Operator coherence dynamics in Grover's quantum search algorithm

Pan, Minghua; Qiu, Daowen

doi:10.1103/physreva.100.012349

Cited by 19 publications

(19 citation statements)

References 34 publications

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“…In particular, the methods could not be easily applied to any mixed state generalization of Grover's algorithm. Quantum coherence [46][47][48] and quantum discord 46 have been considered as resources in the noiseless algorithm as well.…”

Section: Resultsmentioning

confidence: 99%

Quantifying computational advantage of Grover’s algorithm with the trace speed

Gebhart

Pezzé

Smerzi

2021

Sci Rep

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Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we report a close connection between the trace speed and the quantum speed-up in Grover’s search algorithm implemented with pure and pseudo-pure states. For a noiseless algorithm, we find a one-to-one correspondence between the quantum speed-up and the polarization of the pseudo-pure state, which can be connected to a wide class of quantum statistical speeds. For time-dependent partial depolarization and for interrupted Grover searches, the speed-up is specifically bounded by the maximal trace speed that occurs during the algorithm operations. Our results quantify the quantum speed-up with a physical resource that is experimentally measurable and related to multipartite entanglement and quantum coherence.

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Section: Resultsmentioning

confidence: 99%

Quantifying computational advantage of Grover’s algorithm with the trace speed

Gebhart

Pezzé

Smerzi

2021

Sci Rep

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“…(a) Email:panmh@guet.edu.cn (b) Email:situhaozhen@gmail.com (c) Email:zhengshg@pcl.ac.cn It has been shown quantum correlation resources such as entanglement and coherence play important roles in quantum algorithms. Hence, there are many fruitful works on the quantum correlation resources in GSA [18][19][20][21][22][23][24][25][26][27][28].…”

Section: Introduction -mentioning

confidence: 99%

Complementarity between Success Probability and Coherence in Grover Search Algorithm

Pan,

Situ,

Zheng

2022

Preprint

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Coherence plays a very important role in Grover search algorithm (GSA). In this paper, we define the normalization coherence N(C), where C is a coherence measurement. In 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, Ps(t) + N(C(t)) ≃ 1, where C is in terms of the relative entropy of coherence and l1 norm of coherence, t is the number of the search iterations in GSA. Moreover, the equation holds no matter 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 complementary between the success probability and the coherence almost always hold. 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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“…Soon after GSA was proposed, it has aroused scientists' attentions and obtained fruitful research results, such as the generalizations and improvements [16][17][18][19][20][21][22][23][24][25][26], the mechanism of quadratic acceleration [27][28][29][30][31][32][33], experimental verification and the applications [34][35][36][37][38]. At the same time, people began to study the performance of GSA under different noisy environments.…”

Section: Introductionmentioning

confidence: 99%

Performance of Grover search algorithm with diagonalizable noise

Pan¹,

Xiong²,

Zheng³

2021

Preprint

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It is generally believed that Grover search algorithm (GSA) with quantum noise may quickly lose its quadratic speedup over its classical case. In this paper, we partly agree with that by our new findings as follows. First, we investigate different typical diagonalizable noises represented by Bloch vectors, and the results demonstrate that the success probability decreases exponentially to 1/2 and oscillates around 1/2 with the increase of the number of iterations. Second, for some types of noises, such as bit flip and bit-phase flip noises, can improve the performance of GSA for certain parts of the search process. Third, we calculate and analyze the noise threshold of the bit-phase flip noise for the requested success probability and the result shows that GSA with noise within the threshold still outperforms its classical counterpart. According to the above results, some interesting works in the noisy intermediate-scale quantum (NISQ) computing are suggested, such as verifying the correctness of quantum algorithms even with noises and machine learning applications.

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Operator coherence dynamics in Grover's quantum search algorithm

Cited by 19 publications

References 34 publications

Quantifying computational advantage of Grover’s algorithm with the trace speed

Quantifying computational advantage of Grover’s algorithm with the trace speed

Complementarity between Success Probability and Coherence in Grover Search Algorithm

Performance of Grover search algorithm with diagonalizable noise

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