Optimising Matrix Product State Simulations of Shor's Algorithm

Dang, Aidan; Hill, Charles D.; Hollenberg, Lloyd C. L.

doi:10.22331/q-2019-01-25-116

Cited by 31 publications

(27 citation statements)

References 31 publications

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“…Yet, we can estimate the time to compile a circuit with BMT and run it on a quantum computer versus the time to simulate the circuit. The current record of simulation of a quantum program on a digital machine stays at 60 Qubits [Dang et al 2019] śfour more than the previous record, from October of 2018 [Pednault et al 2018]. As mentioned by Dang et al, the simulation of a 50-qubits random state might require up to 18 petabytes of classical computer memory.…”

Section: Rq4: the Influence Of The Target Architecturementioning

confidence: 99%

Qubit allocation as a combination of subgraph isomorphism and token swapping

Siraichi

Santos

Collange

et al. 2019

Proc. ACM Program. Lang.

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In 2016, the first quantum processors have been made available to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, such possibility also brought challenges. One challenge is the so called Qubit Allocation problem: the mapping of a virtual quantum circuit into an actual quantum architecture. There exist solutions to this problem; however, in our opinion, they fail to capitalize on decades of improvements on graph theory. In contrast, this paper shows how to model qubit allocation as the combination of Subgraph Isomorphism and Token Swapping. This idea has been made possible by the publication of an approximative solution to the latter problem in 2016. We have compared our algorithm against five other qubit allocators, all independently designed in the last two years, including the winner of the IBM Challenge. When evaluated in łTokyo", a quantum architecture with 20 qubits, our technique outperforms these state-of-the-art approaches in terms of the quality of the solutions that it finds and the amount of memory that it uses, while showing practical runtime. CCS Concepts: • Computer systems organization → Quantum computing; • Software and its engineering → Compilers; • Theory of computation → Parameterized complexity and exact algorithms.

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Section: Rq4: the Influence Of The Target Architecturementioning

confidence: 99%

Qubit allocation as a combination of subgraph isomorphism and token swapping

Siraichi

Santos

Collange

et al. 2019

Proc. ACM Program. Lang.

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“…Existing classical simulators have typically focused on emulating noiseless circuits. In this case, simulations of quantum circuits with more than 50 qubits have been demonstrated [9][10][11] . There are several techniques for speeding up simulations of certain types of circuits [12][13][14][15][16] or algorithms [17][18][19][20] .…”

Section: Introductionmentioning

confidence: 99%

Low-rank density-matrix evolution for noisy quantum circuits

2021

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In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full matrix. We implement this algorithm using an in-house simulator and show that the low-rank algorithm speeds up simulations by more than two orders of magnitude over existing implementations of full-rank simulators, and with negligible error in the noise effect and final observables. Finally, we demonstrate the utility of the low-rank method as applied to representative problems of interest by using the algorithm to speed up noisy simulations of Grover’s search algorithm and quantum chemistry solvers.

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“…Peter W. Shor with his quantum factoring algorithm has demonstrated theoretically the power of quantum computer over a classical computer. There have been several experiments done to optimize Shor's factoring algorithm such as by optimizing the order finding circuit or optimizing the matrix product state where both shows a significant leap of performance [14], [15]. This research will use Shor's original algorithm despite there being further breakthrough regarding the algorithm since its conception in 1994.…”

Section: Introductionmentioning

confidence: 99%

Implementation of Shor’s Quantum Factoring Algorithm Using ProjectQ Framework

Wicaksono¹,

Wicaksana²

2019

IJEAT

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Prime number factorization is a problem in computer science where the solution to that problem takes super-polynomial time classically. Shor’s quantum factoring algorithm is able to solve the problem in polynomial time by harnessing the power of quantum computing. The implementation of the quantum algorithm itself is not detailed by Shor in his paper. In this paper, an approach and experiment to implement Shor’s quantum factoring algorithm are proposed. The implementation is done using Python and a quantum computer simulator from ProjectQ. The testing and evaluation are completed in two computers with different hardware specifications. User time of the implementation is measured in comparison with other quantum computer simulators: ProjectQ and Quantum Computing Playground. This comparison was done to show the performance of Shor’s algorithm when simulated using different hardware. There is a 33% improvement in the execution time (user time) between the two computers with the accuracy of prime factorization in this implementation is inversely proportional to the number of qubits used. Further improvements upon the program that has been developed for this paper is its accuracy in terms of finding the factors of a number and the number of qubits used, as previously mentioned.

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Optimising Matrix Product State Simulations of Shor's Algorithm

Cited by 31 publications

References 31 publications

Qubit allocation as a combination of subgraph isomorphism and token swapping

Qubit allocation as a combination of subgraph isomorphism and token swapping

Low-rank density-matrix evolution for noisy quantum circuits

Implementation of Shor’s Quantum Factoring Algorithm Using ProjectQ Framework

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