**Tracking a Quantum Particle Using a Quantum Simulator**

*A fundamental problem studied in Quantum Physics is the behavior of a quantum entity (e.g., electron) in various potentials. Quantum Physics assigns spatial probabilities to the electron at each instant of time.*

*The question that T.S. Mahesh’s group at IISER Pune asked is can one retrieve these spatial probabilities directly from a quantum simulator and compare the probabilities with the predictions of Quantum Physics. Such a simulation would be a step towards realizing a large scale quantum simulator. Along with group members Ravi Shankar and Swathi Hegde, T.S. Mahesh describes here some of the group’s recent work on this front along with an overview of the field.*

Our quantum simulator was based on nuclear magnetic dipoles (spins) of bromotrifluorobenzene oriented in a liquid crystal. The active spin-system consists of five-mutually interacting spins - three fluorine nuclei and two hydrogen nuclei (protons). In order to simulate a quantum process, we need to rotate the spins precisely in a way that takes into account both kinetic energy and potential energy. In our experiments (published recently in the journal *Physics Letters A* (378:10)) we used the techniques of Nuclear Magnetic Resonance (NMR) to precisely manipulate the dynamics of quantum simulator. It involved irradiation of the sample with radio-frequency pulses of exact durations and exact powers. When the spins absorb these radiations, they go to some specific quantum states, and after a while they emit the absorbed energy in the form of characteristic radio waves. These waves are detected by an antenna close to the sample, and are processed by computers.

Recent work from T.S. Mahesh’s group demonstrates the spatial probabilities of an electron using a quantum simulator (Image credit: T. S. Mahesh) |

In our experiments, we used four spins for encoding the position of the particle and the fifth one for extracting the probabilities. Here we describe two simple cases: (i) no potential (free particle) and (ii) particle in a square-well potential. In the first case, the probability distribution keeps on spreading out. This means, longer we wait, less certain are we about the position of the particle. The second case leads to a probability distribution that is modulating over time, but is sort of constrained within the square well. So, at regular intervals of time, the particle returns to the initial position with high probability. As we mentioned earlier, the signal from the fifth spin directly encodes the spatial probability of the quantum particle.

Our results showed a reasonable correspondence between the experimental results and the predictions of quantum Physics. In our experiments the main sources of errors include imperfections in initialization, imperfect controls, and decoherence. Imperfect control of spin dynamics arises mainly because of the small differences in the resonance frequencies and because of spatial inhomogeneity in the radio waves. Decoherence is the gradual decay of a quantum state due to external disturbances. These are the main challenges in any future quantum processor, and our work just exemplifies this fact. Currently we are planning to perform more complex quantum simulations with larger number of qubits. This requires development of novel methods in achieving quantum control and in suppressing decoherence.

*- Article by T.S. Mahesh, Swathi S. Hegde, and Ravi Shankar*