Introduction

In this webinar, we covered the material properties that are most important to consider when developing qubits with longer coherence times and looked into how to characterize these materials accurately and efficiently. By focusing on the fundamental properties of the materials, simpler fabrication methods and experimental setups can be used. Additionally, we showed that it is possible to isolate the source of decoherence by studying each individual component of the final qubit. In the following sections, we summarized the key points of each discussed topic while addressing the remaining questions that were asked during the webinar but not directly answered in the live Q&A session.

The recording of the full webinar can be found here. If you would like to learn more about one of the aspects covered in this webinar or would like to see a live demo of a presented measurement, please reach out to us.

Solid-State Qubits and Decoherence

Solid-state qubits can be controlled and manipulated through the application of electric and magnetic fields. For example, DC voltages applied to gate structures in semiconductor quantum dots may change their shape, altering the orbital energy of the confined charge carriers. Alternatively, a voltage may modify a barrier between adjacent dots and change the level splitting that stems from the charge carriers' ability to tunnel between the two dots. Magnetic fields interact with the spin degree of freedom of confined charge carriers and introduce a Zeeman energy splitting between different states of the spin. In superconducting circuits, magnetic fields can be used to alter the effective Josephson energy of a SQUID loop forming part of a superconducting qubit while oscillating AC voltages can be employed to manipulate a qubit's state directly.

This kind of external control on a quantum system is useful and at times necessary, but any external parameter that can be used to manipulate the state or energy structure of a quantum system may also open the door to decoherence of the quantum state.

Decoherence of a quantum system is caused by its interactions with spurious, uncontrolled degrees of freedom of its environment. There exist two fundamental types of decoherence processes (as shown in Figure 1): relaxation, which is caused by energy exchange with the environment, and dephasing, which originates from random fluctuations of the energy of individual levels of the quantum system. Both types can be caused by fluctuations in external control parameters, but they are characterized by different time scales and rely on different effects of the control parameter. If the external control can induce changes in the quantum state of the system, such as a voltage applied to a superconducting transmon circuit, then fluctuations in this voltage at frequencies close to the system level splitting lead to incoherent relaxation of the quantum state. By contrast, controls that change the energy of certain quantum states of the system - such as the gate voltage modifying the size of a semiconductor quantum dot, which may fluctuate at very slow timescales - can lead to a randomization of the phase of any superposition of these states, and therefore to a loss of phase coherence.

Fluctuations may have many different origins, be it variations in the room-temperature control electronics, radiation or vibrations. But the fundamental properties of the materials used to build the quantum systems themselves - the semiconducting and superconducting films, the insulating substrates as well as the oxides covering all surfaces - will also lead to fluctuations in the control parameters and, in turn, decoherence of the quantum system. Understanding the materials better is thus key to manufacturing coherent quantum systems at scale. Some of the open questions in the field are related to the microscopic origin of two-level defects that are manifest in most solid-state systems, the origin of non-equilibrium quasiparticles often found in superconducting circuits, and the origin of the ubiquitous 1/f-type magnetic noise present on almost any surface ever investigated in dilution refrigerators. Systematic studies are necessary to better understand fabrication processes and variations: careful, sensitive measurements are key to this understanding.

Qubit Component Characterization with Lock-in Amplifiers

The process of understanding the main sources of qubit decoherence starts with the characterization of individual material components. This includes transport measurements of superconducting, metallic, and semiconducting materials, of interconnects and of junctions, and from room temperature down to the low temperatures at which qubits operate. The MFLI Lock-in Amplifier serves as a multi-purpose instrument that measures current (I) and voltage (V) across bulk and low-dimensional structures such as 2D electron gases, nanowires, and quantum dots. When the MFLI is upgraded with the MF-MD and MF-DIG options, it is possible to measure AC and DC conductivity, noise and junction characteristics all at the same time. In cases that require characterization on a large scale, up to 8 MFLIs can be operated simultaneously. Further improvements to the speed of the measurements are possible using RF-reflectometry, an approach that is especially effective for quantum dot characterization. In this configuration, the UHFLI Lock-in Amplifier reads the signal from an LC resonator circuit, operating at a few hundred MHz with dwell times of 1 ms or less (see Figure 2). With a 4-order-of-magnitude speed-up without the loss of insight, the UHFLI is well-positioned for scaling up qubit material characterization.

Resonators - Fast Measurement of Center Frequency and Quality Factor

In addition to characterizing the underlying materials as explained above, measuring a proxy element such as a resonator enables researchers to learn more about their final qubit without the need for fabricating the entire qubit. The Pound-Drever-Hall (PDH) method of resonator tracking is ideal for fast characterization of a resonator’s center frequency and quality factor Q. A full schematic of the PDH feedback loop is shown in Figure 3.

By using multiple sidebands with precise phase control at lower frequencies (from DC to 600 MHz with the UHFLI) and up-converting to the resonator's center frequency, the PDH method allows for fast feedback measurements of arbitrarily high resonator center frequencies. Measuring the fast fluctuations of the center frequency help understand dissipation mechanisms. The UHFLI Lock-in Amplifier is ideally suited to these measurements thanks to its minimum demodulator time constant of 30 ns. Further, the UHFLI provides multi-frequency signal generation with the UHF-MF upgrade option as well as easy sideband generation over a wide dynamic range with the UHF-MOD option. Additionally, the UHF-PID option provides fast feedback control with a feedback loop bandwidth of up to 300 kHz.

Do you want to learn more or would like to request a Live demo? Don't hesitate to reach out to us here.