New Study Opens the Path Towards Control of Quantum Walks

Imagine flipping a coin, if it is heads, take a step to the left. If tails, take a step to the right. A simple decision right? Not so much in the quantum realm.

Schematic diagram of this study. The random walk is one of the models of the stochastic process. Image Credit: Haruna Katayama, Hiroshima University.

In the quantum realm, one can move in both directions at the same time, similar to a wave spreading out.

This random process, known as the walker analogy, can be used in traditional as well as quantum algorithms that are employed in advanced technologies, like data search processes and artificial intelligence. But this randomness also makes it hard to control the walk, rendering it harder to design precision systems.

A team of researchers from Japan has demonstrated the mechanism that is fundamental to the directional decision of every quantum step. This finding may allow them to achieve a more controlled walk and introduce a means to possibly manage the direction of movement. The researchers have published their results in Scientific Reports—a Nature Research journal—on October 16th, 2020.

In our study, we focused on the coin determining the behavior of the quantum walk to explore controllability.

Haruna Katayama, Study Author and Graduate Student, Graduate School of Integrated Arts and Sciences, Hiroshima University

In traditional systems, it is the coin that guides the walker in space—either left or right. But in the case of quantum systems, a coin is far less consistent. This is because the walker not only works as a particle stood in one space but also operates as a wave expanded in every probability across time.

We introduced the time-dependent coin of which the probability of landing on heads or tails varies temporally for unveiling the function of the coin.

Haruna Katayama, Study Author and Graduate Student, Graduate School of Integrated Arts and Sciences, Hiroshima University

A time-dependent coin like this can change the position of the walker, found the team; however, the wave feature of the walker concealed the level of physical space controlled by the coin.

We succeeded in clarifying the equivalence of two completely different concepts—the equivalence of the rate of change in coin probability and the velocity of the wave—for the first time.

Haruna Katayama, Study Author and Graduate Student, Graduate School of Integrated Arts and Sciences, Hiroshima University

Katayama continued, “This unveiled mechanism enables us to control the quantum walk on demand by manipulating the coin with preserving the random process, providing core fundamental elements of innovative quantum information processing technologies such as quantum computing.”

The team determined that the rate of coin flipping is directly proportional to the movement of the wave, leading to some amount of control in the movement of the walker.

The walking mechanism enables us to tailor quantum walks as we desire by manipulating the coin-flipping rate,” added Katayama. “In addition, we have found that the quantum walk with the desired trajectory can be realized on demand by designing the coin. Our results open the path towards the control of quantum walks.”

The study was partly funded by the Okawa Foundation for Information and Telecommunications.

Other authors of the study are Noriyuki Hatakenaka, a professor in the Graduate School of Advanced Science and Engineering at Hiroshima University, and Toshiyuki Fujii, a professor in the Department of Physics at Asahikawa Medical University.

Journal Reference:

Katayama, H., et al. (2020) Floquet-engineered quantum walks. Scientific Reports.


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