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arXiv:1304.0645 · Physical Review Letters

Fluxon Readout of a Superconducting Qubit

Kirill G. Fedorov, Anastasia V. Shcherbakova, Michael Johannes Wolf, D. Beckmann, Alexey Vladimirovich Ustinov

Published Apr 25, 2014• 63 citations
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Abstract

An experiment demonstrating a link between classical single-flux quantum digital logic and a superconducting quantum circuit is reported. We implement coupling between a moving Josephson vortex (fluxon) and a flux qubit by reading out of a state of the flux qubit through a frequency shift of the fluxon oscillations in an annular Josephson junction. The energy spectrum of the flux qubit is measured using this technique. The implemented hybrid scheme opens an opportunity to readout quantum states of superconducting qubits with the classical fluxon logic circuits.

DOI
10.1103/physrevlett.112.160502

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Applied Physics Letters•Dec 3, 2007•2 citations
An experiment demonstrating a link between classical single-flux quantum digital logic and a superconducting quantum circuit is reported. We implement coupling between a moving Josephson vortex (fluxon) and a flux qubit by reading out of a state of the flux qubit through a frequency shift of the fluxon oscillations in an annular Josephson junction. The energy spectrum of the flux qubit is measured using this technique. The implemented hybrid scheme opens an opportunity to readout quantum states of superconducting qubits with the classical fluxon logic circuits.
Experiments towards realizing a readout of superconducting qubits by using ballistic Josephson vortices are reported. We measured the microwave radiation induced by a fluxon moving in an annular Josephson junction. By coupling a flux qubit as a current dipole to the annular junction, we detect periodic variations of the fluxon's oscillation frequency versus magnetic flux through the qubit. We found that the scattering of a fluxon on a current dipole can lead to the acceleration of a fluxon regardless of a dipole polarity. We use the perturbation theory and numerical simulations of the perturbed sine-Gordon equation to analyze our results.
In the quest to build a fault-tolerant quantum computer, superconducting circuits based on Josephson junctions have emerged as a leading architecture. Coherence times have increased significantly over the last two decades, and processors with ∼ 50 qubits have been experimentally demonstrated. These systems traditionally utilize microwave frequency control signals, and heterodyne based detection schemes for measurement. Both of these techniques rely heavily on room temperature microwave generators, high-bandwidth lines from room temperature to millikelvin temperatures, and bulky non-reciprocal elements such as cryogenic microwave isolators. Reliance on these elements makes it impractical to scale existing devices up a single order of magnitude, let alone the 5-6 orders of magnitude needed for performing fault-tolerant quantum algorithms. Here, I present results that suggesting superconducting digital logic, namely Single Flux Quantum (SFQ) logic, can replace analog control and measurement techniques, avoiding the significant overhead involved. I describe a scheme for measuring qubits with a device known as a Josephson Photomultiplier (JPM), which crucially stores the result of a qubit measurement in a classical circulating supercurrent within the device and allows for integration with SFQ detection circuitry. This technique is experimentally demonstrated, with single-shot measurement fidelity of 92%. Two methods for accessing this measurement result are presented, one utilizing ballistic fluxons, and another utilizing flux comparison. Initial experimental results of the latter are presented. In addition, I describe a scheme for controlling qubits with sequences of digital SFQ pulses. This method is then used to control a qubit without a microwave signal generator, with results of an average single-qubit gate fidelity of around 95%. When combined, these techniques form a nearly fully digital interface to superconducting qubits, which could allow these systems to scale much more easily.
As superconducting quantum processors increase in size and complexity, the scalability of standard techniques for qubit control and readout becomes a limiting factor. Replacing room temperature analog components with cryogenic digital components could allow for the realization of systems well beyond the current state-of-the-art qubit arrays with tens of qubits. The standard technique for performing a qubit measurement with heterodyne readout uses a quantum-limited cryogenic amplifier chain and requires bulky microwave components inside the refrigerator with multiple control lines and pump signals. Additionally, the result is only accessible in software at room temperature. An alternative method for measuring qubits involves mapping the qubit state onto the photon occupation in a microwave cavity, followed by subsequent photon detection using a Josephson photomultiplier (JPM). The JPM measures the qubit and stores the result in a classical circulating current. To make use of this result, we can leverage existing single flux quantum (SFQ) circuitry. An underdamped Josephson transmission line (JTL) can be coupled to the JPM and fluxons traveling along the JTL are accelerated or delayed, depending on the circulating current state of the JPM. This fluxon delay can then be converted to an SFQ logic signal resulting in a digital qubit readout with a proximal microfabricated device, paving the way for cryogenic digital feedback necessary for error-correcting codes.
We present the results of an analytical study and numerical simulation of the dynamics of a superconducting three-Josephson-junction (3JJ) flux qubit magnetically coupled with rapid single-flux quantum (RSFQ) logic circuit, which demonstrate the fundamental possibility of implementing the simplest logic operations at picosecond times, as well as rapid non-destructive readout. It is shown that when solving optimization problems, the qubit dynamics can be conveniently interpreted as a precession of the magnetic moment vector around the direction of the magnetic field. In this case, the role of magnetic field components is played by combinations of the Hamiltonian matrix elements, and the role of the magnetic moment is played by the Bloch vector. Features of the 3JJ qubit model are discussed during the analysis of how the qubit is affected by exposure to a short control pulse, as are the similarities between the Bloch and Landau-Lifshitz-Gilbert equations. An analysis of solutions to the Bloch equations made it possible to develop recommendations for the use of readout RSFQ circuits in implementing an optimal interface between the classical and quantum parts of the computer system, as well as to justify the use of single-quantum logic in order to control superconducting quantum circuits on a chip.
The states of superconducting quantum bits, as the Josephson phase qubits and flux qubits, are distinguished by magnetic flux generated by a persistent current in a superconducting loop. As the readout circuit contributes decoherence, its coupling to the qubit should be made as weak as possible. We demonstrate a method to maximize the measurement contrast of the two qubit states, thus allowing to significantly decrease the coupling to the readout. This technique is promising for multiqubit circuits since it allows to read out the states of several qubits by using a single readout circuit.