Researchers Explore ‘First Hitting Times’ Impact on Quantum Computing Efficiency

Researchers from the Department of Physics Institute of Nanotechnology and Advanced Materials Bar Ilan University, Institut für Physik Universität Augsburg, and Research Institute CODE University of the Bundeswehr Munich have explored the concept of “first hitting times” on quantum computers. This refers to the time taken for a process or signal to reach a specific level or target for the first time. The team conducted a quantum walk on a ring represented by a directed triangle graph with complex edge weights, using IBM quantum computers. The study found that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters. The research could have implications for the development of quantum algorithms and the broader field of quantum computing.

What is the Impact of First Hitting Times on Quantum Computers?

Quantum computing is a rapidly evolving field, and researchers are constantly exploring new aspects of this technology. One such area of study is the concept of “first hitting times” on a quantum computer. This refers to the time taken for a monitored process or a signal to reach a specific level or target for the first time. This concept has been investigated by a team of researchers from the Department of Physics Institute of Nanotechnology and Advanced Materials Bar Ilan University, Institut für Physik Universität Augsburg, and Research Institute CODE University of the Bundeswehr Munich.

The researchers conducted 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 was detected. The first hitting time statistics were recorded using unitary dynamics interspersed stroboscopically by measurements, which was implemented on IBM quantum computers with a mid-circuit readout option. The statistical aspect of the problem depends on the way the measured path is constructed, an effect that was quantified experimentally.

How Does Quantum Walk Differ from Classical Walk?

In a classical walk, a walker starts at the origin and the first hitting time is the time it takes the walker to reach some other vertex. The basic questions are whether the classical walker will reach the target after an infinite number of steps and what is the distribution of the first passage times to the target state. The mean first hitting time is a widely used quantifier of the process. In finite systems excluding ergodicity breaking, simple random walks are recurrent and hence the classical walker is detected with probability one.

However, for quantum walks with monitoring, the situation is vastly different. Quantum walks may exhibit a quantum speedup for the hitting time, which can be exponential for specific initial states and highly symmetric graphs. However, in some other cases, the quantum search can perform poorly due to destructive interference. This problem can be avoided in principle using specially designed graphs or with a restart strategy.

What are the Key Findings of the Study?

The study found 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. 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. The researchers concluded that for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. Yet finite resolution effects lead to new topological chirality and broadening effects, which disappear in the asymptotic theory with an infinite number of measurements.

What are the Implications of the Study?

The results of this study point the way for the development of novel quantum walk algorithms that exploit measurement-induced effects on quantum computers. The option of mid-circuit readout of qubits on state-of-the-art quantum computers opens opportunities to test the dynamics and statistics of monitored quantum dynamics. The repeated monitoring at predetermined times yields a string of measurement outputs, which can be viewed as a stochastic trajectory varying in time.

This research contributes to the understanding of quantum walks and the impact of first hitting times on quantum computers. It provides valuable insights that could be used to improve the efficiency and effectiveness of quantum computing processes. The findings of this study could also have implications for the development of quantum algorithms and the broader field of quantum computing.