Quantum search degeneration under amplitude noise in queries to the oracle

Rastegin, Alexey E.; Shemet, Anzhelika M.

doi:10.1007/s11128-022-03501-0

Quantum Inf Process

2022

DOI: 10.1007/s11128-022-03501-0

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Quantum search degeneration under amplitude noise in queries to the oracle

Alexey E. Rastegin

Anzhelika M. Shemet

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2024

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Cited by 5 publications

(1 citation statement)

References 44 publications

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“…Soon after GSA was proposed, scientists began to study the performance of GSA under different noisy environments [33][34][35][36][37][38][39][40][41][42][43][44][45][46]. In [40,47], Rastegin et al showed the trade-off between the success probability and coherence in GSA with collective phase flip and amplitude damping noises on oracles.…”

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Complementarity between success probability and coherence in Grover search algorithm

Pan¹,

Situ²,

Zheng³

2022

EPL

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Coherence plays a very important role in Grover search algorithm (GSA). In this paper, we define the normalization coherence , where C is a coherence measurement. By virtue of the constraint of large N and Shannon's maximum entropy principle, a surprising complementary relationship between the coherence and the success probability of GSA is obtained. Namely, , where C is in terms of the relative entropy of coherence and l 1 norm of coherence, t is the number of the search iterations in GSA. Moreover, the equation holds no matter either in ideal or noisy environments. Considering the number of qubits is limited in the recent noisy intermediate-scale quantum (NISQ) era, some exact numerical calculation experiments are presented for different database sizes N with different types of noises. The results show that the complementarity between the success probability and the coherence almost always holds. This work provides a new perspective to improve the success probability by manipulating its complementary coherence, and vice versa. It has an excellent potential for helping quantum algorithms design in the NISQ era.

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mentioning

confidence: 99%

Complementarity between success probability and coherence in Grover search algorithm

Pan¹,

Situ²,

Zheng³

2022

EPL

View full text Add to dashboard Cite

show abstract

Performance of Grover’s search algorithm with diagonalizable collective noises

Pan

Xiong

Zheng

2023

Quantum Inf Process

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Decoherence in Grover search algorithm

Sun

2024

Quantum Inf Process

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Quantum search degeneration under amplitude noise in queries to the oracle

Cited by 5 publications

References 44 publications

Complementarity between success probability and coherence in Grover search algorithm

Complementarity between success probability and coherence in Grover search algorithm

Performance of Grover’s search algorithm with diagonalizable collective noises

Decoherence in Grover search algorithm

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