Materials in superconducting quantum bits
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troduction “Superconducting artificial atoms” are electronic circuits comprising lithographically defined Josephson tunnel junctions, inductors (L), capacitors (C), and interconnects.1 Conceptually, they begin as linear LC resonant circuits (i.e., simple harmonic oscillators), which are then made anharmonic to varying degrees by adding a nonlinear inductive element, the Josephson junction (JJ) (see Figure 1). When cooled to dilution refrigerator temperatures (∼20 millikelvin), these superconducting circuits behave as quantum mechanical oscillators (e.g., “artificial atoms”) exhibiting quantized states of electronic charge, magnetic flux, or junction phase depending on the design parameters of the constituent circuit elements. Such superconducting artificial atoms have already proven to be a useful vehicle for advancing our general understanding of coherence, quantum mechanics, and atomic physics, particularly in regimes not easily accessible with natural atoms and molecules (for reviews, see References 1–6). The term “superconducting qubit” generally refers to the ground and first-excited state of a superconducting artificial atom. Due to the anharmonicity imparted by the JJ, the ground and first-excited states may be uniquely addressed at a frequency, f01, without significantly perturbing the higher-excited states of the artificial atom. These two-lowest states thereby form an effective two-level system (i.e., a
pseudo-“spin-1/2” system), and it is this degree of freedom that is used as the qubit, a quantum bit of information. As quantum mechanical objects, superconducting qubits can be coherently controlled, placed into quantum superposition states, exhibit quantum interference effects, and become entangled with one another. The time scale over which a superconducting qubit maintains this type of quantum mechanical behavior, and thereby remains viable for quantum information applications, is generally called the “coherence time.” The rate at which the qubit loses coherence is related to its interactions with the uncontrolled degrees of freedom in its environment. Within a standard (Bloch-Redfield) picture for spin-1/2 systems, there are two characteristic decay rates that contribute to coherence loss: Γ1 ≡
Γ2 ≡
1 T1
1 1 1 = + T2 2T1 Tϕ
The first is the longitudinal relaxation rate (energy decay rate) Γ1 = 1/T1, which characterizes the time T1 over which the qubit exchanges energy with its environment. Although T1 generally refers to both energy absorption and emission processes, for typical superconducting qubits, the qubit level splitting is
William D. Oliver, Lincoln Laboratory, Massachusetts Institute of Technology; [email protected] Paul B. Welander, SLAC National Accelerator Laboratory; [email protected] DOI: 10.1557/mrs.2013.229
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MRS BULLETIN • VOLUME 38 • OCTOBER 2013 • www.mrs.org/bulletin
© 2013 Materials Research Society
MATERIALS IN SUPERCONDUCTING QUANTUM BITS
box (a charge qubit) by Nakamura and co-workers in 1999.8 In 2002, Vion et al.9 developed the quantronium qubit (a modified charge qub
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