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DOE OSTI2024

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗

DOE OSTI2023

Learning Many-Body Hamiltonians with Heisenberg-Limited Scaling

Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. Here, in this Letter, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting N-qubit local Hamiltonian. After a total evolution time of $\mathscr{O}$⁡(ε –1 ), the proposed algorithm can efficiently estimate any parameter in the N-qubit Hamiltonian to ε error with high probability. Our algorithm uses ideas from quantum simulation to decouple the unknown N-qubit Hamiltonian H into noninteracting patches and learns H using a quantum-enhanced divide-and-conquer approach. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses polylog⁡(ε –1 ) experiments. In contrast, the best existing algorithms require $\mathscr{O}$⁡⁡(ε –2 ) experiments and total evolution time. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Extracting SIMD Parallelism from Recursive Task-Parallel Programs

The pursuit of computational efficiency has led to the proliferation of throughput-oriented hardware, from GPUs to increasingly wide vector units on commodity processors and accelerators. This hardware is designed to efficiently execute data-parallel computations in a vectorized manner. However, many algorithms are more naturally expressed as divide-and-conquer, recursive, task-parallel computations. In the absence of data parallelism, it seems that such algorithms are not well suited to throughput-oriented architectures. This paper presents a set of novel code transformations that expose the data parallelism latent in recursive, task- parallel programs. These transformations facilitate straightforward vectorization of task-parallel programs on commodity hardware. We also present scheduling policies that maintain high utilization of vector resources while limiting space usage. Across several task-parallel benchmarks, we demonstrate both efficient vector resource utilization and substantial speedup on chips using Intel’s SSE4.2 vector units, as well as accelerators using Intel’s AVX512 units. We then show through rigorous sampling that, in practice, our vectorization techniques are effective for a much larger class of programs.

Recursive Programs, task parallelism, vectorizatio↗

DOE OSTI2020

Inversion of downhole electrical measurements for proppant mapping using very fast simulated annealing

Proppant mapping is critical for optimizing fracture treatment design and improving wells’ productivity. An electrode-based resistivity tool concept was developed earlier for proppant mapping in cased-hole wells. An array of insulating gaps is installed and cemented in place as a permanent part of the casing string. The electrical measurements are performed by imposing a voltage across each insulating gap, one at a time, before and after hydraulic fracture operations. The voltages across other insulating gaps near the transmitter gap are recorded. The method relies on direct excitation of the casing, which is expected to overcome the severe limitations of induction tools in cased-hole wells. A forward model based on a finite volume method has been developed to simulate the tool’s response to one or multiple fractures. To enable the implementation of such a practical system in multistage fractured horizontal wells, a fast and robust inversion approach is required. To that end, we have developed a divide-and-conquer approach based on a global optimization algorithm very fast simulated annealing (VFSA). Specifically, the original inverse problem is divided into subproblems and each subproblem can be solved separately using VFSA. The results indicate that our approach can invert the data and output widths and radii of multiple fractures without requiring a large number of forward simulations. The robustness of the inverse solver is also tested by adding Gaussian noise to the synthetic data. We tested example cases that demonstrate that when up to 5% noise is introduced, VFSA still provides very accurate inversion results with moderate uncertainties. Inversion results with some more realistic conditions, e.g., tilted fractures, complex fractures, and so on, are also presented.

Geochemistry & Geophysics↗

DOE OSTI2024

Quantum Circuit Partitioning for Scalable Noise-Aware Quantum Circuit Re-Synthesis

Re-synthesis techniques are utilized to optimize the quantum circuit. To enable scalable re-synthesis a divide-and-conquer approach is adopted that partitions the circuit into smaller blocks, which are optimized independently. Several algorithms have been proposed to minimize the block number while maximizing the gate count of each block. However, they vary in their performance and may not yield the highest output fidelity. We propose a reinforcement learning-based quantum circuit partitioning framework that incorporates the physical properties of the quantum hardware to maximize the output fidelity post-quantum circuit optimization. To accelerate the training, we also propose a noise injection method that enables on-the-fly optimization in the reinforcement learning environment, independent of the adopted optimization/re-synthesis method at the block level. We evaluate our approach compared to different partitioning techniques using various quantum benchmarks executed on IBM Q Hanoi quantum computer.

Charrwi, Mohammad Walid↗