Reducing number of gates in quantum random walk search algorithm via modification of coin operators

Tonchev, Hristo; Danev, P.

doi:10.1016/j.rinp.2023.106327

Cited by 6 publications

(7 citation statements)

References 18 publications

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“…The Hill function is commonly used in biochemistry and systems biology for logistic regression of nonlinear functional dependences. It can be modified in order to obtain an approximation of p(φ) for fixed coin size and functional dependence between the phases, as is made in [32]:…”

Section: Hill Fit For An Arbitrary Coin Sizementioning

confidence: 99%

“…In our previous work [32], we obtain fits of the QRWS simulations for a few particular relations between the walk coin parameters as a function of the coin size m: Table 1. Numerical values for the parameters of the Hill fits of the probability to find solution of QRWS algorithm with coin sizes 8 and 10 and nonlinear functional dependence between the phases as in Eq.…”

Section: Hill Fit For An Arbitrary Coin Sizementioning

confidence: 99%

“…The numerical values of the parameter b(m) of the Hill fit, can be fitted itself for coin sizes between 4 and 11, as is done in our previous work [32]:…”

Section: Parameter B As Function Of αmentioning

confidence: 99%

“…In those works, we show numerical results for relatively small coin size and give prognosis for probability to find solution of QRWS for larger coin size by using supervised machine learning. In [32] we make the prognosis by using modified Hill function to fit the QRWS's probability to find solution as a function of the coin size for a few selected functional dependences between the coin phases. We used those fits to extrapolate both the maximal probability to find solution and the robustness of the algorithm for those phases' relations as a function of the coin size.…”

Section: Introductionmentioning

confidence: 99%

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Semi-empirical method for evaluating the robustness of QRWS algorithm for different coin sizes and functional dependence between coin phases

Tonchev,

Danev

2024

J. Phys.: Conf. Ser.

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In this work we study the quantum random walk search algorithm when the walk coin is constructed by generalized Householder reflection and a phase multiplier. We focus on the algorithm’s robustness against errors in the phases – how the probability to find solution decreases with increasing the errors in those phases. The robustness depends on the functional dependence between the reflection phase φ and the phase multiplier ζ. Here we use interpolations by non-linear logistic regression functions to study a particular functional dependence between angles ζ = -2φ + 3π + α sin(2φ) for different coin sizes and parameters alpha. The obtained results in this work are discussed, together with their limitations.

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Section: Hill Fit For An Arbitrary Coin Sizementioning

confidence: 99%

Section: Hill Fit For An Arbitrary Coin Sizementioning

confidence: 99%

“…The numerical values of the parameter b(m) of the Hill fit, can be fitted itself for coin sizes between 4 and 11, as is done in our previous work [32]:…”

Section: Parameter B As Function Of αmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Semi-empirical method for evaluating the robustness of QRWS algorithm for different coin sizes and functional dependence between coin phases

Tonchev,

Danev

2024

J. Phys.: Conf. Ser.

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“…Discrete Quantum Random Walk (DQRW) algorithm has been in study and applications in physics [1,2,3,4] and mathematics [5,6] as well as in the areas of computational intelligence [7,8], and optimization techniques [9] 1 . While the basic features of classical and quantum discrete random walk are essentially the same, one crucial difference between classical and quantum walks is a non-trivial coin operator [11] in the latter case.…”

Section: Introductionmentioning

confidence: 99%

A simple coin for a $2d$ entangled walk

Zahed¹,

Sen²

2023

Preprint

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We analyze the effect of a simple coin operator, built out of Bell pairs, in a 2d Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion relations of the DQRW. The coin induces entanglement between the spin and position degrees of freedom, which oscillates with time and reaches a constant value asymptotically. We probe the entangling properties of the coin operator further, by two different measures. First, by integrating over the space of initial tensor product states, we determine the Entangling Power of the coin operator. Secondly, we compute the Generalized Relative Rényi Entropy between the corresponding density matrices for the entangled state and the initial pure unentangled state. Both the Entangling Power and Generalized Relative Rényi Entropy behaves similar to the entanglement with time. Finally, in the continuum limit, the specific coin operator reduces the 2d DQRW into two 1d massive fermions coupled to synthetic gauge fields, where both the mass term and the gauge fields are built out of the coin parameters.

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