T. Bækkegaard

The superconducting circuit companion — an introduction with worked examples

  1. S. E. Rasmussen,
  2. K. S. Christensen,
  3. S. P. Pedersen,
  4. L. B. Kristensen,
  5. T. Bækkegaard,
  6. N. J. S. Loft,
  7. and N. T. Zinner
This article is a tutorial on the quantum treatment of superconducting electrical circuits. It is intended for new researchers with limited or no experience with the field, but should
be accessible to anyone with a bachelor’s degree in physics or similar. The tutorial has three parts. The first part introduces the basic methods used in quantum circuit analysis, starting from a circuit diagram and ending with a quantized Hamiltonian truncated to the lowest levels. The second part introduces more advanced methods supplementing the methods presented in the first part. The third part is a collection of worked examples of superconducting circuits. Besides the examples in the third part, the two first parts also includes examples in parallel with the introduction of the methods.
arxiv pdf

Superconducting qutrit-qubit circuit: A toolbox for efficient quantum gates

  1. T. Bækkegaard,
  2. L. B. Kristensen,
  3. N. J. S. Loft,
  4. C. K. Andersen,
  5. D. Petrosyan,
  6. and N. T. Zinner
As classical computers struggle to keep up with Moore’s law, quantum computing may represent a big step in technology and yield significant improvement over classical computing
for many important tasks. Building a quantum computer, however, is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possible, to reduce the amount of required control and operation time and thus improve the quantum state coherence. Here we propose a superconducting circuit for implementing a tunable spin chain consisting of a qutrit (three-level system analogous to spin-1) coupled to two qubits (spin-1/2). Our system can efficiently accomplish various quantum information tasks, including generation of entanglement of the two qubits and conditional three-qubit quantum gates, such as the Toffoli and Fredkin gates, which are universal for reversible classical computations. Furthermore, our system realizes a conditional geometric gate which may be used for holonomic (non-adiabatic) quantum computing. The efficiency, robustness and universality of our circuit makes it a promising candidate to serve as a building block for larger spin networks capable of performing involved quantum computational tasks.
arxiv pdf