towards quantum computing through superconducting electric circuits

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Towards quantum computing through superconducting electric circuits

Jingying Wang

January 2019

In 1981, Richard Feynman proposed a basic quantum computer model, mainly with the intention of simulating quantum systems efficiently. A notable characteristic of quantum computing is the reliance upon qubits as its basic units, which grants the system its complexity. Physical realizations of qubits are difficult since the quantum effects are difficult to observe due to large uncertainties, per the Heisenberg Uncertainty Principle. Using superconductors, which are materials that has zero electric resistance when placed in extremely low temperatures, macroscopic quantum phenomena can be shown in electric circuits, which then allows for interpretation of a two-state quantum system.

A quantum state is a probability that could predict the possible outcome of an isolated quantum system. Quantum states can be described mathematically by wave functions, which are solutions to the Schrödinger equation - an equation that predicts how wave functions change over time. The principle of quantum superposition details that when quantum states are summed, the result would also be a valid quantum state.

Every quantum state can be represented as a linear combination of two or more states. A qubit, which is the basic unit of information in quantum computing, can have an infinite number of states. It is represented by a linear combination of and where the qubit state readout $/phi$ would be . Here, the coefficients are complex numbers that represent the probability that the qubit is measured as one of the two basic states. Using the fact that qubits have an infinite number of states, quantum algorithms can manipulate them in their unmeasured states. However, the physical realization of a qubit must be able to display quantum phenomena on a readily observable scale.

Superconductors have zero electric resistance, allowing electrons to travel freely through them without colliding with their atoms, thus resulting in no dissipations in terms of heat energy. At extremely low temperatures, atom vibrations are dampened, allowing for zero electric resistance. Using up to 1% of a conventional circuit’s energy, superconducting electric circuits could be very economical, accounting for the costs of cooling. One potential material is niobium nitride, which is a superconductor at 16K, a temperature achievable by cooling through liquid helium. (Berggren, 2014) Another potential candidate is graphene, which, when rotated at a specific “magic angle” of 1.1 degrees, is a superconductor that could operate at 100K. (Chu, 2018) (Fig 1)

The superconductivity of graphene at the magical angle is confirmed through passing a threshold voltage through the lattice structure similar to one demonstrated on the left. (Chu, 2018) Measuring the resistance of the material, the current flowed without energy dissipation when a small amount of electrons were added. Amazingly, graphene’s superconductive property is versatile: changing angles will cause it to disappear, whereby it could also act as a insulator. This allows for further experimentation on graphene to be contained in a single device, and poses it as a potential candidate for quantum-classical hybrid systems.

The most common type of qubit is a charge qubit, a superconducting electric circuit. The circuit diagram is as Fig 2. The Josephson junction (with potential energy accumulated when a current flows through) has two superconductors bridged by a weak insulating barrier, allowing a current to flow continuously without an applied voltage, as per the Josephson effect. (Supraconductivite, n.d.) Connected in parallel with a capacitor C, electrons bound to each other in the circuit to form Cooper pairs due to superconductivity when in low temperature. The circuit operates against a biased voltage U so optimal conditions allow for superconductivity.

When the insulating layer in the Josephson junction is replaced by a semiconducting nanowire, theoretical capacity for hybrid systems are created, as well as circuits involving multiple types of qubits. (Nichol, 2015) Researcher DiCarlo applied an electric field to the nanowire through the gate electrode in Fig. 3, causing the resonance frequency of the qubit to change in a range from megahertz to gigahertz. This allows qubits to be connected to each other, as qubits can be coupled when they are brought in resonance. Potential hybrid systems would involve semiconducting nanowires as well as superconductors, offering cost-flexible solutions for a quantum mechanical physical system.

Works Cited

Nichol, John. “Superconducting metamaterial traps quantum light.” Phys.org. 2015. Web. 19 Jan. 2019. <https://phys.org/news/2018-09-superconducting-metamaterial-quantum.html>

Berggren, Karl. “Superconducting circuits.” MIT News. 17 Oct. 2014. Web. 19 Jan. 2019. <http://news.mit.edu/2014/cheaper-superconducting-computer-chips-1017>

Devoret, M. H.. “Superconducting Circuits for Quantum Information: An Outlook.” Science. American Association for the Advancement of Science, 8 Mar. 2013. Web. 19 Jan. 2019. <http://science.sciencemag.org/content/339/6124/1169>

Jennifer Chu, Mit News Office. “Insulator or superconductor? Physicists find graphene is both.” MIT News. 5 Mar. 2018. Web. 19 Jan. 2019. <http://news.mit.edu/2018/graphene-insulator-superconductor-0305>

“All about superconductivity.” Supraconductivite.fr. n.d. Web. 19 Jan. 2019. <http://www.supraconductivite.fr/en/index.php?p=applications-squid-josephson>