Sequential Generation of Matrix-Product States in Cavity QED

We study the sequential generation of entangled photonic and atomic multi-qubit states in the realm of cavity QED. We extend the work of C. Schoen et al. [Phys. Rev. Lett. 95, 110503 (2005)], where it was shown that all states generated in a sequential manner can be classified efficiently in terms of matrix-product states. In particular, we consider two scenarios: photonic multi-qubit states sequentially generated at the cavity output of a single-photon source and atomic multi-qubit states generated by their sequential interaction with the same cavity mode.Comment: 11 page

Quantum computation in silicon-vacancy centers based on nonadiabatic geometric gates protected by dynamical decoupling

Due to strong zero-phonon line emission, narrow inhomogeneous broadening, and stable optical transition frequencies, the quantum system consisting of negatively charged silicon-vacancy (SiV) centers in diamond is highly expected to develop universal quantum computation. We propose to implement quantum computation for the first time using SiV centers placed in a one-dimensional phononic waveguide, for which quantum gates are realized in a nonadiabatic geometric way and protected by dynamical decoupling (DD). The scheme has the feature of geometric quantum computation that is robust to control errors and the advantage of DD that is insensitive to environmental impact. Furthermore, the encoding of qubits in long-lifetime ground states of silicon-vacancy centers can reduce the effect of spontaneous emission. Numerical simulations demonstrate the practicability of the SiV center system for quantum computation and the robustness improvement of quantum gates by DD pulses. This scheme may provide a promising path toward high-fidelity geometric quantum computation in solid-state systems

Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent.Comment: 59 pages, 11 figures, submission to the second journal special issue dedicated to the memory of G\"oran Lindblad, sequel to arXiv:2307.1493

Advanced dynamical decoupling strategies for simulating Hamiltonian interactions

In the field of quantum information, a major challenge is to protect and shield quantum systems from environmental influences, which cause dissipation and decoherence. One approach to address this problem is called dynamical decoupling, where we act on a quantum system with a series of fast and strong local control operations. If done correctly, the system's state gets rotated in discrete steps in its state space in such a way that the effects of the environment cancel up to a certain order. In the first part of this thesis, we will introduce the basics of dynamical decoupling and present a new approach for constructing dynamical decoupling schemes based on sequences of Weyl operators on networks of qudits. This approach goes beyond merely protecting a quantum system, as it is also capable of altering existing Hamiltonian interactions in ways suitable for quantum simulation purposes. We will also investigate how imperfect controls influence the effectiveness of dynamical decoupling and focus particularly on stochastic noise. In the second part of the thesis, we study concrete scenarios for the application of dynamical decoupling. First, we consider the task of quantum state transfer on a linear chain of qubits and use decoupling to protect the transfer from detrimental influences caused by a bend in the chain. We also look at how to design the specific interaction strengths required on the chain to make the state transfer work and extend this result to chains of qudits. Another chapter deals with decoupling the atomic centre-of-mass motion of a trapped atom or ion in a cavity interacting with a radiation field. Finally, we use decoupling to execute sequences of one- and two-qubit quantum gates on a chain of coupled qubits. Particular care is taken to ensure high fidelity operations in the presence of imperfect decoupling pulses

Controlling Quantum Information Devices

Quantum information and quantum computation are linked by a common mathematical and physical framework of quantum mechanics. The manipulation of the predicted dynamics and its optimization is known as quantum control. Many techniques, originating in the study of nuclear magnetic resonance, have found common usage in methods for processing quantum information and steering physical systems into desired states. This thesis expands on these techniques, with careful attention to the regime where competing effects in the dynamics are present, and no semi-classical picture exists where one effect dominates over the others. That is, the transition between the diabatic and adiabatic error regimes is examined, with the use of such techniques as time-dependent diagonalization, interaction frames, average-Hamiltonian expansion, and numerical optimization with multiple time-dependences. The results are applied specifically to superconducting systems, but are general and improve on existing methods with regard to selectivity and crosstalk problems, filtering of modulation of resonance between qubits, leakage to non-compuational states, multi-photon virtual transitions, and the strong driving limit

Fault-tolerant superconducting qubits

For quantum computing to become viable, the inherently fallible nature of qubits must be overcome with quantum error correction (QEC). QEC requires coherent qubits, in a configuration compatible with a given QEC scheme, and quantum logic operations with sufficiently low error. In this thesis, we perform a series of targeted experiments to achieve these goals on a path toward realizing the surface code QEC scheme. We first develop the Xmon variant of the transmon qubit, a highly coherent, planar, and frequency tunable superconducting qubit. With coherence demonstrated, we build an array of five Xmon qubits in a configuration compatible with the surface code, and demonstrate quantum logic operations with sufficiently low error to employ the surface code. These logic gates are characterized with randomized benchmarking, a protocol for determining gate error. We find applications of randomized benchmarking beyond the intended use in gate optimization and decoherence characterization, in addition to exploring the fundamental assumptions of randomized benchmarking. Lastly, we build a nine qubit Xmon transmon array and demonstrate correction of environmental bit-flip errors in a precursor to the surface code