Toolbox for Quantum Computing and Digital Quantum Simulation with Superconducting Qubits

Abstract

Quantum computers make use of the coherent time evolution of a quantum system to map an input to an output. The coherent quantum dynamics allows the system to take on superpositions of states which is not possible in the laws of classical physics. Once quantum computers are built, they can solve certain problems exponentially faster than a classical computer. However, a quantum computer will most likely not be a stand-alone component but rather needs a host of classical electronics for control and readout of the quantum state. In the present thesis we develop tools for the realization of quantum computing and simulation experiments with superconducting circuits. We develop a real-time digital signal processing unit based on a field programmable gate array (FPGA). A practical quantum computer might require several rounds of measurements where, in each step, a set of quantum bits (qubits) has to be reset into a known state. We demonstrate active reset of a qubit using the FPGA unit on timescales of a few hundred nanoseconds. As a further step, we experimentally demonstrate the usage of the FPGA instrument to realize an active feedforward operation for deterministic quantum teleportation. Quantum teleportation allows to transfer the state of a qubit from one location to the other using a classical communication channel and an entangled pair of qubits as a resource. Quantum teleportation thus might be a useful means for data transfer in future quantum computing and communication systems. One of the most promising applications of a quantum computer is the simulation of quantum mechanical models which are hard to simulate with a classical computer. We perform a proof-of-principle experiment, where we demonstrate the digital quantum simulation of the time evolution under three different kinds of interactions between two spins. In particular, we simulate the XY model, the Heisenberg XYZ model, and the quantum mechanical Ising model with transverse magnetic field. The digital quantum simulation is based on a stroboscopic decomposition of the coherent time evolution into a sequence of up to ten two-qubit gates with variable duration and intertwined with single qubit gates. In future experiments, the ability to digitally simulate spin–spin interactions with superconducting qubits could form a building block for digital quantum simulations of complex systems.