We introduce qprof, a new and extensible quantum program profiler able to generate profiling reports of quantum circuits written using various quantum computing frameworks. We describe the internal structure and working of qprof and provide practical examples on quantum circuits with increasing complexity along with benchmarks of the tool execution time on large circuits. This tool will allow researchers to visualise their quantum algorithm implementation in a different and complementary way and reliably localise the bottlenecks for efficient code optimisation.
{"title":"qprof: A gprof-Inspired Quantum Profiler","authors":"Adrien Suau, G. Staffelbach, A. Todri-Sanial","doi":"10.1145/3529398","DOIUrl":"https://doi.org/10.1145/3529398","url":null,"abstract":"We introduce qprof, a new and extensible quantum program profiler able to generate profiling reports of quantum circuits written using various quantum computing frameworks. We describe the internal structure and working of qprof and provide practical examples on quantum circuits with increasing complexity along with benchmarks of the tool execution time on large circuits. This tool will allow researchers to visualise their quantum algorithm implementation in a different and complementary way and reliably localise the bottlenecks for efficient code optimisation.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127542101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited 2-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on synthetic data and different hardware topologies indicate that the error rate and depth can be optimized simultaneously without significant loss. We test our algorithm on a large number of quantum volume circuits, optimizing for error rate and depth; our algorithm significantly reduces the number of CNOTs compared to Qiskit’s default transpiler SABRE [19] and produces circuits that, when executed on hardware, exhibit higher fidelity.
{"title":"Optimal Qubit Assignment and Routing via Integer Programming","authors":"G. Nannicini, L. Bishop, O. Günlük, P. Jurcevic","doi":"10.1145/3544563","DOIUrl":"https://doi.org/10.1145/3544563","url":null,"abstract":"We consider the problem of mapping a logical quantum circuit onto a given hardware with limited 2-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on synthetic data and different hardware topologies indicate that the error rate and depth can be optimized simultaneously without significant loss. We test our algorithm on a large number of quantum volume circuits, optimizing for error rate and depth; our algorithm significantly reduces the number of CNOTs compared to Qiskit’s default transpiler SABRE [19] and produces circuits that, when executed on hardware, exhibit higher fidelity.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134320943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the problem in the CNOT+rotation gate set from a mathematical programming standpoint, offering contributions both in terms of understanding the mathematics of the problem and its efficient solution. Among the results that we present, we are able to derive a 14-CNOT 4-qubit Toffoli decomposition from scratch, and show that the Quantum Shannon Decomposition can be compressed by a factor of two without practical loss of fidelity.
{"title":"Best Approximate Quantum Compiling Problems","authors":"Liam Madden, Andrea Simonetto","doi":"10.1145/3505181","DOIUrl":"https://doi.org/10.1145/3505181","url":null,"abstract":"We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the problem in the CNOT+rotation gate set from a mathematical programming standpoint, offering contributions both in terms of understanding the mathematics of the problem and its efficient solution. Among the results that we present, we are able to derive a 14-CNOT 4-qubit Toffoli decomposition from scratch, and show that the Quantum Shannon Decomposition can be compressed by a factor of two without practical loss of fidelity.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116137458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ArQTiC is an open-source, full-stack software package built for the simulations of materials on quantum computers. It currently can simulate materials that can be modeled by any Hamiltonian derived from a generic, one-dimensional, time-dependent Heisenberg Hamiltonian. ArQTiC includes modules for generating quantum programs for real- and imaginary-time evolution, quantum circuit optimization, connection to various quantum backends via the cloud, and post-processing of quantum results. By enabling users to seamlessly design, execute, and analyze materials simulations on quantum computers, ArQTiC opens this field to a broader community of scientists from a wider range of scientific domains.
{"title":"ArQTiC: A Full-stack Software Package for Simulating Materials on Quantum Computers","authors":"Lindsay Bassman, Connor Powers, W. D. de Jong","doi":"10.1145/3511715","DOIUrl":"https://doi.org/10.1145/3511715","url":null,"abstract":"ArQTiC is an open-source, full-stack software package built for the simulations of materials on quantum computers. It currently can simulate materials that can be modeled by any Hamiltonian derived from a generic, one-dimensional, time-dependent Heisenberg Hamiltonian. ArQTiC includes modules for generating quantum programs for real- and imaginary-time evolution, quantum circuit optimization, connection to various quantum backends via the cloud, and post-processing of quantum results. By enabling users to seamlessly design, execute, and analyze materials simulations on quantum computers, ArQTiC opens this field to a broader community of scientists from a wider range of scientific domains.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123872643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article introduces PyMatching, a fast open-source Python package for decoding quantum error-correcting codes with the minimum-weight perfect matching (MWPM) algorithm. PyMatching includes the standard MWPM decoder as well as a variant, which we call local matching, that restricts each syndrome defect to be matched to another defect within a local neighborhood. The decoding performance of local matching is almost identical to that of the standard MWPM decoder in practice, while reducing the computational complexity. We benchmark the performance of PyMatching, showing that local matching is several orders of magnitude faster than implementations of the full MWPM algorithm using NetworkX or Blossom V for problem sizes typically considered in error correction simulations. PyMatching and its dependencies are open-source, and it can be used to decode any quantum code for which syndrome defects come in pairs using a simple Python interface. PyMatching supports the use of weighted edges, hook errors, boundaries and measurement errors, enabling fast decoding, and simulation of fault-tolerant quantum computing.
{"title":"PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching","authors":"Oscar Higgott","doi":"10.1145/3505637","DOIUrl":"https://doi.org/10.1145/3505637","url":null,"abstract":"This article introduces PyMatching, a fast open-source Python package for decoding quantum error-correcting codes with the minimum-weight perfect matching (MWPM) algorithm. PyMatching includes the standard MWPM decoder as well as a variant, which we call local matching, that restricts each syndrome defect to be matched to another defect within a local neighborhood. The decoding performance of local matching is almost identical to that of the standard MWPM decoder in practice, while reducing the computational complexity. We benchmark the performance of PyMatching, showing that local matching is several orders of magnitude faster than implementations of the full MWPM algorithm using NetworkX or Blossom V for problem sizes typically considered in error correction simulations. PyMatching and its dependencies are open-source, and it can be used to decode any quantum code for which syndrome defects come in pairs using a simple Python interface. PyMatching supports the use of weighted edges, hook errors, boundaries and measurement errors, enabling fast decoding, and simulation of fault-tolerant quantum computing.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122735646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity O(√ GT where T is the query complexity of the classical algorithm (depth of the decision tree) and G is the maximum number of wrong answers by the guessing algorithm [3, 14]. In this article, we show that, given some constraints on the classical algorithms, this quantum algorithm can be implemented in time Õ(√ GT). Our algorithm is based on non-binary span programs and their efficient implementation. We conclude that various graph-theoretic problems including bipartiteness, cycle detection, and topological sort can be solved in time O(n3/2log2n) and with O(n3/2) quantum queries. Moreover, finding a maximal matching can be solved with O(n3/2) quantum queries in time O(n3/2log2n), and maximum bipartite matching can be solved in time O(n2log2n).
{"title":"Time- and Query-optimal Quantum Algorithms Based on Decision Trees","authors":"Salman Beigi, Leila Taghavi, Artin Tajdini","doi":"10.1145/3519269","DOIUrl":"https://doi.org/10.1145/3519269","url":null,"abstract":"It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity O(√ GT where T is the query complexity of the classical algorithm (depth of the decision tree) and G is the maximum number of wrong answers by the guessing algorithm [3, 14]. In this article, we show that, given some constraints on the classical algorithms, this quantum algorithm can be implemented in time Õ(√ GT). Our algorithm is based on non-binary span programs and their efficient implementation. We conclude that various graph-theoretic problems including bipartiteness, cycle detection, and topological sort can be solved in time O(n3/2log2n) and with O(n3/2) quantum queries. Moreover, finding a maximal matching can be solved with O(n3/2) quantum queries in time O(n3/2log2n), and maximum bipartite matching can be solved in time O(n2log2n).","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131670489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Python is a popular programming language known for its flexibility, usability, readability, and focus on developer productivity. The quantum software community has adopted Python on a number of large-scale efforts due to these characteristics, as well as the remote nature of near-term quantum processors. The use of Python has enabled quick prototyping for quantum code that directly benefits pertinent research and development efforts in quantum scientific computing. However, this rapid prototyping ability comes at the cost of future performant integration for tightly coupled CPU-QPU architectures with fast-feedback. Here, we present a language extension to Python that enables heterogeneous quantum-classical computing via a robust C++ infrastructure for quantum just-in-time (QJIT) compilation. Our work builds off the QCOR C++ language extension and compiler infrastructure to enable a single-source, quantum hardware-agnostic approach to quantum-classical computing that retains the performance required for tightly coupled CPU-QPU compute models. We detail this Python extension, its programming model and underlying software architecture, and provide a robust set of examples to demonstrate the utility of our approach.
{"title":"Extending Python for Quantum-classical Computing via Quantum Just-in-time Compilation","authors":"Thien Nguyen, A. McCaskey","doi":"10.1145/3544496","DOIUrl":"https://doi.org/10.1145/3544496","url":null,"abstract":"Python is a popular programming language known for its flexibility, usability, readability, and focus on developer productivity. The quantum software community has adopted Python on a number of large-scale efforts due to these characteristics, as well as the remote nature of near-term quantum processors. The use of Python has enabled quick prototyping for quantum code that directly benefits pertinent research and development efforts in quantum scientific computing. However, this rapid prototyping ability comes at the cost of future performant integration for tightly coupled CPU-QPU architectures with fast-feedback. Here, we present a language extension to Python that enables heterogeneous quantum-classical computing via a robust C++ infrastructure for quantum just-in-time (QJIT) compilation. Our work builds off the QCOR C++ language extension and compiler infrastructure to enable a single-source, quantum hardware-agnostic approach to quantum-classical computing that retains the performance required for tightly coupled CPU-QPU compute models. We detail this Python extension, its programming model and underlying software architecture, and provide a robust set of examples to demonstrate the utility of our approach.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125646669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to special structure in the algorithm or even in the underlying problem. We thus introduce a new simulation method that exploits this sparsity to reduce memory usage and simulation runtime. Moreover, our prototype implementation includes optimizations such as gate (re)scheduling, which amortizes data structure accesses and reduces memory usage. To benchmark our implementation, we run quantum algorithms for factoring, for computing integer and elliptic curve discrete logarithms, and for chemistry. Our simulator successfully runs a factoring instance of a 20-bit number using 102 qubits, and elliptic curve discrete logarithm over a 10-bit curve with 110 qubits. While previous work needed a supercomputer to simulate such instances of factoring, our approach succeeds in less than four minutes using a single core and less than 100 MB of memory. To the best of our knowledge, we are the first to fully simulate a quantum algorithm to compute elliptic curve discrete logarithms.
{"title":"Leveraging State Sparsity for More Efficient Quantum Simulations","authors":"Samuel Jaques, Thomas Häner","doi":"10.1145/3491248","DOIUrl":"https://doi.org/10.1145/3491248","url":null,"abstract":"High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to special structure in the algorithm or even in the underlying problem. We thus introduce a new simulation method that exploits this sparsity to reduce memory usage and simulation runtime. Moreover, our prototype implementation includes optimizations such as gate (re)scheduling, which amortizes data structure accesses and reduces memory usage. To benchmark our implementation, we run quantum algorithms for factoring, for computing integer and elliptic curve discrete logarithms, and for chemistry. Our simulator successfully runs a factoring instance of a 20-bit number using 102 qubits, and elliptic curve discrete logarithm over a 10-bit curve with 110 qubits. While previous work needed a supercomputer to simulate such instances of factoring, our approach succeeds in less than four minutes using a single core and less than 100 MB of memory. To the best of our knowledge, we are the first to fully simulate a quantum algorithm to compute elliptic curve discrete logarithms.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133913457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As quantum computing hardware systems continue to advance, the research and development of performant, scalable, and extensible software architectures, languages, models, and compilers is equally as important to bring this novel coprocessing capability to a diverse group of domain computational scientists. For the field of quantum chemistry, applications and frameworks exist for modeling and simulation tasks that scale on heterogeneous classical architectures, and we envision the need for similar frameworks on heterogeneous quantum-classical platforms. Here, we present the XACC system-level quantum computing framework as a platform for prototyping, developing, and deploying quantum-classical software that specifically targets chemistry applications. We review the fundamental design features in XACC, with special attention to its extensibility and modularity for key quantum programming workflow interfaces and provide an overview of the interfaces most relevant to simulations of chemistry. A series of examples demonstrating some of the state-of-the-art chemistry algorithms currently implemented in XACC are presented, while also illustrating the various APIs that would enable the community to extend, modify, and devise new algorithms and applications in the realm of chemistry.
{"title":"A Backend-agnostic, Quantum-classical Framework for Simulations of Chemistry in C++","authors":"D. Claudino, A. McCaskey, Dmitry I. Lyakh","doi":"10.1145/3523285","DOIUrl":"https://doi.org/10.1145/3523285","url":null,"abstract":"As quantum computing hardware systems continue to advance, the research and development of performant, scalable, and extensible software architectures, languages, models, and compilers is equally as important to bring this novel coprocessing capability to a diverse group of domain computational scientists. For the field of quantum chemistry, applications and frameworks exist for modeling and simulation tasks that scale on heterogeneous classical architectures, and we envision the need for similar frameworks on heterogeneous quantum-classical platforms. Here, we present the XACC system-level quantum computing framework as a platform for prototyping, developing, and deploying quantum-classical software that specifically targets chemistry applications. We review the fundamental design features in XACC, with special attention to its extensibility and modularity for key quantum programming workflow interfaces and provide an overview of the interfaces most relevant to simulations of chemistry. A series of examples demonstrating some of the state-of-the-art chemistry algorithms currently implemented in XACC are presented, while also illustrating the various APIs that would enable the community to extend, modify, and devise new algorithms and applications in the realm of chemistry.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121416795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrew W. Cross, Ali Javadi-Abhari, Thomas Alexander, N. de Beaudrap, L. Bishop, S. Heidel, C. Ryan, P. Sivarajah, J. Smolin, J. Gambetta, Blake R. Johnson
Quantum assembly languages are machine-independent languages that traditionally describe quantum computation in the circuit model. Open quantum assembly language (OpenQASM 2) was proposed as an imperative programming language for quantum circuits based on earlier QASM dialects. In principle, any quantum computation could be described using OpenQASM 2, but there is a need to describe a broader set of circuits beyond the language of qubits and gates. By examining interactive use cases, we recognize two different timescales of quantum-classical interactions: real-time classical computations that must be performed within the coherence times of the qubits, and near-time computations with less stringent timing. Since the near-time domain is adequately described by existing programming frameworks, we choose in OpenQASM 3 to focus on the real-time domain, which must be more tightly coupled to the execution of quantum operations. We add support for arbitrary control flow as well as calling external classical functions. In addition, we recognize the need to describe circuits at multiple levels of specificity, and therefore we extend the language to include timing, pulse control, and gate modifiers. These new language features create a multi-level intermediate representation for circuit development and optimization, as well as control sequence implementation for calibration, characterization, and error mitigation.
{"title":"OpenQASM 3: A Broader and Deeper Quantum Assembly Language","authors":"Andrew W. Cross, Ali Javadi-Abhari, Thomas Alexander, N. de Beaudrap, L. Bishop, S. Heidel, C. Ryan, P. Sivarajah, J. Smolin, J. Gambetta, Blake R. Johnson","doi":"10.1145/3505636","DOIUrl":"https://doi.org/10.1145/3505636","url":null,"abstract":"Quantum assembly languages are machine-independent languages that traditionally describe quantum computation in the circuit model. Open quantum assembly language (OpenQASM 2) was proposed as an imperative programming language for quantum circuits based on earlier QASM dialects. In principle, any quantum computation could be described using OpenQASM 2, but there is a need to describe a broader set of circuits beyond the language of qubits and gates. By examining interactive use cases, we recognize two different timescales of quantum-classical interactions: real-time classical computations that must be performed within the coherence times of the qubits, and near-time computations with less stringent timing. Since the near-time domain is adequately described by existing programming frameworks, we choose in OpenQASM 3 to focus on the real-time domain, which must be more tightly coupled to the execution of quantum operations. We add support for arbitrary control flow as well as calling external classical functions. In addition, we recognize the need to describe circuits at multiple levels of specificity, and therefore we extend the language to include timing, pulse control, and gate modifiers. These new language features create a multi-level intermediate representation for circuit development and optimization, as well as control sequence implementation for calibration, characterization, and error mitigation.","PeriodicalId":365166,"journal":{"name":"ACM Transactions on Quantum Computing","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128739302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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