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Benoit Valiron - One of the best experts on this subject based on the ideXlab platform.
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Concrete resource analysis of the Quantum linear-system algorithm used to compute the electromagnetic scattering cross section of a 2D target
Quantum Information Processing, 2017Co-Authors: Artur Scherer, Siun-chuon Mau, Scott Alexander, Benoit Valiron, Eric BergAbstract:We provide a detailed estimate for the logical resource requirements of the Quantum linear-system algorithm (Harrow et al. in Phys Rev Lett 103:150502, 2009) including the recently described elaborations and application to computing the electromagnetic scattering cross section of a metallic target (Clader et al. in Phys Rev Lett 110:250504, 2013). Our resource estimates are based on the standard Quantum-circuit model of Quantum computation; they comprise circuit width (related to parallelism), circuit depth (total number of steps), the number of qubits and ancilla qubits employed, and the overall number of elementary Quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set $$\{ X, Y, Z, H, S, T, \text{ CNOT } \}$${X,Y,Z,H,S,T,CNOT}. In order to perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper Quantum Programming language and compiler. Our estimates pertain to the explicit example problem size $$N=332{,}020{,}680$$N=332,020,680 beyond which, according to a crude big-O complexity comparison, the Quantum linear-system algorithm is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy $$\varepsilon =0.01$$ε=0.01 requires an approximate circuit width 340 and circuit depth of order $$10^{25}$$1025 if oracle costs are excluded, and a circuit width and circuit depth of order $$10^8$$108 and $$10^{29}$$1029, respectively, if the resource requirements of oracles are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly (using a fine-grained approach rather than relying on coarse big-O asymptotic approximations) how these impressively large numbers arise with an actual circuit implementation of a Quantum algorithm. While our estimates may prove to be conservative as more efficient advanced Quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the algorithmic-level resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.
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Concrete Resource Analysis of the Quantum Linear System Algorithm used to Compute the Electromagnetic Scattering Cross Section of a 2D Target
Quantum Information Processing, 2017Co-Authors: Artur Scherer, Benoit Valiron, Mau Siun-chuon, D. Scott Alexander, Eric Van Den Berg, Thomas ChapuranAbstract:We provide a detailed estimate for the logical resource requirements of the Quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described generalization [Phys. Rev. Lett. 110, 250504 (2013)]. Our resource estimates are based on the standard Quantum-circuit model of Quantum computation; they comprise circuit width, circuit depth, the number of qubits and ancilla qubits employed, and the overall number of elementary Quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}. To perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper Quantum Programming language and compiler. Our estimates pertain to the example problem size N=332,020,680 beyond which, according to a crude big-O complexity comparison, QLSA is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy 0.01 requires an approximate circuit width 340 and circuit depth of order 10^25 if oracle costs are excluded, and a circuit width and depth of order 10^8 and 10^29, respectively, if oracle costs are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly how these impressively large numbers arise with an actual circuit implementation of a Quantum algorithm. While our estimates may prove to be conservative as more efficient advanced Quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.
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The Geometry of Parallelism: Classical, Probabilistic, and Quantum Effects
2017Co-Authors: Ugo Dal Lago, Benoit Valiron, Claudia Faggian, Akira YoshimizuAbstract:We introduce a Geometry of Interaction model for higher-order Quantum computation, and prove its adequacy for a full Quantum Programming language in which entanglement, duplication, and recursion are all available. Our model comes with a multi-token machine, a proof net system, and a PCF-style language. The approach we develop is not specific to Quantum computation, and our model is an instance of a new framework whose main feature is the ability to model commutative effects in a parallel setting. Being based on a multi-token machine equipped with a memory, it has a concrete nature which makes it well suited for building low-level operational descriptions of higher-order languages.
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the geometry of parallelism classical probabilistic and Quantum effects
Symposium on Principles of Programming Languages, 2017Co-Authors: Ugo Dal Lago, Benoit Valiron, Claudia Faggian, Akira YoshimizuAbstract:We introduce a Geometry of Interaction model for higher-order Quantum computation, and prove its adequacy for a fully fledged Quantum Programming language in which entanglement, duplication, and recursion are all available. This model is an instance of a new framework which captures not only Quantum but also classical and probabilistic computation. Its main feature is the ability to model commutative effects in a parallel setting. Our model comes with a multi-token machine, a proof net system, and a -style language. Being based on a multi-token machine equipped with a memory, it has a concrete nature which makes it well suited for building low-level operational descriptions of higher-order languages.
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applying quantitative semantics to higher order Quantum computing
arXiv: Logic in Computer Science, 2013Co-Authors: Michele Pagani, Peter Selinger, Benoit ValironAbstract:Finding a denotational semantics for higher order Quantum computation is a long-standing problem in the semantics of Quantum Programming languages. Most past approaches to this problem fell short in one way or another, either limiting the language to an unusably small finitary fragment, or giving up important features of Quantum physics such as entanglement. In this paper, we propose a denotational semantics for a Quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic.
Mingsheng Ying - One of the best experts on this subject based on the ideXlab platform.
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Reasoning about Parallel Quantum Programs.
arXiv: Logic in Computer Science, 2018Co-Authors: Mingsheng Ying, Yangjia LiAbstract:We initiate the study of parallel Quantum Programming by defining the operational and denotational semantics of parallel Quantum programs. The technical contributions of this paper include: (1) find a series of useful proof rules for reasoning about correctness of parallel Quantum programs; and (2) prove a strong soundness theorem of these proof rules showing that partial correctness is well maintained at each step of transitions in the operational semantics of a parallel Quantum program. This is achieved by partially overcoming the following conceptual challenges that are never present in classical parallel Programming: (i) the intertwining of nondeterminism caused by Quantum measurements and introduced by parallelism; (ii) entanglement between component Quantum programs; and (iii) combining Quantum predicates in the overlap of state Hilbert spaces of component Quantum programs with shared variables. It seems that a full solution to these challenges and developing a (relatively) complete proof system for parallel Quantum programs are still far beyond the current reach.
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q si rangle a Quantum Programming environment
arXiv: Quantum Physics, 2017Co-Authors: Shusen Liu, Mingsheng Ying, Xin Wang, Li Zhou, Ji Guan, Runyao DuanAbstract:This paper describes a Quantum Programming environment, named $Q|SI\rangle$. It is a platform embedded in the .Net language that supports Quantum Programming using a Quantum extension of the $\mathbf{while}$-language. The framework of the platform includes a compiler of the Quantum $\mathbf{while}$-language and a suite of tools for simulating Quantum computation, optimizing Quantum circuits, and analyzing and verifying Quantum programs. Throughout the paper, using $Q|SI\rangle$ to simulate Quantum behaviors on classical platforms with a combination of components is demonstrated. The scalable framework allows the user to program customized functions on the platform. The compiler works as the core of $Q|SI\rangle$ bridging the gap from Quantum hardware to Quantum software. The built-in decomposition algorithms enable the universal Quantum computation on the present Quantum hardware.
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q si rangle a Quantum Programming environment
SCIENTIA SINICA Informationis, 2017Co-Authors: Shusen Liu, Mingsheng Ying, Xin Wang, Li Zhou, Ji Guan, Runyao DuanAbstract:This paper describes a Quantum Programming environment called $Q|SI\rangle $ . It is a platform created in the .NET language to support Quantum Programming as a Quantum extension of the $\mathbf{while}$-language. This platform includes a compiler for the Quantum $\mathbf{while}$-language and a chain of tools for the simulation of Quantum computations, optimization of Quantum circuits, and analysis and verification of Quantum programs. Throughout the paper, $Q|SI\rangle $ is used to simulate Quantum behaviors on classical platforms and demonstrate the combination of components. The scalable framework allows users to program customized functions on the platform. The compiler works as the core of $Q|SI\rangle $ , bridging the gap between Quantum hardware and Quantum software. The built-in decomposition algorithms enable universal Quantum computation on current Quantum hardware.
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foundations of Quantum Programming
2016Co-Authors: Mingsheng YingAbstract:Foundations of Quantum Programming discusses how new Programming methodologies and technologies developed for current computers can be extended to exploit the unique power of Quantum computers, which promise dramatic advantages in processing speed over currently available computer systems. Governments and industries around the globe are now investing vast amounts of money with the expectation of building practical Quantum computers. Drawing upon years of experience and research in Quantum computing research and using numerous examples and illustrations, Mingsheng Ying has created a very useful reference on Quantum Programming languages and important tools and techniques required for Quantum Programming, making the book a valuable resource for academics, researchers, and developers. Demystifies the theory of Quantum Programming using a step-by-step approach Covers the interdisciplinary nature of Quantum Programming by providing examples from many different fields including, engineering, computer science, medicine, and life sciences Includes techniques and tools to solve complex control flow patterns and synchronize computations Presents a coherent and self-contained treatment that will be valuable for academics and industrial researchers and developers
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Quantum Recursion and Second Quantisation
arXiv: Quantum Physics, 2014Co-Authors: Mingsheng YingAbstract:This paper introduces a new notion of Quantum recursion of which the control flow of the computation is Quantum rather than classical as in the notions of recursion considered in the previous studies of Quantum Programming. A typical example is recursive Quantum walks, which are obtained by slightly modifying the construction of the ordinary Quantum walks. The operational and denotational semantics of Quantum recursions are defined by employing the second quantisation method, and they are proved to be equivalent.
Peter Selinger - One of the best experts on this subject based on the ideXlab platform.
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linear dependent type theory for Quantum Programming languages
arXiv: Programming Languages, 2020Co-Authors: Kohei Kishida, Peter SelingerAbstract:Modern Quantum Programming languages integrate Quantum resources and classical control. They must, on the one hand, be linearly typed to reflect the no-cloning property of Quantum resources. On the other hand, high-level and practical languages should also support Quantum circuits as first-class citizens, as well as families of circuits that are indexed by some classical parameters. Quantum Programming languages thus need linear dependent type theory. This paper defines a general semantic structure for such a type theory via certain fibrations of monoidal categories. The categorical model of the Quantum circuit description language Proto-Quipper-M by Rios and Selinger (2017) constitutes an example of such a fibration, which means that the language can readily be integrated with dependent types. We then devise both a general linear dependent type system and a dependently typed extension of Proto-Quipper-M, and provide them with operational semantics as well as a prototype implementation.
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Quantum Programming languages dagstuhl seminar 18381
Dagstuhl Reports, 2019Co-Authors: Michele Mosca, Martin Roetteler, Peter SelingerAbstract:This report documents the program and the outcomes of Dagstuhl Seminar 18381 "Quantum Programming Languages", which brought together researchers from Quantum computing and classical Programming languages.
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applying quantitative semantics to higher order Quantum computing
arXiv: Logic in Computer Science, 2013Co-Authors: Michele Pagani, Peter Selinger, Benoit ValironAbstract:Finding a denotational semantics for higher order Quantum computation is a long-standing problem in the semantics of Quantum Programming languages. Most past approaches to this problem fell short in one way or another, either limiting the language to an unusably small finitary fragment, or giving up important features of Quantum physics such as entanglement. In this paper, we propose a denotational semantics for a Quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic.
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an introduction to Quantum Programming in quipper
Reversible Computation, 2013Co-Authors: Alexander S Green, Peter Selinger, Peter Lefanu Lumsdaine, Neil J Ross, Benoit ValironAbstract:Quipper is a recently developed Programming language for expressing Quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quipper's language features by developing a few well known examples of Quantum computation, including Quantum teleportation, the Quantum Fourier transform, and a Quantum circuit for addition.
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quipper a scalable Quantum Programming language
arXiv: Programming Languages, 2013Co-Authors: Alexander S Green, Peter Selinger, Peter Lefanu Lumsdaine, Neil J Ross, Benoit ValironAbstract:The field of Quantum algorithms is vibrant. Still, there is currently a lack of Programming languages for describing Quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order Quantum Programming language. Quipper has been used to program a diverse set of non-trivial Quantum algorithms, and can generate Quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a Quantum device, but is not dependent on any particular model of Quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze Quantum algorithms.
Artur Scherer - One of the best experts on this subject based on the ideXlab platform.
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Concrete resource analysis of the Quantum linear-system algorithm used to compute the electromagnetic scattering cross section of a 2D target
Quantum Information Processing, 2017Co-Authors: Artur Scherer, Siun-chuon Mau, Scott Alexander, Benoit Valiron, Eric BergAbstract:We provide a detailed estimate for the logical resource requirements of the Quantum linear-system algorithm (Harrow et al. in Phys Rev Lett 103:150502, 2009) including the recently described elaborations and application to computing the electromagnetic scattering cross section of a metallic target (Clader et al. in Phys Rev Lett 110:250504, 2013). Our resource estimates are based on the standard Quantum-circuit model of Quantum computation; they comprise circuit width (related to parallelism), circuit depth (total number of steps), the number of qubits and ancilla qubits employed, and the overall number of elementary Quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set $$\{ X, Y, Z, H, S, T, \text{ CNOT } \}$${X,Y,Z,H,S,T,CNOT}. In order to perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper Quantum Programming language and compiler. Our estimates pertain to the explicit example problem size $$N=332{,}020{,}680$$N=332,020,680 beyond which, according to a crude big-O complexity comparison, the Quantum linear-system algorithm is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy $$\varepsilon =0.01$$ε=0.01 requires an approximate circuit width 340 and circuit depth of order $$10^{25}$$1025 if oracle costs are excluded, and a circuit width and circuit depth of order $$10^8$$108 and $$10^{29}$$1029, respectively, if the resource requirements of oracles are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly (using a fine-grained approach rather than relying on coarse big-O asymptotic approximations) how these impressively large numbers arise with an actual circuit implementation of a Quantum algorithm. While our estimates may prove to be conservative as more efficient advanced Quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the algorithmic-level resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.
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Concrete Resource Analysis of the Quantum Linear System Algorithm used to Compute the Electromagnetic Scattering Cross Section of a 2D Target
Quantum Information Processing, 2017Co-Authors: Artur Scherer, Benoit Valiron, Mau Siun-chuon, D. Scott Alexander, Eric Van Den Berg, Thomas ChapuranAbstract:We provide a detailed estimate for the logical resource requirements of the Quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described generalization [Phys. Rev. Lett. 110, 250504 (2013)]. Our resource estimates are based on the standard Quantum-circuit model of Quantum computation; they comprise circuit width, circuit depth, the number of qubits and ancilla qubits employed, and the overall number of elementary Quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}. To perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper Quantum Programming language and compiler. Our estimates pertain to the example problem size N=332,020,680 beyond which, according to a crude big-O complexity comparison, QLSA is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy 0.01 requires an approximate circuit width 340 and circuit depth of order 10^25 if oracle costs are excluded, and a circuit width and depth of order 10^8 and 10^29, respectively, if oracle costs are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly how these impressively large numbers arise with an actual circuit implementation of a Quantum algorithm. While our estimates may prove to be conservative as more efficient advanced Quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.
Eric Berg - One of the best experts on this subject based on the ideXlab platform.
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Concrete resource analysis of the Quantum linear-system algorithm used to compute the electromagnetic scattering cross section of a 2D target
Quantum Information Processing, 2017Co-Authors: Artur Scherer, Siun-chuon Mau, Scott Alexander, Benoit Valiron, Eric BergAbstract:We provide a detailed estimate for the logical resource requirements of the Quantum linear-system algorithm (Harrow et al. in Phys Rev Lett 103:150502, 2009) including the recently described elaborations and application to computing the electromagnetic scattering cross section of a metallic target (Clader et al. in Phys Rev Lett 110:250504, 2013). Our resource estimates are based on the standard Quantum-circuit model of Quantum computation; they comprise circuit width (related to parallelism), circuit depth (total number of steps), the number of qubits and ancilla qubits employed, and the overall number of elementary Quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set $$\{ X, Y, Z, H, S, T, \text{ CNOT } \}$${X,Y,Z,H,S,T,CNOT}. In order to perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper Quantum Programming language and compiler. Our estimates pertain to the explicit example problem size $$N=332{,}020{,}680$$N=332,020,680 beyond which, according to a crude big-O complexity comparison, the Quantum linear-system algorithm is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy $$\varepsilon =0.01$$ε=0.01 requires an approximate circuit width 340 and circuit depth of order $$10^{25}$$1025 if oracle costs are excluded, and a circuit width and circuit depth of order $$10^8$$108 and $$10^{29}$$1029, respectively, if the resource requirements of oracles are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly (using a fine-grained approach rather than relying on coarse big-O asymptotic approximations) how these impressively large numbers arise with an actual circuit implementation of a Quantum algorithm. While our estimates may prove to be conservative as more efficient advanced Quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the algorithmic-level resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.