Microwave control of superconducting cavity and qubit - Revision history

Yifan: /* Experiment */

2021-04-30T07:10:23Z

Experiment

← Older revision		Revision as of 15:10, 30 April 2021
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	=== Experiment ===		=== Experiment ===

			==== Low-power readout====

	[[File:T2_v2.png\|600px\|center]]		[[File:T2_v2.png\|600px\|center]]

	We set the detuning between the qubit drive and the qubit frequency as 0.3MHz which shows an oscillation of 3.3us period. From the Ramsey measurement, we observe an oscillation with about a 2us period, which also has an exponential decay envelope. However, it is still hard to find a proper fit for these data. We can only make a rough estimate for <math>T_{2}^{\star}</math>, that is <math>T_{2}^{\star}</math> is at the range of 15~30us		We set the detuning between the qubit drive and the qubit frequency as 0.3MHz which shows an oscillation of 3.3us period. From the Ramsey measurement, we observe an oscillation with about a 2us period, which also has an exponential decay envelope. However, it is still hard to find a proper fit for these data. We can only make a rough estimate for <math>T_{2}^{\star}</math>, that is <math>T_{2}^{\star}</math> is at the range of 15~30us

			==== High-power readout====
			[[File:T2_hr.png\|600px\|center]]

			This is the Ramsey measurement by the high-power readout. We can observe an oscillation with a wired waveform. It will be checked in the following experiments. We can make a rough estimate for <math>T_{2}^{\star}</math> as 15~30us.

	==References==		==References==

Yifan: /* Experiment */

2021-04-30T06:51:07Z

Experiment

← Older revision		Revision as of 14:51, 30 April 2021
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	=== Experiment ===		=== Experiment ===

	[[File:~~T2_exp~~.png\|600px\|center]]		[[File:T2_v2.png\|600px\|center]]

	We ~~have done several trials with different settings; however,~~ the ~~final measured signal has no behavior of Ramsey oscillation with exponential decay envelope. As we have learned from~~ the qubit ~~spectroscopy, the amplitudes measured indicate~~ the qubit ~~state that around~~ 0.~~6E-6~~ shows ~~the excited state and 1~~.~~3E-6 represents the ground state~~. From the ~~amplitudes measured at the range of 0~~.~~85E-6~~ to 1.~~05E-6~~, ~~it seems~~ that ~~the qubits can be the states between the excited state and the superposition state. Hence we did not obtain an expectation value of the~~ <math>T_{2}^{\star}</math>.		We set the detuning between the qubit drive and the qubit frequency as 0.3MHz which shows an oscillation of 3.3us period. From the Ramsey measurement, we observe an oscillation with about a 2us period, which also has an exponential decay envelope. However, it is still hard to find a proper fit for these data. We can only make a rough estimate for <math>T_{2}^{\star}</math>, that is <math>T_{2}^{\star}</math> is at the range of 15~30us

	~~The reason for this phenomenon may be that our simple measurement setup does not involve~~ the quantum limit amplifier that can provide an accurate measurement of the qubit state. As a compromise, we do a lot of the averaging to extract the qubit information. In the next experiment, we will troubleshoot this issue. Or further, we will implement a high-power readout protocol to improve the accuracy of ~~the measurement.~~

	==References==		==References==

Yifan: /* Low-power readout */

2021-04-30T06:35:37Z

Low-power readout

← Older revision		Revision as of 14:35, 30 April 2021
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	==== Low-power readout====		==== Low-power readout====
	[[File:Time_rabi_I_Q.png\|600px\|center]]		[[File:Time_rabi_I_Q.png\|600px\|center]]
			Correction: The unit of this figure should be in clock cycle which is defined as 1 clock cycle = 4ns in the OPX device.

	In this figure, with the varying pulse length, there is a platform of amplitude at the beginning from 0 to 600ns, representing that the qubit is still in the ground state. One of the possible speculations is that the drive pulse is so week that it cannot excite the qubit, leaving it in the ground state. After 150ns, the I and Q data show a clear sinusoidal waveform. We can find the proper fit for these data as well. From the analysis, the gaussian pulse of 900ns length with amplitude 0.32V, <math>\sigma</math> is 1/6 of pulse length can realize the <math>\pi</math>-pulse of the qubit.		In this figure, with the varying pulse length, there is a platform of amplitude at the beginning from 0 to 600ns, representing that the qubit is still in the ground state. One of the possible speculations is that the drive pulse is so week that it cannot excite the qubit, leaving it in the ground state. After 150ns, the I and Q data show a clear sinusoidal waveform. We can find the proper fit for these data as well. From the analysis, the gaussian pulse of 900ns length with amplitude 0.32V, <math>\sigma</math> is 1/6 of pulse length can realize the <math>\pi</math>-pulse of the qubit.

Yifan: /* High-power readout */

2021-04-30T06:32:41Z

High-power readout

← Older revision		Revision as of 14:32, 30 April 2021
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	[[File:Power_rabi_I_Q_hr.png\|500px\|center]]		[[File:Power_rabi_I_Q_hr.png\|500px\|center]]

	The is the Power Rabi ~~measurement~~ by the high-power readout. We observe that the trace does not have a <math>sin^{2}</math> envelope. The possible reason is that the high-power readout is not calibrated; therefore, the amplitude change is not proportional to the probability of <math>P_{\|1\rangle}</math>. In this project, we did not implement the calibration of the readout protocol.		The is the Power Rabi measured by the high-power readout. The waveform is opposite compared to the result from the low-power readout. This is because, at the high power readout regime, the amplitude change caused by the qubit state is inverse.
			From this Power Rabi, we observe that the trace does not have a <math>sin^{2}</math> envelope. The possible reason is that the high-power readout is not calibrated; therefore, the amplitude change is not proportional to the probability of <math>P_{\|1\rangle}</math>. In this project, we did not implement the calibration of the readout protocol.

	=== Time-Rabi experiment ===		=== Time-Rabi experiment ===

Yifan: /* Time-Rabi experiment */

2021-04-30T06:21:30Z

Time-Rabi experiment

← Older revision		Revision as of 14:21, 30 April 2021
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	In the Time-Rabi experiment, we fix the drive pulse amplitude and sweep the drive pulse length.		In the Time-Rabi experiment, we fix the drive pulse amplitude and sweep the drive pulse length.

			==== Low-power readout====
	[[File:Time_rabi_I_Q.png\|600px\|center]]		[[File:Time_rabi_I_Q.png\|600px\|center]]
	In this figure, with the varying pulse length, there is a platform of amplitude at the beginning from 0 to 600ns, representing that the qubit is still in the ground state. One of the possible speculations is that the drive pulse is so week that it cannot excite the qubit, leaving it in the ground state. After 150ns, the I and Q data show a clear sinusoidal waveform. We can find the proper fit for these data as well. From the analysis, the gaussian pulse of 900ns length with amplitude 0.32V, <math>\sigma</math> is 1/6 of pulse length can realize the <math>\pi</math>-pulse of the qubit.		In this figure, with the varying pulse length, there is a platform of amplitude at the beginning from 0 to 600ns, representing that the qubit is still in the ground state. One of the possible speculations is that the drive pulse is so week that it cannot excite the qubit, leaving it in the ground state. After 150ns, the I and Q data show a clear sinusoidal waveform. We can find the proper fit for these data as well. From the analysis, the gaussian pulse of 900ns length with amplitude 0.32V, <math>\sigma</math> is 1/6 of pulse length can realize the <math>\pi</math>-pulse of the qubit.

	[[File:Time_rabi.png\|600px\|center]]		[[File:Time_rabi.png\|600px\|center]]

			==== High-power readout====

			[[File:Time_rabi_hr.png\|500px\|center]]

			This is the Time Rabi measured by the high-power readout. The flat stage from 0 to 600ns still exists. Since the calibration of high-power readout is not involved, the trace has no proper <math>\sin^{2}</math> waveform. In addition, we can observe an exponential decay envelope for these data, resulting in that the first peak is higher than the second one.

	== T1 measurement==		== T1 measurement==

Yifan: /* High-power readout */

2021-04-30T05:33:26Z

High-power readout

← Older revision		Revision as of 13:33, 30 April 2021
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	==== High-power readout ====		==== High-power readout ====

	[[File:Power_rabi_hr.png\|500px\|~~left~~]]		[[File:Power_rabi_hr.png\|500px\|center]]
	[[File:Power_rabi_I_Q_hr.png\|500px\|~~right~~]]		[[File:Power_rabi_I_Q_hr.png\|500px\|center]]

	The is the Power Rabi measurement by the high-power readout. We observe that the trace does not have a <math>sin^{2}</math> envelope. The possible reason is that the high-power readout is not calibrated; therefore, the amplitude change is not proportional to the probability of <math>P_{\|1\rangle}</math>. In this project, we did not implement the calibration of the readout protocol.		The is the Power Rabi measurement by the high-power readout. We observe that the trace does not have a <math>sin^{2}</math> envelope. The possible reason is that the high-power readout is not calibrated; therefore, the amplitude change is not proportional to the probability of <math>P_{\|1\rangle}</math>. In this project, we did not implement the calibration of the readout protocol.

Yifan: /* High-power readout */

2021-04-30T05:20:21Z

High-power readout

← Older revision		Revision as of 13:20, 30 April 2021
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	==== High-power readout ====		==== High-power readout ====

	~~<gallery widths=500px heights=170px >~~		[[File:Power_rabi_hr.png\|500px\|left]]
	File:Power_rabi_hr.png		[[File:Power_rabi_I_Q_hr.png\|500px\|right]]
	File:Power_rabi_I_Q_hr.png
	</~~gallery~~>		The is the Power Rabi measurement by the high-power readout. We observe that the trace does not have a <math>sin^{2}</math> envelope. The possible reason is that the high-power readout is not calibrated; therefore, the amplitude change is not proportional to the probability of <math>P_{\|1\rangle}</math>. In this project, we did not implement the calibration of the readout protocol.

	=== Time-Rabi experiment ===		=== Time-Rabi experiment ===

Yifan: /* High-power readout */

2021-04-30T05:12:15Z

High-power readout

← Older revision		Revision as of 13:12, 30 April 2021
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	==== High-power readout ====		==== High-power readout ====

	<gallery ~~mode="traditional"~~ widths=500px heights=170px >		<gallery widths=500px heights=170px >
	File:Power_rabi_hr.png		File:Power_rabi_hr.png
	File:Power_rabi_I_Q_hr.png		File:Power_rabi_I_Q_hr.png

Yifan: /* High-power readout */

2021-04-30T05:10:40Z

High-power readout

← Older revision		Revision as of 13:10, 30 April 2021
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	<gallery mode="traditional" widths=500px heights=170px >		<gallery mode="traditional" widths=500px heights=170px >
	File:Power_rabi_hr.png\|		File:Power_rabi_hr.png
	File:Power_rabi_I_Q_hr.png\|		File:Power_rabi_I_Q_hr.png
	</gallery>		</gallery>

Yifan: /* Power-Rabi experiment */

2021-04-30T05:06:09Z

Power-Rabi experiment

← Older revision		Revision as of 13:06, 30 April 2021
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	We can use this Rabi experiment to calibrate any signal qubit rotation gate that rotates the qubit by an angle <math>\theta</math> around a rotation axis which is rotated from the x-axis on the x-y plane, namely <math>R_{\phi}(\theta)</math>, e.g., <math>\pi</math>-rotation and <math>\pi/2</math>-rotation. However, the <math>\phi</math> cannot be determined from the Rabi oscillations.		We can use this Rabi experiment to calibrate any signal qubit rotation gate that rotates the qubit by an angle <math>\theta</math> around a rotation axis which is rotated from the x-axis on the x-y plane, namely <math>R_{\phi}(\theta)</math>, e.g., <math>\pi</math>-rotation and <math>\pi/2</math>-rotation. However, the <math>\phi</math> cannot be determined from the Rabi oscillations.

			==== Low-power readout ====
	[[File:Power_rabi_I_Q.png\|600px\|center]]		[[File:Power_rabi_I_Q.png\|600px\|center]]
	This is the trace of I and Q and their corresponding fits. If we fix the pulse length to 900ns, we can find a relative amplitude of 0.938 to realize a <math>\pi</math>-rotation which flips the qubit state from the ground state to the excited state. Further, half of this relative amplitude generates a <math>\pi/2</math>-rotation resulting in a superposition state.		This is the trace of I and Q and their corresponding fits. If we fix the pulse length to 900ns, we can find a relative amplitude of 0.938 to realize a <math>\pi</math>-rotation which flips the qubit state from the ground state to the excited state. Further, half of this relative amplitude generates a <math>\pi/2</math>-rotation resulting in a superposition state.
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	[[File:Power_rabi.png\|600px\|center]]		[[File:Power_rabi.png\|600px\|center]]
	This ~~the trace of~~ the <math>\|I +~~1i*Q~~\|</math>, which is obviously a sinusoidal waveform. The highest position reveals the ground state while the lowest position represents the excited state. The qubit oscillates between the ground state and the excited state with respect to the amplitude of the qubit Gaussian drive pulse.		This traces the <math>\|I +iQ\|</math>, which is obviously a sinusoidal waveform. The highest position reveals the ground state, while the lowest position represents the excited state. The qubit oscillates between the ground state and the excited state with respect to the amplitude of the qubit Gaussian drive pulse.

			==== High-power readout ====

			<gallery mode="traditional" widths=500px heights=170px >
			File:Power_rabi_hr.png\|
			File:Power_rabi_I_Q_hr.png\|
			</gallery>

	=== Time-Rabi experiment ===		=== Time-Rabi experiment ===