A5060603833- Web and Library Services
- Quantum Computing Algorithms and Architecture
- Quantum many-body systems
- Quantum Information and Cryptography
- Model Reduction and Neural Networks
- Copyright and Intellectual Property
- Open Education and E-Learning
- Library Collection Development and Digital Resources
- Multimedia Communication and Technology
- Library Science and Administration
- Library Science and Information Systems
- Advanced Thermodynamics and Statistical Mechanics
- Quantum and electron transport phenomena
- Tensor decomposition and applications
- Online and Blended Learning
- Digital Rights Management and Security
- Computational Physics and Python Applications
- Opinion Dynamics and Social Influence
- Parallel Computing and Optimization Techniques
- Smart Parking Systems Research
- Digital Games and Media
- Control and Stability of Dynamical Systems
- Lexicography and Language Studies
- Theoretical and Computational Physics
- Digital Humanities and Scholarship
California Institute of Technology
2020-2025
Imperial College London
2020-2021
University College London
2016-2018
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including classical simulation of quantum many-body systems and circuits. Several applications current interest give rise to tensor with irregular geometries. Finding best possible contraction path for such is a central problem, an exponential effect on computation time memory footprint. In this work, we implement new randomized protocols that find very high quality paths arbitrary large...
The idea to use quantum mechanical devices simulate other systems is commonly ascribed Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through computation, as a potential ``killer application''. Indications of exponential advantage in artificial tasks increased interest this application, thus, it critical understand basis chemistry. Here we gather evidence case most common task chemistry, namely, ground-state energy...
We characterize the variational power of quantum circuit tensor networks in representation physical many-body ground states. Such are formed by replacing dense block unitaries and isometries standard local circuits. explore both matrix product states multiscale entanglement renormalization Ansatz, introduce an adaptive method to optimize resulting circuits high fidelity with more than 104 parameters. benchmark their expressiveness against networks, as well other common architectures, for 1D...
A recent quantum simulation of observables the kicked Ising model on 127 qubits implemented circuits that exceed capabilities exact classical simulation. We show several approximate methods, based sparse Pauli dynamics and tensor network algorithms, can simulate these orders magnitude faster than experiment also be systematically converged beyond experimental accuracy. Our most accurate technique combines a mixed Schrödinger Heisenberg representation with Bethe free entropy relation belief...
The language of quantum physics is essentially linear algebra, making it easy to begin simulating using standard numerical routines.However, the amount classical resources required simulate a system scales exponenially with its size.This imposes, in generic case, dramatic limits on sizes reachable and requires that great care taken order maximise performance.Nonetheless, part due this difficulty, there much be learnt from many-body systems.One useful set tools case information inspired...
Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of correlations many-body systems. However, an experiment, the way measuring entanglement generic mixed state through reconstructive tomography, requiring exponential number measurements system size. Here, we propose machine-learning-assisted scheme measure between arbitrary subsystems size ${N}_{A}$ and ${N}_{B}$, with $\mathcal{O}({N}_{A}+{N}_{B})$ measurements, without any prior knowledge...
einsum is a powerful Swiss army knife for arbitrary tensor contractions and general linear algebra found in the popular numpy (Walt, Colbert, Varoquaux 2011) package.While these expressions can be used to form most mathematical operations NumPy, optimization of becomes increasingly important as naive implementations increase overall scaling resulting dramatic execution time.Expressions with many tensors are particularly prevalent many-body theories such quantum chemistry, particle physics,...
A new framework for approximate evaluation, or contraction, of a tensor network greatly expands the range problems in quantum physics and computer science that may be accurately approximated by methods.
Many-body localization has become an important phenomenon for illuminating a potential rift between non-equilibrium quantum systems and statistical mechanics. However, the nature of transition ergodic localized phases in models displaying many-body is not yet well understood. Assuming that this continuous transition, analytic results show length scale should diverge with critical exponent $\nu \ge 2$ one dimensional systems. Interestingly, stark contrast all exact numerical studies which...
The idea to use quantum mechanical devices simulate other systems is commonly ascribed Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through computation, as a potential ``killer application''. Indications of exponential advantage in artificial tasks increased interest this application, thus, it critical understand basis chemistry. Here we gather evidence case most common task chemistry, namely, ground-state energy...
We use a metalearning neural-network approach to analyze data from measured quantum state. Once our neural network has been trained, it can be used efficiently sample measurements of the state in measurement bases not contained training data. These samples calculate expectation values and other useful quantities. refer this process as "state tomography." encode state's outcome distributions using an parameterized generative network. This allows each stage tomography performed even for large...
We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally formalism. provide pedagogical description these two conventions as implemented for the quimb library. Using hyperoptimized approximate strategies, we present benchmark projected entangled pair state simulations finite Hubbard models defined three-dimensional diamond lattice random regular graphs. Published by American Physical Society 2025
We develop an exact mapping between the one-step replica symmetry breaking cavity method and tensor networks. The two schemes come with complementary mathematical numerical toolboxes that could be leveraged to improve respective states of art. As example, we construct a tensor-network representation Survey Propagation, one best deterministic k-SAT solvers. resulting algorithm outperforms any existent solver by several orders magnitude. comment on generality these ideas, show how extend them...
Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample output distributions two-dimensional circuits. Many attempts to close this have utilized simulations based on tensor network techniques, their limitations shed light improvements hardware required frustrate simulability. In particular, having in excess $\sim 50$ qubits are primarily vulnerable simulation due restrictions gate fidelity connectivity,...
Recently, singlet-triplet measurements in double dots have emerged as a powerful tool quantum information processing. In parallel, dot arrays are being envisaged analog simulators of many-body models. Thus motivated, we explore the potential above for probing and exploiting ground-state Heisenberg spin chain such simulator. We formulate an efficient protocol to discriminate achieved with other likely states. Moreover, transition between phases, arising from addition frustrations $J_1-J_2$...
The single-molecule magnet {Mn84} is a challenge to theory because of its high nuclearity. We directly compute two experimentally accessible observables, the field-dependent magnetization up 75 T and temperature-dependent heat capacity, using parameter-free theory. In particular, we use first-principles calculations derive short- long-range exchange interactions exact partition function resulting classical Potts Ising spin models for all 84 Mn S = 2 spins obtain observables. latter...
We introduce a change of perspective on tensor network states that is defined by the computational graph contraction an amplitude. The resulting class states, which we refer to as functions, inherit conceptual advantages while removing restrictions arising from need converge approximate contractions. use functions compute strict variational estimates energy loopy graphs, analyze their expressive power for ground-states, show can capture aspects volume law time evolution, and provide mapping...
Obtaining the low-energy configurations of spin glasses that have rugged energy landscapes is direct relevance to combinatorial optimization and fundamental science. Search-based heuristics difficulty with this task due existence many local minima are far from optimal. The work M. Rams et al. [Phys. Rev. E 104, 025308 (2021)2470-004510.1103/PhysRevE.104.025308] demonstrates an alternative can bypass issue for planar or quasiplanar geometry: sampling Boltzmann distribution via approximate...
We introduce a change of perspective on tensor network states that is defined by the computational graph contraction an amplitude. The resulting class states, which we refer to as functions, inherit conceptual advantages while removing restrictions arising from need converge approximate contractions. use functions compute strict variational estimates energy loopy graphs, analyze their expressive power for ground show can capture aspects volume law time evolution, and provide mapping general...
The exact nature of the many-body localization transition remains an open question. An aspect which has been posited in various studies is emergence scale invariance around this point, however direct observation phenomenon still absent. Here we achieve by studying logarithmic negativity and mutual information between disjoint blocks varying size across transition. two length scales, block sizes distance them, provide a clear quantitative probe different scales. We find that at obeys...
Tensor network contraction is central to problems ranging from many-body physics computer science. We describe how approximate tensor through bond compression on arbitrary graphs. In particular, we introduce a hyper-optimization over the and strategy itself minimize error cost. demonstrate that our protocol outperforms both hand-crafted strategies in literature as well recently proposed general algorithms variety of synthetic physical regular lattices random further showcase power approach...
Many computational problems can be formulated in terms of high-dimensional functions. Simple representations such functions and resulting computations with them typically suffer from the ``curse dimensionality,'' an exponential cost dependence on dimension. Tensor networks provide a way to represent certain classes polynomial memory. This results where is ameliorated or, some cases, removed, if tensor network representation obtained. Here, we introduce direct mapping arithmetic circuit...
The single-molecule magnet {Mn84} is a challenge to theory due its high nuclearity. Building on our prior work which characterized the structure of spectrum this magnet, we directly compute two experimentally accessible observables, field-dependent magnetization up 75 T and temperature-dependent heat capacity, using parameter free theory. In particular, use first principles calculations derive short- long-range exchange interactions, while exact partition function resulting classical Potts...
Mixed state entanglement measures can act as a versatile probes of many-body systems. However, they are generally hard to compute, often relying on tricky optimizations. One measure that is straightforward compute the logarithmic negativity, yet done naively even this still limited small system sizes. Here, we introduce method negativity for arbitrary subsystems densely represented state, well block matrix product states. The combines lazily evaluated, tensor network representations...