Rank-adaptive tensor network simulations of quantum dynamics
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Petersson, Anders [Lawrence Livermore National Lab↗
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Distributed Quantum Computing for Network Problems and Other Selected Topics
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Eleanor Rieffel↗
Study network-related optimization problems using quantum alternating optimization ansatz
Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics. One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.
Zhihui Wang↗
On the universality of S n -equivariant k -body gates
The importance of symmetries has recently been recognized in quantum machine learning from the simple motto: if a task exhibits a symmetry (given by a group $\mathfrak{G}$), the learning model should respect said symmetry. This can be instantiated via $\mathfrak{G}$-equivariant quantum neural networks (QNNs), i.e. parametrized quantum circuits whose gates are generated by operators commuting with a given representation of $\mathfrak{G}$. In practice, however, there might be additional restrictions to the types of gates one can use, such as being able to act on at most k qubits. In this work we study how the interplay between symmetry and k-bodyness in the QNN generators affect its expressiveness for the special case of $\mathfrak{G}=S_n$, the symmetric group. Our results show that if the QNN is generated by one- and two-body Sn-equivariant gates, the QNN is semi-universal but not universal. That is, the QNN can generate any arbitrary special unitary matrix in the invariant subspaces, but has no control over the relative phases between them. Then, we show that in order to reach universality one needs to include n-body generators (if n is even) or ($n-1$)-body generators (if n is odd). As such, our results brings us a step closer to better understanding the capabilities and limitations of equivariant QNNs.
97 MATHEMATICS AND COMPUTING↗
Faster Tensor Network Decoding for Topological Quantum Codes
We present a fast and Bayes-optimal-approximating tensor network decoder for planar quantum LDPC codes based on the tensor renormalization group algorithm, originally proposed by Levin, and Nave. By precomputing the renormalization group flow for the null syndrome, we need only recompute tensor contractions in the causal cone of the measured syndrome at the time of decoding. This allows us to achieve an overall runtime complexity of ($pnχ^6$) where p is the depolarizing noise rate, and χ is the cutoff value used to control singular value decomposition approximations used in the algorithm. We apply our decoder to the surface code in the code capacity noise model and compare its performance to the original matrix product state (MPS) tensor network decoder introduced by Bravyi, Suchara, and Vargo. The MPS decoder has a p-independent runtime complexity of $\mathcal{O}(nχ^3)$ resulting in significantly slower decoding times compared to our algorithm in the low-p regime.
97 MATHEMATICS AND COMPUTING↗
Exploring Quantum State Preparation Using Tensor Networks and Sparse Wavefunction Simulations
The variational quantum eigenvalue solver is a powerful hybrid quantum-classical approach that has been suggested as a candidate method to run on near-term quantum hardware for computing ground state electronic energies of molecular systems. However, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. We explore a new paradigm for state preparation where we test how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz, we can study molecular electronic structure problems with up to 64 qubits. In addition, we also test a related approach of using tensor networks to optimize quantum circuits in order to benchmark various lattice models. We present results using these approaches and discuss strategies for incorporating these ideas into variational algorithms involving near-term quantum computers. Our results help demonstrate the strength of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction.
quantum computing↗
4-Clique network minor embedding for quantum annealers
Quantum annealing is a quantum algorithm for computing solutions to combinatorial optimization problems. This study proposes a method for minor embedding optimization problems onto sparse quantum annealing hardware graphs called 4-clique network minor embedding. This method is in contrast to the standard minor embedding technique of using a path of linearly connected qubits in order to represent a logical variable state. The 4-clique minor embedding is possible on Pegasus graph connectivity, which is the native hardware graph for some of the current D-Wave quantum annealers. The Pegasus hardware graph contains many cliques of size 4, making it possible to form a graph composed entirely of paths of connected 4-cliques on which a problem can be minor-embedded. The 4-clique chains come at the cost of additional qubit usage on the hardware graph, but they allow for stronger coupling within each chain, thereby increasing chain integrity, reducing chain breaks, and allow for greater usage of the available energy scale for programming logical problem coefficients on current quantum annealers. The 4-clique minor embedding technique is compared with the standard linear path minor embedding with experiments on two D-Wave quantum annealing processors with Pegasus hardware graphs. We show proof-of-concept experiments where the 4-clique minor embeddings can use weak chain strengths while successfully carrying out the computation of minimizing random all-to-all spin glass problem instances. Published by the American Physical Society 2024
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quapprox: A Framework for Benchmarking the Approximability of Variational Quantum Circuit
Most of the existing quantum neural network models, such as variational quantum circuits (VQCs), are limited in their ability to explore the non-linear relationships in input data. This gradually becomes the main obstacle for it to tackle realistic applications, such as natural language processing, medical image processing, and wireless communications. Recently, there have emerged research efforts that enable VQCs to perform non-linear operations. However, it is still unclear on the approximability of a given VQC (i.e., the order of non-linearity that can be handled by a specified design). In response to this issue, we developed an automated tool designed to benchmark the approximation of a given VQC. The proposed tool will generate a set of synthetic datasets with different orders of non-linearity and train the given VQC on these datasets to estimate their approximability. Our experiments benchmark VQCs with different designs, where we know their theoretic approximability. We then show that the proposed tool can precisely estimate the approximability, which is consistent with the theoretic value, indicating that the proposed tool can be used for benchmarking the approximability of a given quantum circuit for learning tasks.
artificial intelligence↗
Recurrent convolutional neural networks for modeling nonadiabatic dynamics of quantum-classical systems
Recurrent neural networks (RNNs) have recently been extensively applied to model the time evolution in fluid dynamics, weather predictions, and even chaotic systems due to their ability to capture temporal dependencies and sequential patterns in data. Here we present an RNN model based on convolutional neural networks for modeling the nonlinear nonadiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The Physics-Aware Recurrent Convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. Here, we apply our RNN approach to learn the space-time evolution of a one-dimensional semiclassical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.
Holstein model↗
SQuaD: Smart Quantum Detection for Photon Recognition and Dark Count Elimination
Quantum detectors of single photons are an essential component for quantum information processing across computing, communication and networking. Today's quantum detection system, which consists of single photon detectors, timing electronics, control and data processing software, is primarily used for counting the number of single photon detection events. However, it is largely incapable of extracting other rich physical characteristics of the detected photons, such as their wavelengths, polarization states, photon numbers, or temporal waveforms. This work, for the first time, demonstrates a smart quantum detection system, SQuaD, which integrates a field programmable gate array (FPGA) with a neural network model, and is designed to recognize the features of photons and to eliminate detector dark-count. The SQuaD is a fully integrated quantum system with high timing-resolution data acquisition, onboard multi-scale data analysis, intelligent feature recognition and extraction, and feedback-driven system control. Our \name experimentally demonstrates 1) reliable photon counting on par with the state-of-the art commercial systems; 2) high-throughput data processing for each individual detection events; 3) efficient dark count recognition and elimination; 4) up to 100% accurate feature recognition of photon wavelength and polarization. Additionally, we deploy the SQuaD to an atomic (erbium ion) photon emitter source to realize noise-free control and readout of a spin qubit in the telecom band, enabling critical advances in quantum networks and distributed quantum information processing.
Linne, Karl C. [U. Chicago (main)] (ORCID:00090009↗
Learning quantum computers' errors using interpretable neural networks
Learning and reducing the errors and noise in quantum computing systems is necessary for achieving quantum computation’s promise. However, rapid advances in experimental quantum computing are making this task increasingly difficult, because state-of-the-art systems now contain hundreds of qubits and many characterization techniques are hard to apply at this scale. Furthermore, complex kinds of errors in these systems, such as crosstalk and non-Markovian effects, must be understood and decreased, but these errors are challenging to study with most existing methods. In this project, we explored using neural networks for scalable characterization of complex errors in quantum computers. We proposed and demonstrated characterizing a quantum computer’s errors with neural networks that have interpretable parameters corresponding to the rates of different kinds of errors, within a sparse Lindbladian parameterization for errors. To enable scaling to many qubit systems, these networks then predict how these errors combine within quantum circuits and impact their outcomes using an efficient approximations. We demonstrated these networks ability to learn coherent crosstalk errors and context-dependent errors in a simulated 4-qubit system.
97 MATHEMATICS AND COMPUTING↗
Absence of Barren Plateaus and Scaling of Gradients in the Energy Optimization of Isometric Tensor Network States
Abstract Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions, which can be studied on classical computers or in the form of variational quantum eigensolvers on quantum computers. Barren plateaus correspond to scenarios where the average amplitude of the energy gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks and for brickwall quantum circuits when the depth increases polynomially in the system size. Here we prove that the variational optimization problems for matrix product states, tree tensor networks, and the multiscale entanglement renormalization ansatz are free of barren plateaus. The derived scaling properties for the gradient variance provide an analytical guarantee for the trainability of randomly initialized tensor network states (TNS) and motivate certain initialization schemes. In a suitable representation, unitary tensors that parametrize the TNS are sampled according to the uniform Haar measure. We employ a Riemannian formulation of the gradient based optimizations which simplifies the analytical evaluation.
Barthel, Thomas↗
A Fast Renormalization Group Tensor network decoder for Planar quantum LDPC codes
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Maurer, Cole Everett↗
Sampling two-dimensional isometric tensor network states
Sampling a quantum system’s underlying probability distributions is an important computational task, e.g., for quantum advantage experiments and quantum Monte Carlo algorithms. Tensor networks are an invaluable tool for efficiently representing states of large quantum systems with limited entanglement. Algorithms for sampling one-dimensional (1D) tensor networks are well-established and utilized in several 1D tensor network methods. In this paper we introduce two novel sampling algorithms for two-dimensional (2D) isometric tensor network states (isoTNS) that generalize existing 1D tensor network sampling algorithms. Our first proposed algorithm performs independent sampling and yields a single configuration together with its associated probability. The second algorithm employs a greedy search strategy to identify high-probability configurations and their corresponding probabilities. Numerical results demonstrate the effectiveness of these algorithms across quantum states with varying entanglement and system size.
Dumitrescu, Eugene [ORNL] (ORCID:0000000158519567)↗
Quantum Frequency Combs with Path Identity for Quantum Remote Sensing
Quantum sensing promises to revolutionize sensing applications by employing quantum states of light or matter as sensing probes. Photons are the clear choice as quantum probes for remote sensing because they can travel to and interact with a distant target. Existing schemes are mainly based on the quantum illumination framework, which requires quantum memory to store a single photon of an initially entangled pair until its twin reflects off a target and returns for final correlation measurements. Existing demonstrations are limited to tabletop experiments, and expanding the sensing range faces various roadblocks, including long-time quantum storage and photon loss and noise when transmitting quantum signals over long distances. We propose a novel quantum sensing framework that addresses these challenges using quantum frequency combs with path identity for remote sensing of signatures (“qCOMBPASS”). The combination of one key quantum phenomenon and two quantum resources—namely, quantum-induced coherence by path identity, quantum frequency combs, and two-mode squeezed light—allows for quantum remote sensing without requiring quantum memory. The proposed scheme is akin to a quantum radar based on entangled frequency-comb pairs that uses path identity to detect, range, or sense a remote target of interest by measuring pulses of one comb in the pair that never traveled to the target but that contains target information “teleported” by quantum-induced coherence by path identity from the other comb in the pair that traveled to the target but is not detected. We develop the basic qCOMBPASS theory, analyze the properties of the qCOMBPASS transceiver, and introduce the qCOMBPASS equation—a quantum analog of the well-known LIDAR equation in classical remote sensing. We also describe an experimental scheme to demonstrate the concept using two-mode squeezed quantum combs. qCOMBPASS can strongly impact various applications in remote quantum sensing, imaging, metrology, and communications. These applications include detection and ranging of low-reflectivity objects, measurement of small displacements of a remote target with precision beyond the standard quantum limit (SQL), standoff hyperspectral quantum imaging, discreet surveillance from space with low detection probability (detect without being detected), very-long-baseline interferometry, quantum Doppler sensing, quantum clock synchronization, and networks of distributed quantum sensors. Published by the American Physical Society 2024
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum Ising model on (2+1)-dimensional anti–de Sitter space using tensor networks
We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using matrix product states (MPS) and matrix product operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure out of time ordered correlators (OTOCs) to explore the scrambling behavior of the theory.
Quantum spin models↗
Attention to quantum complexity
The imminent era of error-corrected quantum computing demands robust methods to characterize quantum state complexity from limited, noisy measurements. We introduce the Quantum Attention Network (QuAN), a classical artificial intelligence (AI) framework leveraging attention mechanisms tailored for learning quantum complexity. Inspired by large language models, QuAN treats measurement snapshots as tokens while respecting permutation invariance. Combined with our parameter-efficient miniset self-attention block, this enables QuAN to access high-order moments of bit-string distributions and preferentially attend to less noisy snapshots. We test QuAN across three quantum simulation settings: driven hard-core Bose-Hubbard model, random quantum circuits, and toric code under coherent and incoherent noise. QuAN directly learns entanglement and state complexity growth from experimental computational basis measurements, including complexity growth in random circuits from noisy data. In regimes inaccessible to existing theory, QuAN unveils the complete phase diagram for noisy toric code data as a function of both noise types, highlighting AI’s transformative potential for assisting quantum hardware.
Kim, Hyejin [Cornell Univ., Ithaca, NY (United Sta↗