QUANTUM COMPUTING WITH ELECTRICAL CIRCUITS: HAMILTONIAN CONSTRUCTION FOR BASIC QUBIT-RESONATOR MODELS
Michael R. Geller · 2008
Recent experiments motivated by applications to quantum information processing are probing a new and fascinating regime of electrical engineering—that of quantum electrical circuits—where macroscopic collective variables such as polarization charge and electric current exhibit quantum coherence. Here I discuss the problem of constructing a quantum mechanical Hamiltonian for the low-frequency modes of such a circuit, focusing on the case of a superconducting qubit coupled to a harmonic oscillator or resonator, an architecture that is being pursued by several experimental groups. 1 Quantum gate design In the quantum circuit model of quantum information processing, an arbitrary unitary transformation on N qubits can be decomposed into a sequence of certain universal two-qubit logical operations acting on pairs of qubits, combined with arbitrary single-qubit rotations [1]. The purpose of quantum gate design is to develop experimental protocols or “machine language code ” to implement these elementary operations. For quantum information processing architectures based on superconducting circuits [2, 3], the first step is to construct an effective Hamiltonian for the system. Whereas the fully