Quantum simulation by filtered Hamiltonian engineering

Ashok Ajoy, Paola Cappellaro

We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.

Sonia G. Schirmer

Ieshan Vaidya

Quantum simulation presents itself as one of the biggest advantages of developing quantum computers. Simulating a quantum system classically is almost impossible beyond a certain system size whereas a controllable quantum system inherently has the resources and computing space to simulate another system. Analog quantum simulation is one of the ways of quantum simulation through which a known system mimics an unknown system. A key aspect of this is the ability to generate the target Hamiltonian using control operations which is referred to as Hamiltonian engineering. One way of doing this is to apply pulse sequences over a length of time such that the average Hamiltonian over this period is the desired one. In this thesis, we discuss the method of filtered Hamiltonian engineering which works in a similar fashion. Using this technique, we create a star topology from a general network of spins. Quantum communication between two parties is an important task for its applications in information theory as well as for its use in a quantum computer. A typical solution to this is using teleportation through the means of shared entangled qubits. Teleportation is not ideal for short-range communication such as between two units in a quantum computer. It has been shown that information can be transported from one node of a quantum spin network to another by natural evolution of the system over time. Such networks are better suited for solid-state based computing architectures as well as for short-range communication. The Hamiltonian that permits such transport however places stringent requirements on the parameters of the network. While individual control of spins cannot be avoided in most cases, excess control can introduce noise. In this thesis, we work on a few models of spin networks that permit information transport with minimal requirements on the parameters of the network.

Barry C. Sanders, Graeme Ahokas, Richard Cleve +1 more

Pai Peng, Xiaoyang Huang, Chao Yin +3 more

Engineering desired Hamiltonians in quantum many-body systems is essential for applications such as quantum simulation, computation, and sensing. Many widely used quantum Hamiltonian engineering sequences are designed using human intuition based on perturbation theory, which may not describe the optimal solution and is unable to accommodate complex experimental imperfections. Here we numerically search for Hamiltonian engineering sequences using deep reinforcement learning (DRL) techniques and experimentally demonstrate that they outperform celebrated decoupling sequences on a solid-state nuclear magnetic resonance quantum simulator. As an example, we aim at decoupling strongly interacting spin-1/2 systems. We train DRL agents in the presence of different experimental imperfections and verify robustness of the output sequences both in simulations and experiments. Surprisingly, many of the learned sequences exhibit a common pattern that had not been discovered before, to our knowledge, but has a meaningful analytical description. We can thus restrict the searching space based on this control pattern, allowing us to search for longer sequences, ultimately leading to sequences that are robust against dominant imperfections in our experiments. Our results not only demonstrate a general method for quantum Hamiltonian engineering, but also highlight the importance of combining black-box artificial intelligence with an understanding of the physical system in order to realize experimentally feasible applications.

Man Luo, J. I. Cirac, Technische Universität München