Readout for Phase Qubits without Josephson Junctions
We present a novel readout scheme for phase qubits which eliminates the read-out SQUID so that the entire qubit and measurement circuitry only requires a single Josephson junction. Our scheme capacitively couples the phase qubit directly to a transmission line and detects its state after the measurement pulse by determining a frequency shift observable in the forward scattering parameter of the readout microwaves. This readout is extendable to multiple phase qubits coupled to a common readout line and can in principle be used for other flux biased qubits having two quasi-stable readout configurations.
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The reliable identification of the quantum state occupation probability of a qubit with high fidelity without introducing detrimental system complexity has been at the center of attention in the design and operation of superconducting qubits in recent yearsNakamura et al. (1999); Martinis et al. (2002); Lang et al. (2003); Robertson et al. (2005). Over the years these trade-offs were optimized for various types of qubits to enhance overall qubit performance Wallraff et al. (2004); Lupascu et al. (2004); Siddiqi et al. (2006). Although some of these new methods could also apply to the phase qubit, measurement techniques for these qubits have remained largely unchanged. The switching of a two or three Josephson junction SQUID into its normal state remains the main technique to identify the qubit state of a phase qubit Palomaki et al. (2006); Ansmann et al. (2009); Hofheinz et al. (2009).
In this letter, we show a novel phase qubit read-out method Farinelli et al. (05/23/2008) which eliminates the SQUID and its associated dissipation entirely Lang et al. (2003). By removing the SQUID we also reduce the number of required Josephson junctions from three or four to only a single Josephson junction, thereby dramatically improving the overall device yield.
The measurement of phase qubits is typically done in two steps (e.g. Cooper et al. (2004)). First, the quantum state is ”measured” by taking advantage of the potential energy landscape such that post measurement the system is in one of two quasi-stable configuration depending on the quantum state prior to measurement. This step has been demonstrated with large single-shot fidelities and reliable performance Ansmann et al. (2009). Finally, the qubit is ”read out” by identifying which of the quasi-stable configurations the system is in. By convention we refer to these configurations as the left (L) and right (R) configuration. Because the L and R configurations correspond to a large difference of the circulating current in the qubit, the obvious choice has been to flux couple a SQUID to the qubit and detect the current at which a SQUID switches to its voltage state. The configuration, L or R, can be identified with high confidence using the SQUID, usually without significant backaction. Recently, however there has been mounting evidence that the SQUID does indeed limit qubit coherence times or at least drastically impacts the repetition rate of the experiment Lang et al. (2003); com ().
Because the L and R configurations in a phase qubit have dramatically different resonance frequencies we propose to identify the system configuration by probing the qubit with microwave pulses using dispersive techniques Wallraff et al. (2004); Lupascu et al. (2004); Siddiqi et al. (2006). We estimate that the correct identification of the L or R configuration is possible with high certainty given read-out times comparable to those using the SQUID. The new technique is made possible by directly coupling the qubit to a microwave feedline and probing the amplitude or phase response of a microwave pulse that passes by the qubit. The new readout is compatible with all existing state-of-the-art phase qubit techniques, including reset and measurement.
We have successfully implemented the most basic operations of this microwave based read out technique. Here we present our experimental results and speculate on further improvements. Because the operation and ”measurement” of the phase qubit does not change dramatically in our implementation we are able to base our design on published literature Cooper et al. (2004); Ansmann et al. (2009); Hofheinz et al. (2009). The basic layout of the qubit circuit is shown in Fig. 1a. We chose a capacitively shunted phase qubit to minimize the number of junction two-level systems in the qubit spectroscopy and maximize measurement fidelity Steffen et al. (2006). In order to ensure long coherence times of the qubit we fabricated the shunting capacitor using an interdigitated comb with the ends shorted together to eliminate parasitic cavity modes com (). The target value for the shunting capacitor is pF. The qubit loop is designed gradiometrically with pH to eliminate sensitivities to stray flux variations and reducing flux coupling to the microwave feedline. The coupling capacitor is chosen to be fF which should limit to about ns for a qubit frequencies near GHz O’Connell et al. (2008).
The fabrication was similar to ref Steffen et al. (2010). An optical micrograph of the fabricated qubit is shown in Fig. 1b. The sample was mounted inside an RF-tight box and cooled down in a dilution refrigerator. The bias lines were configured as outlined in Fig. 1c. The flux bias line is filtered with a low pass bronze powder filter, matched to impedance, with a GHz cut-off frequency Milliken et al. (2007).
The qubit is calibrated by executing a pulse sequence similar to the one shown in Fig. 2. A reset pulse is applied to the flux line and added to the flux bias line via a DC-block at room temperature. However, neither the microwave pulse ”rotate” nor the subsequent measurement pulse ”measure” is applied to the qubit. The microwave readout signal is mixed with itself rather than a separate microwave source tuned to the same frequency to eliminate phase drift between the microwave generators. The resultant I and Q signals at DC are filtered and digitized using an Acqiris data acquisition board and averaged on board using sufficient averages for acceptable signal-to-noise ratios. We then plot the amplitude response versus flux in Fig. 3. To better visualize the results we plot the negative amplitude for a negative reset pulse (black) and the positive amplitude for a positive reset pulse (white). Whenever the qubit is hysteretic (between and ) the frequency response is vastly different depending on which reset pulse was applied, showing that the L and R configurations have very different resonant frequencies.
We now set the DC flux to which is close to the edge of where hysteresis observed. Depending on the reset pulse two resonance frequencies can be observed. The lower one corresponds to the configuration in which the phase is located in the shallow well (L configuration) - this is the configuration where the qubit is operated. The higher one, , corresponds to the R configuration. We are interested in because this is the expected resonant frequency after the phase tunnels from the L to R configuration during measurement. From here on all experiments follow standard phase qubit protocols with the only difference being how the signal is measured. In this case we measure the amplitude response at with respect to the reference, defined by the result obtained when the measurement pulse is absent. In principle we only need to calibrate the reference once, but we obtain improved results by continually recording the reference value because of small drifts. Also note since we choose to average the homodyne voltage on the data acquisition card, we are not performing a single shot read out. Due to the dB of attenuation the signal is reduced almost a factor of ten so that the high fidelity single shot acquisition times for would have been prohibitively long ( ms assuming the experiment is limited to the noise generated by the HEMT). By replacing the attenuators with properly designed isolators it will be possible to reduce the required acquisition times to s, comparable to those using a SQUID based single-shot read out.
Following standard phase qubit pulse sequences we are able to characterize the qubit. We show in Fig. 4 the results for Rabi oscillations and a experiment for a qubit frequency of GHz ( GHz). The energy relaxation time is found to be approximately ns. We believe this value is limited by because a separate sample using a SQUID based read out gave ns and because ns is close to the observed coherence time. An improvement in should therefore be possible by simply reducing the size of the coupling capacitor.
We have clearly demonstrated the basic principle of a new microwave method of reading out phase qubits. It is instructive to discuss how the current implementation relates to other experimental practicalities as well as to scalability. The most significant drawback of our technique is the fact that the times of the qubit are somewhat affected by the coupling to the feedline. This is perfectly acceptable, however, if one is interested in studying qubit spectroscopy Kline et al. (2009). However, because of the large size of frequency shifts for the L and R configurations we believe that it should be possible to also circumvent this limitation. By coupling the qubit to other linear elements we estimate it should still be possible to observe a frequency shift dependent on the qubit configuration without limiting coherence times com (). We note that our proposed scheme is a step towards multiplexing many phase qubits off a single feedline, similar to readout schemes for photon detectors Day et al. (2003).
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