Next Article in Journal
Remarks on Limit Theorems for the Free Quadratic Forms
Next Article in Special Issue
Efficient Circuit Implementations of Continuous-Time Quantum Walks for Quantum Search
Previous Article in Journal
Corrected Thermodynamics of Black Holes in f(R) Gravity with Electrodynamic Field and Cosmological Constant
Previous Article in Special Issue
Continuous-Time Quantum Walk in Glued Trees: Localized State-Mediated Almost Perfect Quantum-State Transfer
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States

by
Qingyuan Wang
1,*,
Silin Ren
1,
Ruoyu Yin
1,*,
Klaus Ziegler
2,
Eli Barkai
1 and
Sabine Tornow
3,*
1
Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
2
Institut für Physik, Universität Augsburg, 86135 Augsburg, Germany
3
Research Institute CODE, University of the Bundeswehr Munich, 81739 Munich, Germany
*
Authors to whom correspondence should be addressed.
Entropy 2024, 26(10), 869; https://doi.org/10.3390/e26100869
Submission received: 2 July 2024 / Revised: 6 October 2024 / Accepted: 14 October 2024 / Published: 16 October 2024
(This article belongs to the Special Issue Quantum Walks for Quantum Technologies)

Abstract

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements.
Keywords: quantum walk; quantum computing; dark and bright states quantum walk; quantum computing; dark and bright states

Correction Statement

Due to some errors in article production, there is an extra sentence in the main text, which is not related to the content of the article. This information has been removed. The correction doesn't affect the specific contents of the article.

Share and Cite

MDPI and ACS Style

Wang, Q.; Ren, S.; Yin, R.; Ziegler, K.; Barkai, E.; Tornow, S. First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States. Entropy 2024, 26, 869. https://doi.org/10.3390/e26100869

AMA Style

Wang Q, Ren S, Yin R, Ziegler K, Barkai E, Tornow S. First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States. Entropy. 2024; 26(10):869. https://doi.org/10.3390/e26100869

Chicago/Turabian Style

Wang, Qingyuan, Silin Ren, Ruoyu Yin, Klaus Ziegler, Eli Barkai, and Sabine Tornow. 2024. "First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States" Entropy 26, no. 10: 869. https://doi.org/10.3390/e26100869

APA Style

Wang, Q., Ren, S., Yin, R., Ziegler, K., Barkai, E., & Tornow, S. (2024). First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States. Entropy, 26(10), 869. https://doi.org/10.3390/e26100869

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop