arXiv subjects

Bryan K. Clark

Publications and source records attributed to Bryan K. Clark.

At least 37 records · Page 2Linked to original sources

arXiv2024

Neural network backflow for ab-initio quantum chemistry

The ground state of second-quantized quantum chemistry Hamiltonians provides access to an important set of chemical properties. Wavefunctions based on ML architectures have shown promise in approximating these ground states in a variety of physical systems. In this work, we show how to achieve state-of-the-art energies for molecular Hamiltonians using the the neural network backflow wave-function. To accomplish this, we optimize this ansatz with a variant of the deterministic optimization scheme based on SCI introduced by [Li, et. al JCTC (2023)] which we find works better than standard MCMC sampling. For the molecules we studied, NNBF gives lower energy states than both CCSD and other neural network quantum states. We systematically explore the role of network size as well as optimization parameters in improving the energy. We find that while the number of hidden layers and determinants play a minor role in improving the energy, there is significant improvements in the energy from increasing the number of hidden units as well as the batch size used in optimization with the batch size playing a more important role.

physics.chem-ph↗

arXiv2024

Constant-depth preparation of matrix product states with adaptive quantum circuits

Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it was shown that the AKLT state -- a paradigmatic example of an MPS -- can be exactly prepared with an adaptive quantum circuit of constant-depth, an impossible feat with local unitary gates due to its nonzero correlation length [Smith et al., PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming optimal preparation protocols that rely on unitary circuits alone. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states.

quant-ph↗

arXiv2024

Learning dynamic quantum circuits for efficient state preparation

Dynamic quantum circuits (DQCs) incorporate mid-circuit measurements and gates conditioned on these measurement outcomes. DQCs can prepare certain long-range entangled states in constant depth, making them a promising route to preparing complex quantum states on devices with a limited coherence time. Almost all constructions of DQCs for state preparation have been formulated analytically, relying on special structure in the target states. In this work, we approach the problem of state preparation variationally, developing scalable tensor network algorithms which find high-fidelity DQC preparations for generic states. We apply our algorithms to critical states, random matrix product states, and subset states. We consider both DQCs with a fixed number of ancillae and those with an extensive number of ancillae. Even in the few ancillae regime, the DQCs discovered by our algorithms consistently prepare states with lower infidelity than a static quantum circuit of the same depth. Notably, we observe constant fidelity gains across system sizes and circuit depths. For DQCs with an extensive number of ancillae, we introduce scalable methods for decoding measurement outcomes, including a neural network decoder and a real-time decoding protocol. Our work demonstrates the power of an algorithmic approach to generating DQC circuits, broadening their scope of applications to new areas of quantum computing.

quant-ph↗

arXiv2024

Quantum Hardware-Enabled Molecular Dynamics via Transfer Learning

The ability to perform ab initio molecular dynamics simulations using potential energies calculated on quantum computers would allow virtually exact dynamics for chemical and biochemical systems, with substantial impacts on the fields of catalysis and biophysics. However, noisy hardware, the costs of computing gradients, and the number of qubits required to simulate large systems present major challenges to realizing the potential of dynamical simulations using quantum hardware. Here, we demonstrate that some of these issues can be mitigated by recent advances in machine learning. By combining transfer learning with techniques for building machine-learned potential energy surfaces, we propose a new path forward for molecular dynamics simulations on quantum hardware. We use transfer learning to reduce the number of energy evaluations that use quantum hardware by first training models on larger, less accurate classical datasets and then refining them on smaller, more accurate quantum datasets. We demonstrate this approach by training machine learning models to predict a molecule's potential energy using Behler-Parrinello neural networks. When successfully trained, the model enables energy gradient predictions necessary for dynamics simulations that cannot be readily obtained directly from quantum hardware. To reduce the quantum resources needed, the model is initially trained with data derived from low-cost techniques, such as Density Functional Theory, and subsequently refined with a smaller dataset obtained from the optimization of the Unitary Coupled Cluster ansatz. We show that this approach significantly reduces the size of the quantum training dataset while capturing the high accuracies needed for quantum chemistry simulations.

physics.chem-ph↗

arXiv2024

Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this paper, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure (POVM), we compactly represent quantum states with autoregressive transformer neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of String States to partially restore the symmetry of the autoregressive transformer neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo to sample restricted Boltzmann machines. Our work provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

cond-mat.str-el↗

arXiv2024

Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states, including a wide range of architectures such as Transformer and recurrent neural network (RNN), for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries or anyonic constraint. We prove that our methods can provide exact representation for the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We variationally optimize our symmetry incorporated autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We simulate the dynamics and the ground states of the quantum link model of $\text{U(1)}$ lattice gauge theory, obtain the phase diagram for the 2D $\mathbb{Z}_2$ gauge theory, determine the phase transition and the central charge of the $\text{SU(2)}_3$ anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.

cond-mat.str-el↗

arXiv2024

Approximate t-designs in generic circuit architectures

Unitary t-designs are distributions on the unitary group whose first t moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate t-designs. Here we show that these bounds can be extended to any fixed architecture of Haar-random two-site gates. This is accomplished by relating the spectral gaps of such architectures to those of 1D brickwork architectures. Our bound depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. When this quantity is independent of width, the circuit forms an approximate t-design in linear depth. We also give an implicit bound for nondeterministic architectures in terms of properties of the corresponding distribution over fixed architectures.

quant-ph↗

arXiv2024

Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers

Quantum process tomography is a powerful tool for understanding quantum channels and characterizing properties of quantum devices. Inspired by recent advances using classical shadows in quantum state tomography [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020).], we have developed ShadowQPT, a classical shadow method for quantum process tomography. We introduce two related formulations with and without ancilla qubits. ShadowQPT stochastically reconstructs the Choi matrix of the device allowing for an a-posteri classical evaluation of the device on arbitrary inputs with respect to arbitrary outputs. Using shadows we then show how to compute overlaps, generate all $k$-weight reduced processes, and perform reconstruction via Hamiltonian learning. These latter two tasks are efficient for large systems as the number of quantum measurements needed scales only logarithmically with the number of qubits. A number of additional approximations and improvements are developed including the use of a pair-factorized Clifford shadow and a series of post-processing techniques which significantly enhance the accuracy for recovering the quantum channel. We have implemented ShadowQPT using both Pauli and Clifford measurements on the IonQ trapped ion quantum computer for quantum processes up to $n=4$ qubits and achieved good performance.

quant-ph↗

arXiv2023

FiND: Few-shot three-dimensional image-free confocal focusing on point-like emitters

Confocal fluorescence microscopy is widely applied for the study of point-like emitters such as biomolecules, material defects, and quantum light sources. Confocal techniques offer increased optical resolution, dramatic fluorescence background rejection and sub-nanometer localization, useful in super-resolution imaging of fluorescent biomarkers, single-molecule tracking, or the characterization of quantum emitters. However, rapid, noise-robust automated 3D focusing on point-like emitters has been missing for confocal microscopes. Here, we introduce FiND (Focusing in Noisy Domain), an imaging-free, non-trained 3D focusing framework that requires no hardware add-ons or modifications. FiND achieves focusing for signal-to-noise ratios down to 1, with a few-shot operation for signal-to-noise ratios above 5. FiND enables unsupervised, large-scale focusing on a heterogeneous set of quantum emitters. Additionally, we demonstrate the potential of FiND for real-time 3D tracking by following the drift trajectory of a single NV center indefinitely with a positional precision of < 10 nm. Our results show that FiND is a useful focusing framework for the scalable analysis of point-like emitters in biology, material science, and quantum optics.

physics.optics↗

arXiv2023

Pre-optimizing variational quantum eigensolvers with tensor networks

The variational quantum eigensolver (VQE) is a promising algorithm for demonstrating quantum advantage in the noisy intermediate-scale quantum (NISQ) era. However, optimizing VQE from random initial starting parameters is challenging due to a variety of issues including barren plateaus, optimization in the presence of noise, and slow convergence. While simulating quantum circuits classically is generically difficult, classical computing methods have been developed extensively, and powerful tools now exist to approximately simulate quantum circuits. This opens up various strategies that limit the amount of optimization that needs to be performed on quantum hardware. Here we present and benchmark an approach where we find good starting parameters for parameterized quantum circuits by classically simulating VQE by approximating the parameterized quantum circuit (PQC) as a matrix product state (MPS) with a limited bond dimension. Calling this approach the variational tensor network eigensolver (VTNE), we apply it to the 1D and 2D Fermi-Hubbard model with system sizes that use up to 32 qubits. We find that in 1D, VTNE can find parameters for PQC whose energy error is within 0.5% relative to the ground state. In 2D, the parameters that VTNE finds have significantly lower energy than their starting configurations, and we show that starting VQE from these parameters requires non-trivially fewer operations to come down to a given energy. The higher the bond dimension we use in VTNE, the less work needs to be done in VQE. By generating classically optimized parameters as the initialization for the quantum circuit one can alleviate many of the challenges that plague VQE on quantum computers.

quant-ph↗

arXiv2023

Nearly-frustration-free ground state preparation

Solving for quantum ground states is important for understanding the properties of quantum many-body systems, and quantum computers are potentially well-suited for solving for quantum ground states. Recent work has presented a nearly optimal scheme that prepares ground states on a quantum computer for completely generic Hamiltonians, whose query complexity scales as $δ^{-1}$, i.e. inversely with their normalized gap. Here we consider instead the ground state preparation problem restricted to a special subset of Hamiltonians, which includes those which we term "nearly-frustration-free": the class of Hamiltonians for which the ground state energy of their block-encoded and hence normalized Hamiltonian $α^{-1}H$ is within $δ^y$ of -1, where $δ$ is the spectral gap of $α^{-1}H$ and $0 \leq y \leq 1$. For this subclass, we describe an algorithm whose dependence on the gap is asymptotically better, scaling as $δ^{y/2-1}$, and show that this new dependence is optimal up to factors of $\log δ$. In addition, we give examples of physically motivated Hamiltonians which live in this subclass. Finally, we describe an extension of this method which allows the preparation of excited states both for generic Hamiltonians as well as, at a similar speedup as the ground state case, for those which are nearly frustration-free.

quant-ph↗

arXiv2023

Leveraging generative adversarial networks to create realistic scanning transmission electron microscopy images

The rise of automation and machine learning (ML) in electron microscopy has the potential to revolutionize materials research through autonomous data collection and processing. A significant challenge lies in developing ML models that rapidly generalize to large data sets under varying experimental conditions. We address this by employing a cycle generative adversarial network (CycleGAN) with a reciprocal space discriminator, which augments simulated data with realistic spatial frequency information. This allows the CycleGAN to generate images nearly indistinguishable from real data and provide labels for ML applications. We showcase our approach by training a fully convolutional network (FCN) to identify single atom defects in a 4.5 million atom data set, collected using automated acquisition in an aberration-corrected scanning transmission electron microscope (STEM). Our method produces adaptable FCNs that can adjust to dynamically changing experimental variables with minimal intervention, marking a crucial step towards fully autonomous harnessing of microscopy big data.

cond-mat.mtrl-sci↗

arXiv2023

Analysis of Many-body Localization Landscapes and Fock Space Morphology via Persistent Homology

We analyze functionals that characterize the distribution of eigenstates in Fock space through a tool derived from algebraic topology: persistent homology. Drawing on recent generalizations of the localization landscape applicable to mid-spectrum eigenstates, we introduce several novel persistent homology observables in the context of many-body localization that exhibit transitional behavior near the critical point. We demonstrate that the persistent homology approach to localization landscapes and, in general, functionals on the Fock space lattice offer insights into the structure of eigenstates unobtainable by traditional means.

cond-mat.dis-nn↗

arXiv2022

Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctions

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the $U(1)$ degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous $U(1)$ system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

hep-lat↗

arXiv2022

Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation

Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave function that obeys gauge symmetry. In this paper, we have developed gauge equivariant neural network wave function techniques for simulating continuous-variable quantum lattice gauge theories in the Hamiltonian formulation. We have applied the gauge equivariant neural network approach to find the ground state of 2+1-dimensional lattice gauge theory with U(1) gauge group using variational Monte Carlo. We have benchmarked our approach against the state-of-the-art complex Gaussian wave functions, demonstrating improved performance in the strong coupling regime and comparable results in the weak coupling regime.

hep-lat↗

arXiv2022

Gauge equivariant neural networks for quantum lattice gauge theories

Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Zd gauge group on different geometries. Focusing on the special case of Z2 gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wavefunction for the Z2 theory away from the exactly solvable limit, and to demonstrate the confining/deconfining phase transition of the Wilson loop order parameter.

cond-mat.str-el↗

arXiv2022

Simulating Quantum Mechanics with a $θ$-term and an 't Hooft Anomaly on a Synthetic Dimension

A topological $θ$-term in gauge theories, including quantum chromodynamics in 3+1 dimensions, gives rise to a sign problem that makes classical Monte Carlo simulations impractical. Quantum simulations are not subject to such sign problems and are a promising approach to studying these theories in the future. In the near term, it is interesting to study simpler models that retain some of the physical phenomena of interest and their implementation on quantum hardware. For example, dimensionally-reducing gauge theories on small spatial tori produces quantum mechanical models which, despite being relatively simple to solve, retain interesting vacuum and symmetry structures from the parent gauge theories. Here we consider quantum mechanical particle-on-a-circle models, related by dimensional reduction to the 1+1d Schwinger model, that possess a $θ$-term and realize an 't Hooft anomaly or global inconsistency at $θ= π$. These models also exhibit the related phenomena of spontaneous symmetry breaking and instanton-anti-instanton interference in real time. We propose an experimental scheme for the real-time simulation of a particle on a circle with a $θ$-term and a $\mathbb{Z}_n$ potential using a synthetic dimension encoded in a Rydberg atom. Simulating the Rydberg atom with realistic experimental parameters, we demonstrate that the essential physics can be well-captured by the experiment, with expected behavior in the tunneling rate as a function of $θ$. Similar phenomena and observables can also arise in more complex quantum mechanical models connected to higher-dimensional nonabelian gauge theories by dimensional reduction.

quant-ph↗

arXiv2021

Quantifying Unitary Flow Efficiency and Entanglement for Many-Body Localization

We probe the bulk geometry of the Wegner Wilson Flow (WWF) in the context of many-body localization, by addressing efficiency and bulk entanglement growth measures through approximating upper bounds on the boundary entanglement entropy. We connect these upper bounds to the Fubini-Study metric and clarify how a central quantity, the information fluctuation complexity, distinguishes bulk unitary rotation from entanglement production. We also give a short new proof of the small incremental entangling theorem in the absence of ancillas, achieving a dimension-independent, universal factor of $c= 2$.

cond-mat.dis-nn↗