Quantum Algorithm Design: Techniques and Applications

Shao, Changpeng; Yang, Li; Li, Hongbo

doi:10.1007/s11424-019-9008-0

Cited by 61 publications

(29 citation statements)

References 169 publications

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“…Because both the products of unitary operations and linear combinations of unitary (LCU) operations can be realized by duality quantum algorithm, it has a lot of applications to investigate novel quantum systems [ 16 , 17 , 18 , 19 , 20 , 21 , 76 , 77 , 78 , 79 , 80 ], e.g., systems of large-scale silicon quantum photonics, efficient quantum simulations of open quantum systems, quantum secure computing, passive quantum error correction, etc. Duality quantum algorithm has become one of the strongest tool in designing quantum algorithms [ 81 ]. Recently, scientists apply the method to design a full quantum algorithm for quantum chemistry simulation [ 82 ].…”

Section: Duality Quantum Algorithmmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

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Section: Duality Quantum Algorithmmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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“…where (83d) follows from (33). Combining (82) and (83), we can see that T L 1 ≤ 1, hence the proof is completed.…”

mentioning

confidence: 62%

“…The evaluation of eigenvalues and eigenvectors is a fundamental subroutine in many existing quantum algorithms, such as Shor's algorithm, the Harrow-Hassidim-Lloyd (HHL) algorithm, and in Hamiltonian simulation [12], [30]- [33]. In early contributions, quantum phase estimation [28,Sec.…”

Section: B Quantum Channelsmentioning

confidence: 99%

Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems

Xiong

Chandra

et al. 2020

IEEE Access

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“…This implementation has double the resource requirements of the first architecture but has the benefit of improvement in execution time. The time complexity is determined as in (20) and the space complexity is given by (21).…”

Section: Cmac Configurationsmentioning

confidence: 99%

“…An experimental realization of a quantum computing silicon chip was fabricated in the work of Qiang et al 18 In contrast to other realizations, this quantum chip does not use product of unitary operation architecture as proposed in the work of Benioff, 1 it employed the linear combinations of unitary (LCU) operations architecture, proposed in the work of Gui-Lu. 19 The LCU has found extensive applications in quantum algorithms recently, as reviewed in the work of Shao et al, 20 extending to quantum machine learning, 21 secure multiparty computing, 22 and passive error correction. 23 Despite having operational quantum hardware, there are critical problems and challenges 24 in these systems that need to be solved.…”

Section: Introductionmentioning

confidence: 99%

Scaling reconfigurable emulation of quantum algorithms at high precision and high throughput

El-Araby

Caliga

2019

Quantum Engineering

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Summary The general approach for emulating quantum algorithms on classical platforms has been through representing them as gate‐based quantum circuits. However, direct implementation of quantum circuits significantly increases the hardware resource utilization and system latency of classical emulators. In this paper, we investigate multiple implementation models alternative to conventional emulation approaches, as feasible solutions to the scalability problem in classical emulation of quantum circuits. In the first model, the quantum circuit functionality is reduced to equivalent, arithmetic (multiply‐and‐accumulate) operations and combined with two computation methods, based on lookup and dynamic generation. In the second model, a kernel operation is extracted from the quantum circuit based on its functionality, and the kernel is iterated through all input quantum states. The proposed emulation models provide space and time optimizations, significantly reducing resource utilizations and latencies and improving scalability. We use these models to develop a highly scalable hardware emulator that is based on reconfigurable technology for efficient simulations of full quantum algorithms and circuits. Our hardware implementations support single precision floating point arithmetic for improved accuracy, and contain fully pipelined designs for high throughput. We investigate quantum algorithms such as quantum Fourier transform and quantum wavelet transform and explore different hardware architectures and optimizations. Experimental results and analysis are provided for the architectures in terms of resource consumption and emulation time. The experiments are carried out on a high‐performance reconfigurable computing system and the obtained results show that the proposed emulator is feasible for running and testing a variety of quantum algorithms.

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Quantum Algorithm Design: Techniques and Applications

Cited by 61 publications

References 169 publications

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems

Scaling reconfigurable emulation of quantum algorithms at high precision and high throughput

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