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arXiv:cond-mat/0611680 · Physical Review B

Reading out the state of a flux qubit by Josephson transmission line solitons

Arkady Fedorov, Alexander Shnirman, Gerd Schön, Anna Kidiyarova-Shevchenko

Published Jun 7, 2007• 48 citations
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Abstract

We describe the readout process of the state of a Josephson flux qubit via solitons in Josephson transmission lines (JTLs) as they are in use in the standard rapid single flux quantum technology. We consider the situation where the information about the state of the qubit is stored in the time delay of the soliton. We analyze dissipative underdamped JTLs, take into account their jitter, and provide estimates of the measuring time and efficiency of the measurement for relevant experimental parameters.

DOI
10.1103/physrevb.75.224504

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We describe the readout process of the state of a Josephson flux qubit via solitons in Josephson transmission lines (JTLs) as they are in use in the standard rapid single flux quantum technology. We consider the situation where the information about the state of the qubit is stored in the time delay of the soliton. We analyze dissipative underdamped JTLs, take into account their jitter, and provide estimates of the measuring time and efficiency of the measurement for relevant experimental parameters.
A detailed design is given for a flux qubit readout using ballistic fluxons. In this scheme, fluxons propagate through an underdamped Josephson transmission line (JTL) coupled to the qubit, whose state affects the fluxon propagation time. For strong qubit–JTL coupling, and far from the symmetry point, a qubit can be measured with fidelity greater than 99% and measurement time of 4 ns. The readout circuit requires additional rapid single flux quantum (RSFQ) interface circuitry to launch and receive the delayed flux solitons. The parameters of this driver and receiver have been optimized to produce low fluxon speed at launch and impedance matching at the receiver. The delayed solitons are compared to a reference line using a detector with time resolution of better than 16 ps. Both the JTL and RSFQ interface were designed for the Nb 30 A cm −2 process developed at VTT, Finland, with postdeposition of the Al qubit at IPHT, Germany.
We theoretically investigate a readout scheme of the quantum state of a superconducting qubit based on time delay of a single flux quantum (SFQ), also known as a fluxon, propagating in a Josephson transmission line (JTL). We concretely study the time-delay readout based on capacitive coupling between a transmon qubit and a JTL, and we evaluate the time delay depending on the qubit state. We also reveal a feature of the absence of fluxon pinning and exponential suppression of nonadiabatic transitions caused by the propagating fluxon, which is advantageous for the time-delay readout. We extend the analysis to a multi-level transmon as well. Owing to the spectral gap in the JTL, the radiative decay of the qubit mediated by the JTL is exponentially suppressed, and thus the transmission line itself also serves as a filter protecting the qubit. The readout scheme requires neither complicated wiring to low-temperature stages nor bulky microwave components, which are bottlenecks for integration of a large-scale superconducting quantum computer.
We suggest a magnetic flux detector that can be optimized with respect to the measurement back action, e.g., for the situation of quantum measurements. The detector is based on manipulation of ballistic motion of individual fluxons in a Josephson transmission line (JTL), with the output information contained in either probabilities of fluxon transmission and reflection, or time delay associated with the fluxon propagation through the JTL. We calculate the detector characteristics of the JTL and derive equations for conditional evolution of the measured system both in the transmission and reflection and the time-delay regimes. Combination of the quantum-limited detection with control over individual fluxons should make the JTL detector suitable for implementation of nontrivial quantum measurement strategies, including conditional measurements and feedback control schemes.
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.
A direct technique for the measurement of jitter in a Josephson transmission line (JTL), which is similar to an approach used to measure complementary metal-oxide-semiconductor latch metastability, is presented. The experiment yields a one-sigma jitter value of 74 fs per JTL stage in 1 kA/cm2rapid single flux quantum technology. The experimental configuration has been modeled with JSIM, and the result agrees with the experimental data. Additionally, an analytical model has been developed to assess the scaling of the jitter-to-stage delay ratio with critical current density of the Josephson junctions comprising the JTL. Finally, we compare the measured upper bound jitter per stage of a 65-nm complementary metal-oxide-semiconductor inverter chain with that of a 1 kA/cm2JTL.