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.Comment: 21 pages, 8 figure

Tackling Unbounded State Spaces in Continuing Task Reinforcement Learning

While deep reinforcement learning (RL) algorithms have been successfully applied to many tasks, their inability to extrapolate and strong reliance on episodic resets inhibits their applicability to many real-world settings. For instance, in stochastic queueing problems, the state space can be unbounded and the agent may have to learn online without the system ever being reset to states the agent has seen before. In such settings, we show that deep RL agents can diverge into unseen states from which they can never recover due to the lack of resets, especially in highly stochastic environments. Towards overcoming this divergence, we introduce a Lyapunov-inspired reward shaping approach that encourages the agent to first learn to be stable (i.e. to achieve bounded cost) and then to learn to be optimal. We theoretically show that our reward shaping technique reduces the rate of divergence of the agent and empirically find that it prevents it. We further combine our reward shaping approach with a weight annealing scheme that gradually introduces optimality and log-transform of state inputs, and find that these techniques enable deep RL algorithms to learn high performing policies when learning online in unbounded state space domains

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Quantum algorithm and circuit design solving the Poisson equation

The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error \varepsilon. We assume we are given a supersposition of function evaluations of the right hand side of the Poisson equation. The algorithm produces a quantum state encoding the solution. The number of quantum operations and the number of qubits used by the circuit is almost linear in d and polylog in \varepsilon^{-1}. We present quantum circuit modules together with performance guarantees which can be also used for other problems.Comment: 30 pages, 9 figures. This is the revised version for publication in New Journal of Physic

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.Comment: 22 page

Use of a mixed tissue RNA design for performance assessments on multiple microarray formats

The comparability and reliability of data generated using microarray technology would be enhanced by use of a common set of standards that allow accuracy, reproducibility and dynamic range assessments on multiple formats. We designed and tested a complex biological reagent for performance measurements on three commercial oligonucleotide array formats that differ in probe design and signal measurement methodology. The reagent is a set of two mixtures with different proportions of RNA for each of four rat tissues (brain, liver, kidney and testes). The design provides four known ratio measurements of >200 reference probes, which were chosen for their tissue-selectivity, dynamic range coverage and alignment to the same exemplar transcript sequence across all three platforms. The data generated from testing three biological replicates of the reagent at eight laboratories on three array formats provides a benchmark set for both laboratory and data processing performance assessments. Close agreement with target ratios adjusted for sample complexity was achieved on all platforms and low variance was observed among platforms, replicates and sites. The mixed tissue design produces a reagent with known gene expression changes within a complex sample and can serve as a paradigm for performance standards for microarrays that target other species

The molecular portraits of breast tumors are conserved acress microarray platforms

Background Validation of a novel gene expression signature in independent data sets is a critical step in the development of a clinically useful test for cancer patient risk-stratification. However, validation is often unconvincing because the size of the test set is typically small. To overcome this problem we used publicly available breast cancer gene expression data sets and a novel approach to data fusion, in order to validate a new breast tumor intrinsic list. Results A 105-tumor training set containing 26 sample pairs was used to derive a new breast tumor intrinsic gene list. This intrinsic list contained 1300 genes and a proliferation signature that was not present in previous breast intrinsic gene sets. We tested this list as a survival predictor on a data set of 311 tumors compiled from three independent microarray studies that were fused into a single data set using Distance Weighted Discrimination. When the new intrinsic gene set was used to hierarchically cluster this combined test set, tumors were grouped into LumA, LumB, Basal-like, HER2+/ER-, and Normal Breast-like tumor subtypes that we demonstrated in previous datasets. These subtypes were associated with significant differences in Relapse-Free and Overall Survival. Multivariate Cox analysis of the combined test set showed that the intrinsic subtype classifications added significant prognostic information that was independent of standard clinical predictors. From the combined test set, we developed an objective and unchanging classifier based upon five intrinsic subtype mean expression profiles (i.e. centroids), which is designed for single sample predictions (SSP). The SSP approach was applied to two additional independent data sets and consistently predicted survival in both systemically treated and untreated patient groups. Conclusion This study validates the breast tumor intrinsic subtype classification as an objective means of tumor classification that should be translated into a clinical assay for further retrospective and prospective validation. In addition, our method of combining existing data sets can be used to robustly validate the potential clinical value of any new gene expression profile