a hybrid BKT and Ising universality class of topological phase transition has been established, along with the discovery of a multicritical point where three phase transition lines intersect.
Article
Materials Science, Multidisciplinary
Miguel Frias-Perez, Mari Carmen Banuls
Summary: This paper presents a tensor network method, called the transverse folding algorithm, for computing time-dependent local observables in out-of-equilibrium quantum spin chains. The method overcomes the limitations of matrix product states when the entanglement grows slower in time than in space. A contraction strategy based on the exact light cone structure of the tensor network is proposed, which can be combined with the hybrid truncation approach to improve the efficiency of the method. The performance of this strategy is demonstrated for transport coefficients and potential extensions to other dynamical quantities are discussed.
Article
Materials Science, Multidisciplinary
Nils Niggemann, Bjorn Sbierski, Johannes Reuther
Summary: The study introduces a general functional renormalization group approach based on Majorana fermions to improve the accuracy of treating frustrated quantum spin systems at finite temperatures. By implementing spin operators via an SO(3) symmetric Majorana representation, the method shows significantly enhanced accuracy compared to previous methods at finite temperatures. The development of functional renormalization group approaches with Majorana fermions expands the applicability of such methods in a broader scope.
Article
Physics, Multidisciplinary
Peng-Fei Zhou, Ying Lu, Jia-Hao Wang, Shi-Ju Ran
Summary: Efficient methods for accessing quantum entanglement in many-body systems have been a long-standing concern due to exponential scaling complexity. In this study, a Schmidt tensor network state (Schmidt TNS) is proposed, which efficiently represents the Schmidt decomposition of quantum states of finite and infinite sizes with nontrivial bipartition boundary. The key idea is to represent the Schmidt coefficients and transformations as tensor networks with linearly scaled complexity. Simulation results demonstrate the validity of the Schmidt TNS, showing that the encoded Schmidt coefficients are weakly entangled, supporting the efficiency of using matrix product states (MPS) for encoding.
PHYSICAL REVIEW LETTERS
(2023)
Article
Quantum Science & Technology
Yuchen Guo, Shuo Yang
Summary: Quantum decoherence caused by imperfect manipulation of quantum devices is a crucial issue in the NISQ era. The traditional method of using error rates to parameterize quantum noise channels does not provide an explicit relationship between the decoherence effect and the error rate. This study proposes characterizing the decoherence effect of a noise channel based on the physical implementability of its inverse, which quantifies the difficulty of simulating the noise inverse using accessible quantum channels. Two concise inequalities are established to connect the decrease in state purity and logarithmic negativity after a noise channel to the physical implementability of the noise inverse, which should be decomposed as mutually orthogonal unitaries or product channels. Numerical demonstrations are conducted on commonly adopted two-qubit noise models, and the results contribute to the theoretical research on the entanglement properties of noise channels and provide guiding principles for quantum circuit design.
NPJ QUANTUM INFORMATION
(2023)
Article
Physics, Multidisciplinary
Xun Gao, Eric R. Anschuetz, Sheng-Tao Wang, J. Ignacio Cirac, Mikhail D. Lukin
Summary: This research demonstrates the powerful resource of generative modeling derived from quantum correlations. It provides an unconditional proof that quantum-inspired models surpass conventional Bayesian networks in expressive power and verifies their applicability through numerical tests. This has significant implications for designing quantum machine learning protocols and improving classical algorithms using ideas from quantum foundations.
Article
Optics
Jack Y. Araz, Michael Spannowsky
Summary: This paper compares classical Tensor Networks (TN) with TN-inspired quantum circuits in the context of machine learning. The study shows that classical TNs require larger dimensions and result in a flat loss landscape, making optimization challenging. By using quantitative metrics, the paper also demonstrates that classical TNs require more training samples compared to TN-inspired quantum circuits. Additionally, the study explores the possibility of hybrid classical-quantum TNs and presents different TN ansatzes.
Article
Materials Science, Multidisciplinary
Manuel Schneider, Johann Ostmeyer, Karl Jansen, Thomas Luu, Carsten Urbach
Summary: Tensor networks are a powerful tool for simulating various physical models, overcoming sign problems in Monte Carlo simulations. Using imaginary-time evolution, accurate estimators for ground states of models like the Hubbard model have been provided. A method to directly simulate the subspace with an odd number of fermions has also been presented.
Article
Quantum Science & Technology
Jose Garre-Rubio, Laurens Lootens, Andras Molnar
Summary: We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This characterization provides a set of quantities satisfying the coupled pentagon equations, which give complete invariants for an MPO symmetry protected phase. Our techniques facilitate the numerical study and match the known renormalization fixed point classifications. Additionally, we recover the symmetry protected topological order classification and explore the interplay between time reversal symmetry and MPO symmetries.
Article
Quantum Science & Technology
Paul K. Faehrmann, Mark Steudtner, Richard Kueng, Maria Kieferova, Jens Eisert
Summary: This article introduces a new quantum simulation approach that combines the advantages of randomized compiling and higher-order multi-product formulas, proposing a framework for programmable quantum simulators and two new multi-product formula algorithms. This framework reduces circuit depth, especially suitable for early quantum computers.
Article
Physics, Mathematical
J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, I Roth
Summary: Many quantum information protocols require the use of random unitaries, and unitary t-designs are often used as an alternative to Haar-random unitaries. In this work, we explore the non-Clifford resources needed to break the limitation of only being able to implement up to 3-designs with Clifford operations. We find that injecting a certain number of non-Clifford gates into a random Clifford circuit can produce an epsilon-approximate t-design, regardless of the system size. We also derive new bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
M. Hinsche, M. Ioannou, A. Nietner, J. Haferkamp, Y. Quek, D. Hangleiter, J. -P. Seifert, J. Eisert, R. Sweke
Summary: The task of learning a probability distribution from samples is common in the natural sciences. This study extensively characterizes the learnability of output distributions from local quantum circuits. The results show that Clifford circuit output distributions are efficiently learnable, but the injection of a single T gate makes density modeling task difficult. Additionally, generative modeling of universal quantum circuits is hard for any learning algorithm, classical or quantum, indicating no quantum advantage for probabilistic modeling tasks.
PHYSICAL REVIEW LETTERS
(2023)
Article
Multidisciplinary Sciences
Mohammadamin Tajik, Marek Gluza, Nicolas Sebe, Philipp Schuettelkopf, Federica Cataldini, Joao Sabino, Frederik Moller, Si-Cong Ji, Sebastian Erne, Giacomo Guarnieri, Spyros Sotiriadis, Jens Eisert, Jorg Schmiedmayer
Summary: We investigate signal propagation in a quantum field simulator of the Klein-Gordon model using two strongly coupled parallel one-dimensional quasi-condensates. We observe the propagation of correlations along sharp light-cone fronts by measuring local phononic fields after a quench. The curved propagation fronts and reflection at sharp edges are observed when the local atomic density is inhomogeneous. By comparing the data with theoretical predictions, we find agreement with curved geodesics of an inhomogeneous metric.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Quantum Science & Technology
Johannes Jakob Meyer, Marian Mularski, Elies Gil-Fuster, Antonio Anna Mele, Francesco Arzani, Alissa Wilms, Jens Eisert
Summary: Variational quantum machine learning is a widely studied application of near-term quantum computers. This work explores how symmetries of the learning problem can be used to construct quantum learning models with symmetrical outcomes. By utilizing tools from representation theory, a standard gateset can be transformed into an equivariant gateset that respects the symmetries of the problem. The proposed methods are benchmarked on toy problems and show a substantial increase in generalization performance.
Review
Physics, Multidisciplinary
Dominik Hangleiter, Jens Eisert
Summary: Quantum random sampling is the main proposal to demonstrate the computational advantage of quantum computers over classical computers. Recent large-scale implementations of quantum random sampling have possibly surpassed the capabilities of existing classical hardware for simulation. This review comprehensively discusses the theoretical basis and practical implementation of quantum random sampling, as well as its classical simulation, and explores open questions and potential applications in the field.
REVIEWS OF MODERN PHYSICS
(2023)
Article
Multidisciplinary Sciences
J. Helsen, M. Ioannou, J. Kitzinger, E. Onorati, A. H. Werner, J. Eisert, I. Roth
Summary: With quantum computing devices becoming more complex, there is a need for tools that can provide precise diagnostic information about quantum operations. The authors propose a new approach that uses random gate sequences and native measurements followed by classical post-processing to estimate various gate set properties. They also discuss applications for optimizing quantum gates and diagnosing cross-talk. This research is important for the development and improvement of quantum computing devices.
NATURE COMMUNICATIONS
(2023)
Article
Multidisciplinary Sciences
F. H. B. Somhorst, R. van der Meer, M. Correa Anguita, R. Schadow, H. J. Snijders, M. de Goede, B. Kassenberg, P. Venderbosch, C. Taballione, J. P. Epping, H. H. van den Vlekkert, J. Timmerhuis, J. F. F. Bulmer, J. Lugani, I. A. Walmsley, P. W. H. Pinkse, J. Eisert, N. Walk, J. J. Renema
Summary: This study demonstrates that in a unitarily evolving system, single-mode measurements can converge to a thermal state using photons in an integrated optical interferometer. The resolution to the paradox between unitary evolution and the second law of thermodynamics is the recognition that the global unitary evolution of a multi-partite quantum state causes local subsystems to evolve towards maximum-entropy states. The experiment utilizes a programmable integrated quantum photonic processor to manipulate quantum states and shows the potential of photonic devices for simulating non-Gaussian states.
NATURE COMMUNICATIONS
(2023)
Article
Quantum Science & Technology
Ingo Roth, Jadwiga Wilkens, Dominik Hangleiter, Jens Eisert
Summary: Extracting tomographic information about quantum states is crucial in developing high-precision quantum devices. This study shows that by exploiting the low-rank structure of quantum states, a scalable 'blind' tomography scheme can be achieved with a computationally efficient post-processing algorithm. The efficiency of the scheme is further improved by utilizing the sparse structure of the calibrations.
Article
Optics
Niklas Pirnay, Ryan Sweke, Jens Eisert, Jean-Pierre Seifert
Summary: Density modeling is the task of learning an unknown probability density function from samples, and it is a central problem in unsupervised machine learning. This research demonstrates that fault-tolerant quantum computers can offer a superpolynomial advantage over classical learning algorithms in a specific density modeling problem, assuming standard cryptographic assumptions. The results also provide insights for future distribution learning separations between quantum and classical learning algorithms, including the relationship between hardness results in supervised learning and distribution learning.
Article
Materials Science, Multidisciplinary
Philipp Schmoll, Augustine Kshetrimayum, Jan Naumann, Jens Eisert, Yasir Iqbal
Summary: We investigate the ground state of the spin S = 1/2 Heisenberg antiferromagnet on the shuriken lattice, and found that a valence bond crystal with resonances over length six loops emerges as the ground state, yielding the lowest reported estimate of the ground state energy for this model. We also study the model in the presence of an external magnetic field and find the emergence of 0, 1/3, and 2/3 magnetization plateaus, with the 1/3 and 2/3 plateau states respecting translation and point group symmetries and featuring loop-four plaquette resonances.
Article
Quantum Science & Technology
Konstantin Tiurev, Peter-Jan H. S. Derks, Joschka Roffe, Jens Eisert, Jan-Michael Reiner
Summary: This study develops topological surface codes adapted to known noise structures and investigates their performance with specific decoders. Experimental results show that this approach significantly improves error thresholds and reduces failure rates. Furthermore, the study reveals the importance of tailored surface codes in correcting local noise.
Article
Quantum Science & Technology
Jarn de Jong, Frederik Hahn, Jens Eisert, Nathan Walk, Anna Pappa
Summary: Sharing multi-partite quantum entanglement allows for diverse secure communication tasks. In this work, an anonymous CKA protocol for three parties is proposed, implemented in a highly practical network setting using a linear cluster state among quantum nodes. The protocol protects the identities of the participants and contributes to identifying feasible quantum communication tasks for network architectures beyond point-to-point.
Article
Materials Science, Multidisciplinary
A. Bauer, J. Eisert, C. Wille
Summary: This paper discusses fixed-point models for topological phases of matter using tensor networks, presenting a more general fixed-point ansatz not affected by certain restrictions, potentially providing a microscopic fixed-point description of chiral phases with strategies for concrete examples.
Article
Quantum Science & Technology
Noa Feldman, Augustine Kshetrimayum, Jens Eisert, Moshe Goldstein
Summary: We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. The method involves stochastic sampling of matrix elements to calculate their moments, providing Renyi entropies and negativities. The method is tested on the one-dimensional critical XX chain and the two-dimensional toric code, showing satisfactory results.
