arXiv subjects

Ian D. Kivlichan

Publications and source records attributed to Ian D. Kivlichan.

11 recordsLinked to original sources

arXiv2022

CrowdWorkSheets: Accounting for Individual and Collective Identities Underlying Crowdsourced Dataset Annotation

Human annotated data plays a crucial role in machine learning (ML) research and development. However, the ethical considerations around the processes and decisions that go into dataset annotation have not received nearly enough attention. In this paper, we survey an array of literature that provides insights into ethical considerations around crowdsourced dataset annotation. We synthesize these insights, and lay out the challenges in this space along two layers: (1) who the annotator is, and how the annotators' lived experiences can impact their annotations, and (2) the relationship between the annotators and the crowdsourcing platforms, and what that relationship affords them. Finally, we introduce a novel framework, CrowdWorkSheets, for dataset developers to facilitate transparent documentation of key decisions points at various stages of the data annotation pipeline: task formulation, selection of annotators, platform and infrastructure choices, dataset analysis and evaluation, and dataset release and maintenance.

cs.HC↗

arXiv2021

Measuring and Improving Model-Moderator Collaboration using Uncertainty Estimation

Content moderation is often performed by a collaboration between humans and machine learning models. However, it is not well understood how to design the collaborative process so as to maximize the combined moderator-model system performance. This work presents a rigorous study of this problem, focusing on an approach that incorporates model uncertainty into the collaborative process. First, we introduce principled metrics to describe the performance of the collaborative system under capacity constraints on the human moderator, quantifying how efficiently the combined system utilizes human decisions. Using these metrics, we conduct a large benchmark study evaluating the performance of state-of-the-art uncertainty models under different collaborative review strategies. We find that an uncertainty-based strategy consistently outperforms the widely used strategy based on toxicity scores, and moreover that the choice of review strategy drastically changes the overall system performance. Our results demonstrate the importance of rigorous metrics for understanding and developing effective moderator-model systems for content moderation, as well as the utility of uncertainty estimation in this domain.

cs.LG↗

arXiv2020

Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization

Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energies per unit cell), as is often the goal for condensed-phase systems. In this context, simulations of the Hubbard and plane-wave electronic structure models with $N < 10^5$ fermionic modes can be performed with roughly $O(1)$ and $O(N^2)$ T complexities. We perform numerics revealing tradeoffs between the error and gate complexity of a Trotter step; e.g., we show that split-operator techniques have less Trotter error than popular alternatives. By compiling to surface code fault-tolerant gates and assuming error rates of one part per thousand, we show that one can error-correct quantum simulations of interesting, classically intractable instances with a few hundred thousand physical qubits.

quant-ph↗

arXiv2019

Phase estimation with randomized Hamiltonians

Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical inference to glean estimates of the eigenvalues from the resulting data. Here, we show a generalization of this framework where each of the steps in the simulation uses a different Hamiltonian. This allows the precision of the Hamiltonian to be changed as the phase estimation precision increases. Additionally, through the use of importance sampling, we can exploit knowledge about the ground state to decide how frequently each Hamiltonian term should appear in the evolution, and minimize the variance of our estimate. We rigorously show, if the Hamiltonian is gapped and the sample variance in the ground state expectation values of the Hamiltonian terms sufficiently small, that this process has a negligible impact on the resultant estimate and the success probability for phase estimation. We demonstrate this process numerically for two chemical Hamiltonians, and observe substantial reductions in the number of terms in the Hamiltonian; in one case, we even observe a reduction in the number of qubits needed for the simulation. Our results are agnostic to the particular simulation algorithm, and we expect these methods to be applicable to a range of approaches.

quant-ph↗

arXiv2019

OpenFermion: The Electronic Structure Package for Quantum Computers

Quantum simulation of chemistry and materials is predicted to be an important application for both near-term and fault-tolerant quantum devices. However, at present, developing and studying algorithms for these problems can be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. To help bridge this gap and open the field to more researchers, we have developed the OpenFermion software package (www.openfermion.org). OpenFermion is an open-source software library written largely in Python under an Apache 2.0 license, aimed at enabling the simulation of fermionic models and quantum chemistry problems on quantum hardware. Beginning with an interface to common electronic structure packages, it simplifies the translation between a molecular specification and a quantum circuit for solving or studying the electronic structure problem on a quantum computer, minimizing the amount of domain expertise required to enter the field. The package is designed to be extensible and robust, maintaining high software standards in documentation and testing. This release paper outlines the key motivations behind design choices in OpenFermion and discusses some basic OpenFermion functionality which we believe will aid the community in the development of better quantum algorithms and tools for this exciting area of research.

quant-ph↗

arXiv2018

Quantum Chemistry in the Age of Quantum Computing

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging complexity landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry such as the electronic structure of molecules. In the past two decades significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This article is an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing, and quantum computing researchers who would like to explore applications in quantum chemistry.

quant-ph↗

arXiv2018

qTorch: The Quantum Tensor Contraction Handler

Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN) contraction is an algorithmic method that can efficiently simulate some quantum circuits, often greatly reducing the computational cost over methods that simulate the full Hilbert space. In this study we implement a tensor network contraction program for simulating quantum circuits using multi-core compute nodes. We show simulation results for the Max-Cut problem on 3- through 7-regular graphs using the quantum approximate optimization algorithm (QAOA), successfully simulating up to 100 qubits. We test two different methods for generating the ordering of tensor index contractions: one is based on the tree decomposition of the line graph, while the other generates ordering using a straight-forward stochastic scheme. Through studying instances of QAOA circuits, we show the expected result that as the treewidth of the quantum circuit's line graph decreases, TN contraction becomes significantly more efficient than simulating the whole Hilbert space. The results in this work suggest that tensor contraction methods are superior only when simulating Max-Cut/QAOA with graphs of regularities approximately five and below. Insight into this point of equal computational cost helps one determine which simulation method will be more efficient for a given quantum circuit. The stochastic contraction method outperforms the line graph based method only when the time to calculate a reasonable tree decomposition is prohibitively expensive. Finally, we release our software package, qTorch (Quantum TensOR Contraction Handler), intended for general quantum circuit simulation.

quant-ph↗

arXiv2018

Quantum Simulation of Electronic Structure with Linear Depth and Connectivity

As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the electronic structure Hamiltonian in exactly $N$ depth and with $N^2/2$ two-qubit entangling gates, and prepare arbitrary Slater determinants in at most $N/2$ depth, all assuming only a minimal, linearly connected architecture. We conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities. These results represent significant practical improvements on the cost of most Trotter based algorithms for both variational and phase estimation based simulation of quantum chemistry.

quant-ph↗

arXiv2017

Bounding the costs of quantum simulation of many-body physics in real space

We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system and using a high-order finite difference approximation to the kinetic energy operator. We find that our algorithm can simulate $η$ interacting particles using a number of calculations of the pairwise interactions that scales, for a fixed spatial grid spacing, as $\tilde{O}(η^2)$, versus the $\tilde{O}(η^5)$ time required by previous methods (assuming the number of orbitals is proportional to $η$), and scales super-polynomially better with the error tolerance than algorithms based on the Lie-Trotter-Suzuki product formula. Finally, we analyze discretization errors that arise from the spatial grid and show that under some circumstances these errors can remove the exponential speedups typically afforded by quantum simulation.

quant-ph↗

arXiv2017

Exponentially More Precise Quantum Simulation of Fermions in the Configuration Interaction Representation

We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New Journal of Physics 18, 033032 (2016)], we employ a recently developed technique for simulating Hamiltonian evolution, using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require $\widetilde{\cal O}(N)$ qubits, where $N$ is the number of single-particle spin-orbitals, the CI matrix representation requires $\widetilde{\cal O}(η)$ qubits where $η\ll N$ is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as $\widetilde{\cal O}(η^2 N^3 t)$.

quant-ph↗

arXiv2015

Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization

We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision, an exponential improvement over all prior methods. The two algorithms developed in this work rely on a second quantized encoding of the wavefunction in which the state of an $N$ spin-orbital system is encoded in ${\cal O}(N)$ qubits. Our first algorithm requires at most $\widetilde{\cal O}(N^8 t)$ gates. Our second algorithm involves on-the-fly computation of molecular integrals, in a way that is exponentially more precise than classical sampling methods, by using the truncated Taylor series simulation technique. Our second algorithm has the lowest gate count of any approach to second quantized quantum chemistry simulation in the literature, scaling as $\widetilde{\cal O}(N^{5} t)$. The approaches presented here are readily applicable to a wide class of fermionic models, many of which are defined by simplified versions of the chemistry Hamiltonian.

quant-ph↗