Superconducting Circuits and Quantum Information

Abstract

Superconducting circuits can behave like atoms making transitions between two levels. Such circuits can test quantum mechanics at macroscopic scales and be used to conduct atomic-physics experiments on a silicon chip.Quantum bits, or qubits, form the heart of quantuminformation processing schemes. Because of the quantum parallelism and entanglement that arise from the superposition of states in two-level qubit systems, researchers expect eventual quantum computers to tackle tasks, such as factoring large numbers and simulating large quantum systems, that no ordinary computers can do in a practical time frame.Quantum computing involves preparing, manipulating, and reading out the quantum states of a many-qubit system. So it is desirable to have qubits that can be individually controlled. Moreover, they should be scalable; that is, simply adding more qubits should create a larger circuit capable of more complex calculations. Solid-state qubits satisfy these requirements.Fortunately, very small solid-state devices can behave quantum mechanically. As the size of a bulk conductor becomes increasingly smaller, its quasi-continuous electron conduction band turns into discrete energy levels. An example is a quantum dot, in which electrons are confined to a small semiconducting or metallic box or island composed of millions of atoms. The problem is that the electron states of that island quickly decohere as the microscopic degrees of freedom strongly interact with the environment. A bulk superconductor, in contrast, is composed of many paired electrons that condense into a single-level state. This superconducting state involves macroscopic degrees of freedom and thus exhibits better quantum coherence. By reducing the size of the superconductor, one can reduce the coupling of the superconducting state to the environment and thereby further improve the quantum coherence.Various experiments on superconducting circuits have demonstrated as much [1,2,3,4,5] and those schemes are regarded as promising candidates of qubits that can process quantum information (see Physics Today, June 2002, page 14). Not surprisingly, there is a deep analogy between natural atoms and the artificial atoms composed of electrons confined in small superconducting islands. Both have discrete energy levels and exhibit coher- * J.Q. You (jqyou@fudan.edu.cn) is a professor of physics at Fudan University in Shanghai, China. Franco Nori (nori@umich.edu) is a professor of physics and applied physics at the University of Michigan in Ann Arbor and the director of the Digital Materials Laboratory at Japan's Institute of Physical and Chemical Research (RIKEN). ent quantum oscillations between those levels-so-called Rabi oscillations. But whereas natural atoms are driven using visible or microwave photons that excite electrons from one state to another, the artificial atoms in the circuits are driven by currents, voltages, and microwave photons. The resulting electric and magnetic fields control the tunneling of electrons between the superconducting island and ...

Amplitude spectroscopy of two coupled qubits

“…Recently much attention has been focused on the spectroscopy of Josephson junction-superconducting circuits with a weak link which can be considered as "macroscopic atoms" with sizes of the order of tens or hundreds of micrometers 1,2 . Single Josephson-junction qubits are characterized by relatively long relaxation times (tens of microseconds) which allows to consider them as one of the most promising elements for the realization of quantum information processors 3 .…”

Nanomechanical-resonator-assisted induced transparency in a Cooper-pair box system

“…where the CPB qubit states |± z are eigenstates of S z with the excited state |+ z = |e and the ground state |− z = |g , the oscillator states |N ± are position-displaced Fock states, and λ 0 is defined in equation (27). Note that |+, N + and |−, N − form, respectively, an orthonormal basis with M + |N + = δ M N and M − |N − = δ M N , but the states |N + and |N − are not mutually orthogonal and their inner products are given by [53,54] …”

Instabilities of the Dicke model with field interactions

“…It has been attracted considerable attentions recently, mainly due to the fact that the Dicke model is closely related to many recent interesting fields in quantum optics and condensed matter physics, such as the superradiant behavior by an ensemble of quantum dots [2] and Bose-Einstein condensates [3], coupled arrays of optical cavities used to simulate and study the behavior of strongly correlated systems [4], and superconducting charge qubits [5,6]. It is known from the previous studies [7,8,9] that the full DM undergoes the second-order quantum phase transition [10].…”