Complementarity between success probability and coherence in Grover search algorithm

Pan, Minghua; Situ, Haozhen; Zheng, Shenggen

doi:10.1209/0295-5075/ac7165

Cited by 9 publications

(7 citation statements)

References 49 publications

(55 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The local diffusion operator also has the advantage of reducing circuit errors. It is also interesting to explore how the local diffusion operator influences the coherence and the success probability [49]. We leave those questions for future study.…”

Section: Benchmark Resultsmentioning

confidence: 99%

Quantum search on noisy intermediate-scale quantum devices

Zhang¹,

Yu²,

Korepin³

2022

EPL

View full text Add to dashboard Cite

Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's algorithm was designed without considering the physical resources, such as depth, in the real implementations. Therefore, Grover's algorithm can be improved for NISQ devices. In this paper, we demonstrate how to implement quantum search algorithms better on NISQ devices. We present detailed benchmarks of the five-qubit quantum search algorithm on different quantum processors, including IBMQ, IonQ, and Honeywell quantum devices. We report the highest success probability of the five-qubit search algorithm compared to previous works. Our results show that designing the error-aware quantum search algorithms is possible, which can maximally harness the power of NISQ computers.

show abstract

Section: Benchmark Resultsmentioning

confidence: 99%

Quantum search on noisy intermediate-scale quantum devices

Zhang¹,

Yu²,

Korepin³

2022

EPL

View full text Add to dashboard Cite

show abstract

“…x k ( )  and r k z ( ) cos2 q k when t N.  Following the idea in [72], we define the normalized a C as…”

Section: Complementarity Relations Between Tsallis Relative α Entropy...mentioning

confidence: 99%

“…Likewise, similar methods have been applied to other algorithms, including the Deutsch-Jozsa algorithm and Shor's algorithm [70], and it is found that coherence depletion always exists [70,71]. Pan, Situ and Zheng [72] have displayed the complementarity relation between coherence and the success probability in GSA via the l 1 norm of coherence. Coherence determines the performance of Shor's algorithm by bounding the success probability from below and above [73].…”

Section: Introductionmentioning

confidence: 98%

Tsallis relative α entropy of coherence dynamics in Grover′s search algorithm

Fei

2023

Commun. Theor. Phys.

View full text Add to dashboard Cite

Quantum coherence plays a central role in Grover's search algorithm. We study the Tsallis relative $\alpha$ entropy of coherence dynamics of the evolved state in Grover's search algorithm. We prove that the Tsallis relative $\alpha$ entropy of coherence decreases with the increase of the success probability, and derive the complementarity relations between the coherence and the success probability. We show that the operator coherence of the first $H^{\otimes n}$ relies on the size of the database $N$, the success probability and the target states for $\alpha\in(1,2]$. Moreover, we illustrate the relations between the coherence and the entanglement of the superposition state of targets, as well as the coherence producing and deleting in the Grover iterations.

show abstract

“…Formalized in terms of a quantum resource theory [3][4][5][6][7][8] the equivalence between coherence and entanglement (the fuel behind applications such as quantum dense coding [9], unhackable cryptography [10] and teleportation [11]) was recognized early on [12][13][14]. Recently, the role of coherence and its depletion during the execution of quantum algorithms has received increasing attention [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Cohering and decohering power of massive scalar fields under instantaneous interactions

Kollas¹,

Moustos²,

Muñoz³

2022

Preprint

View full text Add to dashboard Cite

Employing a non-perturbative approach based on an instantaneous interaction between a twolevel Unruh-DeWitt detector and a massive scalar field, we investigate the ability of the field to generate or destroy coherence in the detector by deriving the cohering and decohering power of the induced quantum evolution channel. For a field in a coherent state a previously unnoticed effect is reported whereby the amount of coherence that the field generates displays a revival pattern with respect to the size of the detector. It is demonstrated that by including mass in a thermal field the set of maximally coherent states of the detector decoheres less compared to a zero mass. In both of the examples mentioned, by making a suitable choice of detector radius, field energy and coupling strength it is possible to infer the mass of the field by either measuring the coherence present in the detector in the case of an interaction with a coherent field or the corresponding decoherence of a maximally coherent state in the case of a thermal field. In view of recent advances in the study of Proca metamaterials, these results suggest the possibility of utilising the theory of massive electromagnetism for the construction of novel applications for use in quantum technologies.

show abstract

Complementarity between success probability and coherence in Grover search algorithm

Cited by 9 publications

References 49 publications

Quantum search on noisy intermediate-scale quantum devices

Quantum search on noisy intermediate-scale quantum devices

Tsallis relative α entropy of coherence dynamics in Grover′s search algorithm

Cohering and decohering power of massive scalar fields under instantaneous interactions

Contact Info

Product

Resources

About