Resistant and susceptible pea lines harbour different root-rot pathogens and antagonistic fungi

Disease resistance encompasses the mechanisms that allow a plant to withstand or ward off a pathogen. The molecular responses of plants under pathogen attack and the underlying genetics have been extensively studied. However, resistance is not only a trait defined by the warfare between pathogen and host. In fact, resistance is an emergent phenotype of the interactions between the microbial community and the host. Fungal root diseases threaten pea (Pisum sativum L.) cultivation, and therefore a valuable protein source and important crop in low-input farming systems. Resistance in current pea varieties against multiple root pathogens is lacking. In order to acknowledge the rhizosphere microbiome as an integral part of the environment, 261 pea genotypes were screened for resistance on naturally infested field soil in a pot-based experiment. Thereof, eight lines with contrasting disease levels were selected and tested on four soils with different disease pressure in a follow-up pot experiment. Along root rot assessments, pea pathogens (F. solani, F. oxysporum, F. avenaceum, A. euteiches, P. ultimum and D. pinodella) and arbuscular mycorrhizal fungi were quantified in diseased roots using qPCR assays. The amount of fungal DNA detected in the roots differed among the pea genotypes and the four soils and a significant pea genotype x soil interaction was evidenced for several pathogen species. For example, the quantity of F. avenaceum in the roots mostly depends on the soil (two-way ANOVA, p < 0.01) and differs significantly between pea genotypes (p = 0.013). F. oxysporum and F. solani quantities showed significant pea genotype x soil interactions (p < 0.01 for both species). Significant correlations were found between F. avenaceum and F. solani quantity and root rot index (rs = 0.38, p < 0.01 and rs = 0.56, p < 0.01, respectively ). On the other hand, F. oxysporum quantity shows no relationship with root rot (rs = 0.007, p = 0.95). These results suggest differential roles of the microbes in the pea root rot and highlight the importance of incorporating the complexity of the soil microbiome at early stages of resistance screenings and breeding efforts. Resistance breeding against root rot will be challenged by the fact that soil microbes interact with each other and the plant and that their composition varies between different soils. Further insights into plant-microbe interactions and emerging molecular plant breeding tools will fuel future plant breeding

Handling Non-Unitaries in Quantum Circuit Equivalence Checking

Quantum computers are reaching a level where interactions between classical and quantum computations can happen in real-time. This marks the advent of a new, broader class of quantum circuits: dynamic quantum circuits. They offer a broader range of available computing primitives that lead to new challenges for design tasks such as simulation, compilation, and verification. Due to the non-unitary nature of dynamic circuit primitives, most existing techniques and tools for these tasks are no longer applicable in an out-of-the-box fashion. In this work, we discuss the resulting consequences for quantum circuit verification, specifically equivalence checking, and propose two different schemes that eventually allow to treat the involved circuits as if they did not contain non-unitaries at all. As a result, we demonstrate methodically, as well as, experimentally that existing techniques for verifying the equivalence of quantum circuits can be kept applicable for this broader class of circuits.Comment: 7 pages, 4 figures, old title: "Towards Verification of Dynamic Quantum Circuits", revised manuscript, added experimental result

Reducing the Compilation Time of Quantum Circuits Using Pre-Compilation on the Gate Level

In order to implement a quantum computing application, problem instances must be encoded into a quantum circuit and then compiled for a specific platform. The lengthy compilation process is a key bottleneck in this workflow, especially for problems that arise repeatedly with a similar yet distinct structure (each of which requires a new compilation run thus far). In this paper, we aim to overcome this bottleneck by proposing a comprehensive pre-compilation technique that tries to minimize the time spent for compiling recurring problems while preserving the solution quality as much as possible. The following concepts underpin the proposed approach: Beginning with a problem class and a corresponding quantum algorithm, a predictive encoding scheme is applied to encode a representative problem instance into a general-purpose quantum circuit for that problem class. Once the real problem instance is known, the previously constructed circuit only needs to be adjusted -- with (nearly) no compilation necessary. Experimental evaluations on QAOA for the MaxCut problem as well as a case study involving a satellite mission planning problem show that the proposed approach significantly reduces the compilation time by several orders of magnitude compared to Qiskit's compilation schemes while maintaining comparable compiled circuit quality. All implementations are available on GitHub (https://github.com/cda-tum/mqt-problemsolver) as part of the Munich Quantum Toolkit (MQT).Comment: 11 pages, 8 Figures, minor changes, to be published at International Conference on Quantum Computing and Engineering (QCE), 202

Towards Hamiltonian Simulation with Decision Diagrams

This paper proposes a novel approach to Hamiltonian simulation using Decision Diagrams (DDs), which are an exact representation based on exploiting redundancies in representations of quantum states and operations. While the simulation of Hamiltonians has been studied extensively, scaling these simulations to larger or more complex systems is often challenging and may require approximations or new simulation methods altogether. DDs offer such an alternative that has not yet been applied to Hamiltonian simulation. In this work, we investigate the behavior of DDs for this task. To this end, we review the basics of DDs such as their construction and present how the relevant operations for Hamiltonian simulation are implemented in this data structure -- leading to the first DD-based Hamiltonian simulation approach. Based on several series of evaluations and comparisons, we then discuss insights about the performance of this complementary approach. Overall, these studies show that DDs indeed may offer a promising new data structure which, for certain examples, can provide orders of magnitudes of improvement compared to the state-of-the-art, yet also comes with its own, fundamentally different, limitations.Comment: 12 pages, 4 figure

On Optimal Subarchitectures for Quantum Circuit Mapping

Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some device is quantum circuit mapping, where the circuit is transformed such that it complies with the architecture's limited qubit connectivity. Because the search space in quantum circuit mapping grows exponentially in the number of qubits, it is desirable to consider as few of the device's physical qubits as possible in the process. Previous work conjectured that it suffices to consider only subarchitectures of a quantum computer composed of as many qubits as used in the circuit. In this work, we refute this conjecture and establish criteria for judging whether considering larger parts of the architecture might yield better solutions to the mapping problem. We show that determining subarchitectures that are of minimal size, i.e., of which no physical qubit can be removed without losing the optimal mapping solution for some quantum circuit, is a very hard problem. Based on a relaxation of the criteria for optimality, we introduce a relaxed consideration that still maintains optimality for practically relevant quantum circuits. Eventually, this results in two methods for computing near-optimal sets of subarchitectures\unicode{x2014}providing the basis for efficient quantum circuit mapping solutions. We demonstrate the benefits of this novel method for state-of-the-art quantum computers by IBM, Google and Rigetti.Comment: 19 pages, 9 figures, 3 table

Compiler Optimization for Quantum Computing Using Reinforcement Learning

Any quantum computing application, once encoded as a quantum circuit, must be compiled before being executable on a quantum computer. Similar to classical compilation, quantum compilation is a sequential process with many compilation steps and numerous possible optimization passes. Despite the similarities, the development of compilers for quantum computing is still in its infancy-lacking mutual consolidation on the best sequence of passes, compatibility, adaptability, and flexibility. In this work, we take advantage of decades of classical compiler optimization and propose a reinforcement learning framework for developing optimized quantum circuit compilation flows. Through distinct constraints and a unifying interface, the framework supports the combination of techniques from different compilers and optimization tools in a single compilation flow. Experimental evaluations show that the proposed framework-set up with a selection of compilation passes from IBM's Qiskit and Quantinuum's TKET-significantly outperforms both individual compilers in over 70% of cases regarding the expected fidelity. The framework is available on GitHub (https://github.com/cda-tum/MQTPredictor).Comment: 6 pages, 3 figure

Mapping Quantum Circuits to IBM QX Architectures Using the Minimal Number of SWAP and H Operations

The recent progress in the physical realization of quantum computers (the first publicly available ones--IBM's QX architectures--have been launched in 2017) has motivated research on automatic methods that aid users in running quantum circuits on them. Here, certain physical constraints given by the architectures which restrict the allowed interactions of the involved qubits have to be satisfied. Thus far, this has been addressed by inserting SWAP and H operations. However, it remains unknown whether existing methods add a minimum number of SWAP and H operations or, if not, how far they are away from that minimum--an NP-complete problem. In this work, we address this by formulating the mapping task as a symbolic optimization problem that is solved using reasoning engines like Boolean satisfiability solvers. By this, we do not only provide a method that maps quantum circuits to IBM's QX architectures with a minimal number of SWAP and H operations, but also show by experimental evaluation that the number of operations added by IBM's heuristic solution exceeds the lower bound by more than 100% on average. An implementation of the proposed methodology is publicly available at http://iic.jku.at/eda/research/ibm_qx_mapping

Verifying Results of the IBM Qiskit Quantum Circuit Compilation Flow

Realizing a conceptual quantum algorithm on an actual physical device necessitates the algorithm's quantum circuit description to undergo certain transformations in order to adhere to all constraints imposed by the hardware. In this regard, the individual high-level circuit components are first synthesized to the supported low-level gate-set of the quantum computer, before being mapped to the target's architecture---utilizing several optimizations in order to improve the compilation result. Specialized tools for this complex task exist, e.g., IBM's Qiskit, Google's Cirq, Microsoft's QDK, or Rigetti's Forest. However, to date, the circuits resulting from these tools are hardly verified, which is mainly due to the immense complexity of checking if two quantum circuits indeed realize the same functionality. In this paper, we propose an efficient scheme for quantum circuit equivalence checking---specialized for verifying results of the IBM Qiskit quantum circuit compilation flow. To this end, we combine characteristics unique to quantum computing, e.g., its inherent reversibility, and certain knowledge about the compilation flow into a dedicated equivalence checking strategy. Experimental evaluations confirm that the proposed scheme allows to verify even large circuit instances with tens of thousands of operations within seconds or even less, whereas state-of-the-art techniques frequently time-out or require substantially more runtime. A corresponding open source implementation of the proposed method is publicly available at https://github.com/iic-jku/qcec.Comment: 10 pages, to be published at International Conference on Quantum Computing and Engineering (QCE20

Towards an Automated Framework for Realizing Quantum Computing Solutions

Quantum computing is fast evolving as a technology due to recent advances in hardware, software, as well as the development of promising applications. To use this technology for solving specific problems, a suitable quantum algorithm has to be determined, the problem has to be encoded in a form suitable for the chosen algorithm, it has to be executed, and the result has to be decoded. To date, each of these tedious and error-prone steps is conducted in a mostly manual fashion. This creates a high entry barrier for using quantum computing -- especially for users with little to no expertise in that domain. In this work, we envision a framework that aims to lower this entry barrier by allowing users to employ quantum computing solutions in an automatic fashion. To this end, interfaces as similar as possible to classical solvers are provided, while the quantum steps of the workflow are shielded from the user as much as possible by a fully automated backend. To demonstrate the feasibility and usability of such a framework, we provide proof-of-concept implementations for two different classes of problems which are publicly available on GitHub (https://github.com/cda-tum/MQTProblemSolver). By this, this work provides the foundation for a low-threshold approach of realizing quantum computing solutions with no or only moderate expertise in this technology.Comment: 6 pages, 4 figure

Tensor Networks or Decision Diagrams? Guidelines for Classical Quantum Circuit Simulation

Classically simulating quantum circuits is crucial when developing or testing quantum algorithms. Due to the underlying exponential complexity, efficient data structures are key for performing such simulations. To this end, tensor networks and decision diagrams have independently been developed with differing perspectives, terminologies, and backgrounds in mind. Although this left designers with two complementary data structures for quantum circuit simulation, thus far it remains unclear which one is the better choice for a given use case. In this work, we (1) consider how these techniques approach classical quantum circuit simulation, and (2) examine their (dis)similarities with regard to their most applicable abstraction level, the desired simulation output, the impact of the computation order, and the ease of distributing the workload. As a result, we provide guidelines for when to better use tensor networks and when to better use decision diagrams in classical quantum circuit simulation.Comment: 7 pages, 4 figures, comments welcom