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All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

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

Qingyuan Wang¹, Silin Ren¹, Ruoyu Yin¹

¹Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel.

Entropy (Basel, Switzerland)

|October 25, 2024

Summary

This summary is machine-generated.

We explored quantum walks on a ring using IBM quantum computers, observing quantized return times and dark states. These quantum phenomena are robust to noise but affected by measurement limitations.

Keywords:

dark and bright states quantum computing quantum walk

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Area of Science:

Quantum Physics
Quantum Computing
Complex Systems

Background:

Quantum walks are quantum analogues of classical random walks, exhibiting unique phenomena.
Monitored quantum walks involve measurements during the walk, influencing the system's evolution.
Hitting time statistics are crucial for understanding traversal times in dynamic systems.

Purpose of the Study:

To experimentally investigate first hitting time statistics of a monitored quantum walk on a directed triangle graph.
To explore the impact of complex edge weights and measurement protocols on quantum walk dynamics.
To verify theoretical predictions regarding quantized return times and dark states in a quantum computing environment.

Main Methods:

Implementation of a quantum walk on a ring using a directed triangle graph with complex edge weights.
Utilizing IBM quantum computers with midcircuit readout for stroboscopic measurements.
Recording first hitting time statistics by monitoring the quantum walker until detection.

Main Results:

Experimental verification of quantized mean return times to a target state, showing discontinuities related to topological interpretations.
Observation of detection probabilities less than one or zero, linked to dark-state physics, dependent on initial state and measurement protocol.
Demonstration that first hitting times are resilient to noise on the studied IBM quantum computer.

Conclusions:

Quantum walks exhibit quantized return times and dark states due to eigenvalue degeneracies, with experimental validation.
Finite measurements introduce broadening effects, modifying topological quantization and chiral effects predicted by asymptotic theory.
The study highlights the potential and limitations of current quantum computers for simulating complex quantum dynamics.