Quantum Algorithms

Mosca, Michele

doi:10.1007/978-1-4614-1800-9_144

Cited by 32 publications

(35 citation statements)

References 111 publications

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“…Promising quantum algorithms now exist for a range of problems such as factorization, searching, order and period finding, eigenvalue estimation, phase estimation and discrete logarithms [32]. We study eight quantum benchmarks of significant scale.…”

Section: Benchmarksmentioning

confidence: 99%

Compiler Management of Communication and Parallelism for Quantum Computation

Heckey

Patil

Javadi-Abhari

et al. 2015

Proceedings of the Twentieth International Conference on Architectural Support for Programming Languages and Operating Systems

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Quantum computing (QC) offers huge promise to accelerate a range of computationally intensive benchmarks. Quantum computing is limited, however, by the challenges of decoherence: i.e., a quantum state can only be maintained for short windows of time before it decoheres. While quantum error correction codes can protect against decoherence, fast execution time is the best defense against decoherence, so efficient architectures and effective scheduling algorithms are necessary. This paper proposes the Multi-SIMD QC architecture and then proposes and evaluates effective schedulers to map benchmark descriptions onto Multi-SIMD architectures. The Multi-SIMD model consists of a small number of SIMD regions, each of which may support operations on up to thousands of qubits per cycle.Efficient Multi-SIMD operation requires efficient scheduling. This work develops schedulers to reduce communication requirements of qubits between operating regions, while also improving parallelism.We find that communication to global memory is a dominant cost in QC. We also note that many quantum benchmarks have long serial operation paths (although each operation may be data parallel). To exploit this characteristic, we introduce LongestPath-First Scheduling (LPFS) which pins operations to SIMD regions to keep data in-place and reduce communication to memory.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. ASPLOS '15, March 14-18, 2015, Istanbul, Turkey. Copyright c 2015 ACM 978-1-4503-2835-7/15/03. . . $15.00. http://dx.doi.org/10.1145 The use of small, local scratchpad memories also further reduces communication. Our results show a 3% to 308% improvement for LPFS over conventional scheduling algorithms, and an additional 3% to 64% improvement using scratchpad memories. Our work is the most comprehensive software-to-quantum toolflow published to date, with efficient and practical scheduling techniques that reduce communication and increase parallelism for full-scale quantum code executing up to a trillion quantum gate operations.

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Section: Benchmarksmentioning

confidence: 99%

Compiler Management of Communication and Parallelism for Quantum Computation

Heckey

Patil

Javadi-Abhari

et al. 2015

Proceedings of the Twentieth International Conference on Architectural Support for Programming Languages and Operating Systems

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“…Quantum algorithms [12,14,68,69] and communication protocols [6,70,71] are described using a language of quantum circuits [53]. While this method is convenient in the case of simple algorithms, it is very hard to operate on compound or abstract data types like arrays or integers using this notation [19,72].…”

Section: Quantum Programming Languagesmentioning

confidence: 99%

Models of quantum computation and quantum programming languages

Miszczak¹

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.

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“…These results come in three sections. First, we concentrate on two particular group theoretic problems, Group Intersection and Double Coset Membership, showing that these problems reduce to other group problems with known efficient quantum algorithms for many instances, yielding Many problems that have quantum algorithms exponentially faster than the best known classical algorithms turn out to be special cases of the Hidden Subgroup problem (HSP) for abelian groups, which can be solved using the Quantum Fourier Transform [Mos99,Joz00]. Other interesting problems, such as Graph Isomorphism are special cases of general Hidden Subgroup, for which no efficient quantum algorithm is currently known.…”

Section: Introductionmentioning

confidence: 99%

Quantum Algorithms for a Set of Group Theoretic Problems

Fenner

Zhang

2015

Int. J. Found. Comput. Sci.

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We study two group theoretic problems, Group Intersection and Double Coset Membership, in the setting of black-box groups, where Double Coset Membership generalizes a set of problems, including Group Membership, Group Factorization, and Coset Intersection. No polynomial-time classical algorithms are known for these problems. We show that for solvable groups, there exist efficient quantum algorithms for Group Intersection if one of the underlying solvable groups has a smoothly solvable commutator subgroup, and for Double Coset Membership if one of the underlying solvable groups is smoothly solvable. We also study the decision versions of Stabilizer and Orbit Coset, which generalizes Group Intersection and Double Coset Membership, respectively. We show that they reduce to Orbit Superposition under certain conditions. Finally, we show that Double Coset Membership and Double Coset Nonmembership have zero knowledge proof systems.

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Quantum Algorithms

Cited by 32 publications

References 111 publications

Compiler Management of Communication and Parallelism for Quantum Computation

Compiler Management of Communication and Parallelism for Quantum Computation

Models of quantum computation and quantum programming languages

Quantum Algorithms for a Set of Group Theoretic Problems

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