Quantum Computing. Melanie Swan

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3.3.2 Superconducting circuits: Standard gate model

      The most prominent approach to quantum computing is superconducting circuits. Qubits are formed by an electrical circuit with oscillating current and controlled by electromagnetic fields. Superconductors are materials which have zero electrical resistance when cooled below a certain temperature. (In fact, it is estimated that more than half of the basic elements in the periodic table become superconducting if they are cooled to sufficiently low temperatures.) Mastering superconducting materials could be quite useful since as a general rule, about 20% of electricity is lost due to resistance. The benefit of zero electrical resistance for quantum computing is that electrons can travel completely unimpeded without any energy dissipation. When the temperature drops below the critical level, two electrons (which usually repel each another) form a weak bond and become a so-called Cooper pair that experiences no resistance when going through metal (tunneling) and which can be manipulated in quantum computing.

      Superconducting materials are used in quantum computing to produce superconducting circuits that look architecturally similar to classical computing circuits, but are made from qubits. There is an electrical circuit with oscillating current in the shape of a superconducting loop that has the circulating current and a corresponding magnetic field that can hold the qubits in place. Current is passed through the superconducting loop in both directions to create the two states of the qubit. More technically, the superconducting loop is a superconducting quantum interference device (SQUID) magnetometer (a device for measuring magnetic fields), which has two superconductors separated by thin insulating layers to form two parallel Josephson junctions. Josephson junctions are key to quantum computing because they are nonlinear superconducting inductors that create the energy levels needed to make a distinct qubit.

      Specifically, the nonlinearity of the Josephson inductance breaks the degeneracy of the energy-level spacings, allowing the dynamics of the system to be restricted to only the 2-qubit states. The Josephson junctions are necessary to produce the qubits; otherwise, the superconducting loop would just be a circuit. The point is that the linear inductors in a traditional circuit are replaced with the Josephson junction, which is a nonlinear element that produces energy levels with different spacings from each other that can be used as a qubit. Josephson (after whom the Josephson junction is named) was awarded the Nobel Prize in Physics in 1973 for work predicting the tunneling behavior of superconducting Cooper pairs.

      As an example of a superconducting system, Google’s qubits are electrical oscillators constructed from aluminum (niobium is also used), which becomes superconducting when cooled to below 1 K (−272°C). The oscillators store small amounts of electrical energy. When the oscillator is in the 0 state, it has zero energy, and when the oscillator is in the 1 state, it has a single quantum of energy. The two states of the oscillator with 0 or 1 quantum of energy are the logical states of the qubit. The resonance frequency of the oscillators is 6 gigahertz (which corresponds to 300 millikelvin) and sets the energy differential between the 0 and 1 states. The frequency is low enough so that control electronics can be built from readily available commercial components and also high enough so that the ambient thermal energy does not scramble the oscillation and introduce errors. In another example, Rigetti has a different architecture. This system consists of a single Josephson junction qubit on a sapphire substrate. The substrate is embedded in a copper waveguide cavity. The waveguide is coupled to qubit transitions to perform quantum computations (Rigetti et al., 2012).

      3.3.2.1Superconducting materials

      Superconducting materials is an active area of ongoing research (Table 3.2). The discovery of “high-temperature superconductors” in 1986 led to the feasibility of using superconducting circuits in quantum computing (and the 1987 Nobel Prize in Physics) (Bednorz & Muller, 1986). Before high-temperature superconductors, ordinary superconductors were known materials that become superconducting at critical temperatures below 30 K (−303°C), when cooled with liquid helium. High-temperature superconductors constitute advanced materials because transition temperatures can be as high as 138 K (−135°C), and materials can be cooled to superconductivity with liquid nitrogen instead of helium. Initially, only certain compounds of copper and oxygen were found to have high-temperature superconducting properties (for example, varieties of copper oxide compounds such as bismuth strontium calcium copper oxide and yttrium barium copper oxide). However, since 2008, several metal-based compounds (such as iron, aluminum, copper, and niobium) have been found to be superconducting at high temperatures too.

Table 3.2. Superconducting materials.