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NTT technical review

Coherent Coupling between 4300 Superconducting Flux Qubits and a Microwave Resonator

Yuichiro Matsuzaki, Kosuke Kakuyanagi, Hiraku Toida, Hiroshi Yamaguchi, William J. Munro, Shiro Saito

Published Jul 1, 2017• 2 citations
Publisher

Abstract

1 Qubit: In classical computation, a bit to store information can represent either 0 or 1.However, a quantum bit (qubit) obeys quantum mechanics, so the state of a qubit can contain a superposition of 0 and 1. *2 Josephson junction: A structure composed of two superconductors coupled by a thin insulator.This induces a supercurrent that flows without applied voltage due to a tunneling effect.

DOI
10.53829/ntr201707fa5

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1 Qubit: In classical computation, a bit to store information can represent either 0 or 1.However, a quantum bit (qubit) obeys quantum mechanics, so the state of a qubit can contain a superposition of 0 and 1. *2 Josephson junction: A structure composed of two superconductors coupled by a thin insulator.This induces a supercurrent that flows without applied voltage due to a tunneling effect.
The authors propose a qubit-qubit coupling scheme for superconducting flux quantum bits (qubits), where quantized Josephson junction resonator and microwave irradiation are utilized. The junction is used as a tunable inductance controlled by changing the bias current flowing through the junction, and thus the circuit works as a tunable resonator. This enables them to make any qubits interact with the resonator. Entanglement between two of many qubits whose level splittings satisfy some conditions is formed by microwave irradiation causing a two-photon Rabi oscillation. Since the size of the resonator can be as large as submillimeters and qubits interact with it via mutual inductance, their scheme makes it possible to construct a quantum gate involving remote qubits.
The leading approach to attempt quantum computing is based on superconductors. In particular, Circuit Quantum Electrodynamic systems (circuit QED) are used to couple photons stored in a microwave resonator to a quantum bit (qubit), allowing the qubit to be controlled and measured. A lumped element parallel RLC circuit will be used to model a superconducting coplanar microwave resonator, in order to gain an intuitive understanding of how various parameters affect its electromagnetic properties, and how they can be optimised to provide desired specifications. Resonator quality factors will also be realised, which describe the effects of coupling the microwave resonator to external input/output transmission lines. The qubit is generated by a superconducting capacitively shunted Josephson Junction; the transmon, and its operation and non-linear behaviour will be discussed in this report. The transmon is integrated with a microwave resonator to generate the circuit QED system, and the derivation of the systems Hamiltonian will allow us to determine the equations describing the behaviour of the system, and therefore how it may be controlled and measured. The Bloch sphere will be introduced, which provides a useful geometric representation of the state space of a two-level quantum system. Mapping the derived Hamiltonian to the time-dependent Schrodinger equation facilitates realisation of control mechanisms of the qubit based on rotations about the Bloch sphere.
Superconducting circuits containing Josephson junctions have previously been shown to exist in superpositions of states of electric charge and of superconducting phase. This superposition manifests itself in so-called Rabi oscillations between the two energy levels produced by the superposition. In his Perspective, Clarke highlights the report of Chiorescu et al. , who demonstrate that a superconducting ring containing three Josephson junctions also exhibits Rabi oscillations, and thus exists in a superposition of magnetic flux states. The experiments are elegant demonstrations of coherence in superconducting circuits, and are potentially of interest as quantum bits in a future computer.
A quantum computer is an information processing machine, much like an ordinary classical computer, but its function is based on quantum mechanical principles. To be able to construct such a machine would be a fantastic accomplishment---to have total control over a quantum system is a dream for both physicists and science-fiction enthusiasts. The basic information unit in a quantum computer is the quantum bit, or qubit for short. A quantum computer consists of many coupled qubits. To get a single qubit to work properly, would be a major step towards building this machine. Here we study two different qubit ideas. The central element in both setups is the superconducting tunnel junction---the Josephson junction. By connecting the Josephson junctions to standard electronics in a clever way, a qubit can be realised. With these constructions it is in principle very easy to manipulate and read out the quantum probabilities, by varying voltages and currents in time. However, this ease of manipulation has a cost: strong interactions with uncontrolled degrees of freedom of the environment transfer information from the qubit. For superconducting qubits this decoherence is typically very fast. There are ways to deal with the decoherence. One way is to tune the circuit parameters so that the decoherence becomes minimal. Another way is to engineer the qubits so fast so that the effect of decoherence becomes small. In this thesis, we will apply both these strategies. Specifically, the measurement speed of the second qubit we study, turns out to be very sensitive to the topology of the phase space of the detector variables.
We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving, it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.
Quantum computing is a novel paradigm for information processing that promises computational speedup for certain computational tasks while not being driven by Moore's law. Superconducting circuits based on Josephson junctions are one of the leading approaches for implementing the quantum bits, or qubits, in a quantum processor. Most superconducting qubit architectures involve circuit quantum electrodynamics, where the qubits are analogous to artificial atoms that are coupled to superconducting linear resonant cavities. This scheme allows for the readout of individual qubits, the manipulation of single-qubit states, and the generation of entanglement between qubits. The performance of current state-of-the-art systems is limited by decoherence of the qubits and associated gate errors. Nonetheless, experiments have been performed that already demonstrate a significant computational speedup compared to classical processing. Future implementations of fault-tolerant quantum computers will require the development of quantum error correction. Initial tests of elements of error correction in superconducting qubit arrays are underway.