Time reversal and charge conjugation in an embedding quantum simulator

04 August 2015

Prof. Kim’s trapped-ion group at Center of Quantum Information realizes the first embedding quantum simulator¹.

The ‘unphysical’ process in the original Hilbert space, where the evolution of the two-component Majorana spinor is considered. The unphysical processes can be implemented in physical systems through the embedding scheme, which maps the original Hilbert space to the enlarged Hilbert space. After the physical process, the final results are remapped to the original space. The embedding quantum simulator is built in a single ¹⁷¹Yb⁺ ion trapped in a linear Paul trap, where the enlarged space is encoded in the ground-state manifold of the ion.

Quantum simulators are devices designed to simulate the properties of ideal quantum models. With the help of quantum simulators, it is possible to study quantum systems which could not be efficiently simulated by classical means. Up to now, research on quantum simulators is focused on simulating realistic systems, whereas the basic principals of quantum mechanics require the dynamics of isolated systems to be unitary. On the other hand, there exist physically meaningful operations, such as the time-reversal and charge-conjugation operations, which can only be implemented by anti-unitary processes. In classically intractable quantum systems, it is theoretically difficult to implement such operations.

In order to solve this problem, Prof. Enrique Solano’s theory group in Universidad del Pais Vasco proposed the concept of embedding quantum simulator. The essential idea of the embedding quantum simulator is the embedding mapping, which maps non-unitary processes in the original Hilbert space to unitary processes in the enlarged Hilbert space. The advantage of this proposal is that “unphysical” (anti-unitary) operations can be implemented at arbitrary times without quantum state tomography and quantum-classical interfaces.

Trapped-ion system is one of the most potential platforms for developing “practical” quantum simulators, which possesses prominent tunability and scalability, thus has the possibility of outperforming classical computational devices. Under the leadership of Prof. Kihwan Kim, the ion-trap group in the Center of Quantum Information constructed the first embedding quantum simulator in a trapped-ion system. The embedding quantum simulator possesses the abilities of implementing “unphysical” processes and realizing “unphysical” operations. The experiments show the simulation of the celebrated “unphysical” relativistic equation, the Majorana equation, and observe novel phenomena, such as non-conservation of momentum and charge of a free Majorana particle. Then, the authors show how to implement time reversal and charge conjugation in the embedding simulator.

Time reversal and charge conjugation during the Majorana dynamics, which are forbidden by the laws of quantum mechanics. Performed in the momentum space with the embedding simulator.

The experiments explore a completely new direction in the field of quantum simulation, and introduce “unphysical” operations into the toolbox of quantum simulation. The embedding quantum simulator can also be used to measure physically meaningful non-observables, such as the entanglement monotones and multi-time correlation functions.

The experiments were carried out by IIIS PhD candidates Xiang Zhang, Yang-chao Shen and Jun-hua Zhang. The research was funded by National Basic Research Program of China, the National Natural Science Foundation of China, and the recruitment program of global youth experts of China.