Improved upper bounds for the hitting times of quantum walks

Atia, Yosi; Chakraborty, Shantanav

doi:10.1103/physreva.104.032215

Cited by 9 publications

(6 citation statements)

References 30 publications

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“…Compared to the algorithms based on CTQW [17,26], our algorithms has a better query complexity, and can be adapted to succeed with certainty. On the contrary, the implementation of the CTQW operator e iHt from oracle O involves the use of linear combination tool in Hamiltonian simulation, thus error is introduced inevitably.…”

Section: Related Workmentioning

confidence: 99%

“…Thus combined with fixed-point amplitude amplification [27,28], the overall query complexity is O(n 8.5 ), where n 8.5 = n 1/2 • n 4•2 . Lately it was improved to O(n 2.5 log 2 n) [26]. In contrast, any classical algorithm requires 2 Ω(n) queries [17,29].…”

Section: Related Workmentioning

confidence: 99%

“…However, our proof of Lemma 4.2 is simpler than the one for [26, Lemma 3], as it does not involve integral or characteristic functions of continuous random variables. Moreover, their intermediate step [26,Lemma 4] considers the Frobenius norm of the difference between density matrices, which introduces a strange factor of √ 3. Lemma 4.2 shows that when the iteration number t is chosen according to some specific distribution on [T ] := {0, 1, • • • , T − 1}, the average success probability has a lower bound that is related to the characteristic of the eigenvalue angles of M U and the products of the first and the last term of the eigenvectors.…”

Section: The Helper Lemmamentioning

confidence: 99%

See 2 more Smart Citations

Recovering the original simplicity: succinct and deterministic quantum algorithm for the welded tree problem

Li,

Luo

2024

Preprint

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This work revisits quantum algorithms for the well-known welded tree problem, proposing a very succinct quantum algorithm based on the simplest coined quantum walks. It simply iterates the naturally defined coined quantum walk operator for a predetermined time and finally measure, where the predetermined time can be efficiently computed on classical computers. Then, the algorithm returns the correct answer deterministically, and achieves exponential speedups over any classical algorithm. The significance of the results may be seen as follows. (i) Our algorithm is rather simple compared with the one in (Jeffery and Zur, STOC'2023), which not only breaks the stereotype that coined quantum walks can only achieve quadratic speedups over classical algorithms, but also demonstrates the power of the simplest quantum walk model. (ii) Our algorithm theoretically achieves certainty of success, which is not possible with existing methods. Thus, it becomes one of the few examples that exhibit exponential separation between deterministic (exact) quantum and randomized query complexities, which may also change people's perception that since quantum mechanics is inherently probabilistic, it is impossible to have a deterministic quantum algorithm with exponential speedups for the welded tree problem.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: The Helper Lemmamentioning

confidence: 99%

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Recovering the original simplicity: succinct and deterministic quantum algorithm for the welded tree problem

Li,

Luo

2024

Preprint

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“…The critical characteristic that leads to the speed of an MCMC algorithm is the Markov Chain mixing time, the time it takes for the MCMC algorithm to reach the equilibrium distribution [65]. Quantum algorithms can result in a quadratic speed-up over classical analogues in reaching equilibrium [60,66], though proving that quantum walks lead to speed gains for MCMC algorithms in general, is still an active field of research [66][67][68]. Parton shower algorithms are related to, but due to the state memory implied by shower ordering conditions distinct from, MCMC algorithms.…”

Section: Jhep11(2022)035mentioning

confidence: 99%

Collider events on a quantum computer

Gustafson

Prestel

Spannowsky

et al. 2022

J. High Energ. Phys.

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High-quality simulated data is crucial for particle physics discoveries. Therefore, parton shower algorithms are a major building block of the data synthesis in event generator programs. However, the core algorithms used to generate parton showers have barely changed since the 1980s. With quantum computers’ rapid and continuous development, dedicated algorithms are required to exploit the potential that quantum computers provide to address problems in high-energy physics. This paper presents a novel approach to synthesising parton showers using the Discrete QCD method. The algorithm benefits from an elegant quantum walk implementation which can be embedded into the classical toolchain. We use the ibm_algiers device to sample parton shower configurations and generate data that we compare against measurements taken at the ALEPH, DELPHI and OPAL experiments. This is the first time a Noisy Intermediate-Scale Quantum (NISQ) device has been used to simulate realistic high-energy particle collision events.

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“…In the class of parametrized Hamiltonians, an exceptionally diffused and useful example is that of quantum walks (QWs). QWs are a universal and versatile tool that can be harnessed to perform a plethora of tasks ranging from energy transport [42][43][44] to quantum algorithms, [45][46][47][48][49][50][51] quantum computation, [52][53][54] and quantum communication. 55 In particular, continuous-time quantum walks (CTQWs) are the quantum analog of classical random walks [56][57][58][59] that describe the continuous evolution of a quantum particle over a set of discrete positions.…”

Section: Introductionmentioning

confidence: 99%

Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning

Gianani

Benedetti

2023

AVS Quantum Science

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The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum walks, the parameters themselves may not be directly accessible, and, thus, it is necessary to find alternative estimation strategies exploiting other observables. Here, we perform the multiparameter estimation of the Hamiltonian parameters characterizing a continuous-time quantum walk over a line graph with n-neighbor interactions using a deep neural network model fed with experimental probabilities at a given evolution time. We compare our results with the bounds derived from estimation theory and find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.

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Improved upper bounds for the hitting times of quantum walks

Cited by 9 publications

References 30 publications

Recovering the original simplicity: succinct and deterministic quantum algorithm for the welded tree problem

Recovering the original simplicity: succinct and deterministic quantum algorithm for the welded tree problem

Collider events on a quantum computer

Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning

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