ENGINEERING AND OPERATING A SUPERCONDUCTING WAVEGUIDE QED SYSTEM
3.3 Experimental setup and operation
The experimental setup and operation used in this thesis follows common practice in superconducting qubit experiments and is detailed in App.B-Dand Sec. 3.3-3.4 of [133]. In the following, we highlight a few aspects that have played an important role in improving the qubit coherence and performing multi-qubit operations.
Thermalization of the waveguide
The cryogenic setup used for experiments in this thesis follows the general rules of cryogenic engineering [176]. In addition, for waveguide QED experiments, especially the ones in the passband regime, minimizing the thermal photon number in the waveguide is crucial to prevent extra dephasing of qubits [176–179] that directly see the waveguide photons. Detailed in Chapter4and App.B, we have used well-thermalized attenuators to achieve better thermal anchoring of the waveguide to the mixing chamber plate. More specifically, we have used the cold attenuators
from B. Palmer’s group [177] or commercial attenuators1, all of which have been anchored to their cryogenic stage directly or via thick copper pieces for good thermal conduction.
Grounding
In this subsection, we emphasize the importance of reducing the ground noise, which has been the limitation on the qubit coherence in our setup. The ability to tune the frequency of a qubit also introduces a channel for additional frequency noise, i.e., dephasing. The Z line—responsible for tuning the qubit frequency via the current—is shorted to the ground close to the SQUID (Fig.3.1a), thus coupling the ground noise to the qubit. As pedagogically elaborated in Chapter 3 of [180], careless ground connections could result in ground noise from noisy instruments and ground loops that can pick up noisy ground current or magnetic field.
The immediate ground a qubit sees in the dilution refridgerator (DF in short) is the cryostat ground. The Bluefors LD-250 DF we use is designed to be electrically floating (>1MΩ), isolated from the gas handling unit and the DF frame, such that it can be connected to a clean ground. During the DF installation and subsequent in- stallations of new pieces especially on top of the DF, we need to be careful that metal pieces including bolts and nuts2do not make accidenta electrical connection. After making changes to the cryostat connection, we should check whether the electrical isolation is maintained. Besides connected to a clean ground, the cryostat ground is connected to the power supply of high-electron-mobility transistor (HEMT) ampli- fiers, in which case the use of low-noise power supply is necessary3. The majority of the signal lines connected to the DF only carry high frequency signals, where inner-outer DC blocks4 can be used to break the formation of ground loops at low frequency. The DC connection to the DC voltage source for Z lines is necessary, demanding careful electrical connection design5. The DC connection to arbitrary waveform generator (AWG6) channels producing flux pulses is also unavoidable be-
1QMC-CRYOATT from Quantum Microwave or 4880-5523-XX-CRYO from XMA
2We use Polyethylene Terephthalate (PET) wraps for metal tubes and nylon bolts and nuts if necessary.
3We avoid using switching mode power supplies that is noisier than their linear counterparts. In out setup, we use LNF-PBA linear power block from Quantum Microwave.
4Inmet 8039 or CD9519 from Centric RF
5We mount the breakout board and the DC voltage source (QDAC from QDevil) to an instrument rack via nylon bolts and nuts. In addition, we use a USB isolator (UH401 from B&B SmartWorx) to break the electrical connection via the USB connection port.
6Quantum Machines OPX+
cause rejecting the DC component of the flux pulses leads to severe pulse distortion.
We take care of the AWG ground by electrically isolating the instrument chassis from the rack and using EM interference filtering units7to connect the AWG to the power strip.
Voltage supply
VG Ground loop
Z line VS
•
•
L L
M LZ
•
•
L
M L LZ
VG
a b c
Figure 3.6: Ground loop and common-mode choke. a, Circuit diagram showing a voltage supply providing tuning current for a Z line, whereas the connection to ground at the Z line and the voltage supply creates a ground loop with the noise voltage VG. b, Circuit diagram showing voltage supply VS creating a differential mode current (arrow) to bias the Z line (LZ), which is not affected by the common mode choke (L = M). c, Circuit diagram showing the ground noise VG creating common mode currents (arrows) that could influence the Z line current, which sees the impedancejωLfrom the common mode choke (L=M). This figure is inspired from [180].
From the above analysis, we see that the cryostat ground is still inevitably con- nected to the earth ground at multiple points, forming ground loops (Fig. 3.6a).
To reduce the noise from the ground loops, we use common-mode chokes to sup- press the influence from ground noise [180]. A common-mode choke introduces mutual inductance between the signal line and the return line, resulting in a large impedance for the common-mode current from the ground noise while maintaining zero impedance for the differential-mode current from the signal source (Fig.3.6b- c). In practice, the common-mode choke can be implemented by wrapping the transmission line around a Ferrite ring or surrounding the transmission line with Ferrite snap-on beads8.
To probe the noise level when implementing the above measures, we either measure the spectrum by connecting a transmission line from the DF to a spectrum analyzer or measuring the coherence time of a qubit. The spectrum analyzer measurement is especially quick and useful when the device is at room temperature or when the flux lines are not connected to the qubits. Using this method, we have observed
7AREC148FG-N515 from OnFilter
8We use both Mix 31 Ferrite covering 1-300 MHz and Mix 75 Ferrite covering 150 kHz-10 MHz.
that the common-mode chokes play the role of lowering the noise power. The qubit coherence is the ultimate target to optimize. For example, we have observed that adding a single Ferrite snap-on bead9 on the flux pulse line improves theT2∗ from 733 ns to 938 ns, which is further improved to 1.1µs with 15 beads.
Multi-qubit system operation
Calibrating and operating a multi-qubit system requires systematic approaches, in- volving individual-qubit-level up to system-level operations. It is not realistic to manually specifying the dependencies among the operations and assigning param- eters to all the tuning knobs for every experiment. To operate a multi-qubit or even a NISQ device, we need both efficient infrastructure and strategies.
An efficient infrastructure in our case means a platform that registers and manages resources for easy access from high-level users. The resources include hardware resources, which can be categorized as classical hardware (such as the AWG and the DC voltage supply) and quantum hardware (such as a quantum simulator). The resources also include software ones such as the parameters for a control pulse.
In this thesis, we build the infrastructure based on the QUA language developed by Quantum Machines that programs OPX+, which is in charge of qubit control and read-out. The compatibility of the QUA language with the Python environ- ment allows us to register and control other hardware in a single script. The QUA language also provides the abstraction of low-level controls, e.g., wrapping the ar- bitrary waveform of aπ-pulse operation onInput line 1intoplay(’pi’, ’q1’). The parameters, such as the ones providing details for the pulses and the physical connections are specified in theconfiguration. To achieve higher-level abstrac- tion and include parameters specifying the status of the quantum hardware or control over other classical hardware, we construct the quantum processing unit database (qpu_db), which is based on the packages10developed by Quantum Machines.
Equipped with the above infrastructure, we can develop strategies to operate the multi-qubit system. The ultimate goal is to construct a routine that efficiently or even automatically calibrates the system and performs the experiments we have designed. Towards this goal, we use graph-based strategies [181] supported by the Quantum Machines packages. In our case, an experiment consists of multiple functional graphs, e.g., a graph for classical hardware calibration, a graph for
9Mix 75, SNO75-1/2 from Palomar Engineers
10entropylabandentropylab_qpudb. https://github.com/entropy-lab/entropy
Quantum chaotic evolution
Single_Q_CalGraphs
Experiment
Multi_Q_Cal Many-body_Evol
Nodes
Q1_spec Q2_spec
Q10_spec
Multi_Q tuning
Q1_spec Q2_spec
Q10_spec
Q1_Rabi Q1_readout_opti Q2_Rabi Q2_readout_opti
Q10_Rabi Q10_readout_opti
Node execution
Input qpu_db
Prepare Run_prog
(QUA) Analyze_data
qpu_db
Classical hardware Quantum hardware
QDAC LO OPX+
Quantum simulator
Config Input
••• ••• ••• •••
• • •
• • • • •
• • •
Figure 3.7: Multi-qubit system operation. An example experiment (Quan- tum chaotic evolution) consists of three graphs: single-qubit calibration graph (Single_Q_Cal), multi-qubit calibration graph (Multi_Q_Cal), and many-body evolution graph (Many-body_Evol). The graphSingle_Q_Calconsists of multi- ple nodes with inter-dependency, including Qjspectroscopy (Qj_spec), multi-qubit bias tuning (Multi_Qtuning), Qj Rabi (Qj_Rabi), and Qj read-out optimization (Qj_readout_opti). The node Q10_spec takes the input parameters and the qpu_db to prepare the control of classical hardware such as QDAC and the local oscillators (LO), and generate theconfiguration(config) to feed into the QUA program (Run_prog). The QUA program controls the OPX+, which both sends signals into and collect information from the quantum simulator. The node then analyzes and visualizes the data (Analyze_data), and updates theqpu_dbfor the next node.
single-qubit calibration, and a graph for multi-qubit experiment. These graphs can be run sequentially or individually depending on the users’ demand. Each graph consists of multiple nodeswhich complete specific calibrations or operations such as qubit spectroscopy, optimal read-out condition calibration, or tuning all qubits on-resonance to interact under the Hamiltonian. Each node is defined in a relatively generic way such that it can be used for different elements and parameters. More specifically, when initializing a node, we pass input parameters such as the qubit
label, the sweeping range, and the center frequency into a qubit spectroscopy node.
By specifying these node parameters and the dependency among the nodes, we have constructed a graph. During the execution of nodes on the directed graph, it is important to keep track of the parameters renewed from the calibrations, where the infrastructure qpu_db plays the role of registering the most up-to-date status of the system. Within each node, the program takes the input parameters and the current qpu_db to update the status of classical hardware and construct the configurationto control the OPX+. After the operation, the node is responsible of collecting and analyzing the data, as well as updating theqpu_dbif necessary. A structural illustration of running an experiment is shown in Fig.3.7.
The above infrastructure and graph-based strategies have enabled the automatic experimental run starting from single-qubit calibration, multi-qubit calibration, to chaotic quantum many-body evolution described in Chapter6. The automatic run can continue for more than 10 hours under the usual condition that the experimental system is stable. Although not yet implemented, the running strategies can be further developed to handle more complicated situations such as checking whether a calibration remains valid and running partial calibrations as needed [181].
C h a p t e r 4