Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation.

Calculating molecular energies is likely to be one of the first useful applications to achieve quantum supremacy, performing faster on a quantum than a classical computer. However, if future quantum devices are to produce accurate calculations, errors due to environmental noise and algorithmic approximations need to be characterized and reduced. In this study, we use the high performance qHiPSTER software to investigate the effects of environmental noise on the preparation of quantum chemistry states. We simulated 18 16-qubit quantum circuits under environmental noise, each corresponding to a unitary coupled cluster state preparation of a different molecule or molecular configuration. Additionally, we analyze the nature of simple gate errors in noise-free circuits of up to 40 qubits. We find that, in most cases, the Jordan-Wigner (JW) encoding produces smaller errors under a noisy environment as compared to the Bravyi-Kitaev (BK) encoding. For the JW encoding, pure dephasing noise is shown to produce substantially smaller errors than pure relaxation noise of the same magnitude. We report error trends in both molecular energy and electron particle number within a unitary coupled cluster state preparation scheme, against changes in nuclear charge, bond length, number of electrons, noise types, and noise magnitude. These trends may prove to be useful in making algorithmic and hardware-related choices for quantum simulation of molecular energies.

Parallel scalability of Hartree-Fock calculations.

Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

High-Performance 3D Compressive Sensing MRI Reconstruction Using Many-Core Architectures.

Compressive sensing (CS) describes how sparse signals can be accurately reconstructed from many fewer samples than required by the Nyquist criterion. Since MRI scan duration is proportional to the number of acquired samples, CS has been gaining significant attention in MRI. However, the computationally intensive nature of CS reconstructions has precluded their use in routine clinical practice. In this work, we investigate how different throughput-oriented architectures can benefit one CS algorithm and what levels of acceleration are feasible on different modern platforms. We demonstrate that a CUDA-based code running on an NVIDIA Tesla C2050 GPU can reconstruct a 256 × 160 × 80 volume from an 8-channel acquisition in 19 seconds, which is in itself a significant improvement over the state of the art. We then show that Intel's Knights Ferry can perform the same 3D MRI reconstruction in only 12 seconds, bringing CS methods even closer to clinical viability.

High-performance 3D compressive sensing MRI reconstruction.

Compressive Sensing (CS) is a nascent sampling and reconstruction paradigm that describes how sparse or compressible signals can be accurately approximated using many fewer samples than traditionally believed. In magnetic resonance imaging (MRI), where scan duration is directly proportional to the number of acquired samples, CS has the potential to dramatically decrease scan time. However, the computationally expensive nature of CS reconstructions has so far precluded their use in routine clinical practice - instead, more-easily generated but lower-quality images continue to be used. We investigate the development and optimization of a proven inexact quasi-Newton CS reconstruction algorithm on several modern parallel architectures, including CPUs, GPUs, and Intel's Many Integrated Core (MIC) architecture. Our (optimized) baseline implementation on a quad-core Core i7 is able to reconstruct a 256 × 160×80 volume of the neurovasculature from an 8-channel, 10 × undersampled data set within 56 seconds, which is already a significant improvement over existing implementations. The latest six-core Core i7 reduces the reconstruction time further to 32 seconds. Moreover, we show that the CS algorithm benefits from modern throughput-oriented architectures. Specifically, our CUDA-base implementation on NVIDIA GTX480 reconstructs the same dataset in 16 seconds, while Intel's Knights Ferry (KNF) of the MIC architecture even reduces the time to 12 seconds. Such level of performance allows the neurovascular dataset to be reconstructed within a clinically viable time.

Mapping high-fidelity volume rendering for medical imaging to CPU, GPU and many-core architectures.

Medical volumetric imaging requires high fidelity, high performance rendering algorithms. We motivate and analyze new volumetric rendering algorithms that are suited to modern parallel processing architectures. First, we describe the three major categories of volume rendering algorithms and confirm through an imaging scientist-guided evaluation that ray-casting is the most acceptable. We describe a thread- and data-parallel implementation of ray-casting that makes it amenable to key architectural trends of three modern commodity parallel architectures: multi-core, GPU, and an upcoming many-core Intel architecture code-named Larrabee. We achieve more than an order of magnitude performance improvement on a number of large 3D medical datasets. We further describe a data compression scheme that significantly reduces data-transfer overhead. This allows our approach to scale well to large numbers of Larrabee cores.