Session S36: Spin Qubit Measurement I

Theoretical Constructions of Exchange-Only Entangling and Leakage Control Gates

It was first shown 22 years ago that composite sequences of exchange pulses generated by computational searching and algorithmic optimization methods allow universal control over qubits encoded in decoherence-free subsystems (DFS) [1].  It was shown 11 years ago, again via computational search, that such control may be done more efficiently and without spin-polarization [2].  In the past decade, increased theoretical understanding of these control strategies have allowed analytic understanding and minimum-resource-theorems for these sequences [3].  This understanding has also yielded tools to derive new sequences which mitigate the spread of leakage out of the DFS, with utility in facilitating quantum error correction.  Experiments in arrays of 6 Si/SiGe dots are starting to prove these constructions practical and performant [4,5].   This talk will provide theoretical constructions for exchange-gate-synthesis useful for both analytic and computational derivation of new control pathways.  I will provide logical understanding of some previous computer-generated sequences [2,6].  Finally, I will provide examples of new leakage-mitigation strategies, with brief indication of their experimental implementation and performance expectations in silicon.

[1] DiVincenzo et al., Nature 408, 339 (2000)

[2] Fong and Wandzura, Quantum. Inf. Comp. 11, 1003 (2011)

[3] Zeuch and Bonesteel, Phys. Rev. A 93, 010303 (2016)

[4] Andrews et al., Nature Nanotechnol. 14, 747 (2019)

[5] Ha et al., arXiv:2107.10916

[6] Langrock and DiVincenzo, arXiv:2012.09517   

Symmetry Protected Entanglement

Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this talk, we study the effect of symmetry on tripartite entanglement properties of typical states in  symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive explicit expression for the logarithmic entanglement negativity of systems with $\mathbb{Z}_N$ and $U(1)$ symmetry groups. To this end, we develop a diagrammatic method to incorporate partial transpose within random matrix theory of symmetric states and formulate a perturbation theory in the inverse of the Hilbert space dimension. We further present entanglement phase diagrams as the subsystem sizes are varied and show that there are qualitative differences between systems with and without symmetries.    

Latched readout for the semiconductor quantum dot hybrid qubit

We explain and demonstrate a latched readout scheme for the semiconductor quantum dot hybrid qubit (QDHQ), working at the 5-electron (4,1)-(3,2) charge configuration. This configuration enables latching into either the (3,1) or the (4,2) charge states which can be detected with time-averaged or single-shot measurement. Here we demonstrate a single-shot measurement fidelity of 90.2% achieved using only a single electron reservoir for the double-quantum-dot pair; this will become increasingly important when scaling to larger arrays.  We also show that the 5-electron QDHQ has an improved readout window in gate voltage space when compared with the 3-electron QDHQ, which is sometimes limited by small valley splitting in Si/SiGe heterostructures. This combination of latched readout and an enhanced readout window in gate voltage space makes the 5-electron QDHQ a promising semiconductor quantum dot qubit with fast manipulation and a relatively long coherence time.   

Operation of quantum dot spin qubits at elevated temperatures

Quantum computers are expected to outperform conventional computers for a range of important problems, from molecular simulation to search algorithms, once they can be scaled up to large numbers of quantum bits (qubits), typically millions. Spin qubits in silicon MOS quantum dots are one of the big contenders for a scalable, solid state-based quantum computing platform. Here, the qubits are encoded as the spin states of individual electrons confined in electrostatically-gated quantum dots. The great potential of this system has been demonstrated through various experiments over the last few years, with coherence times of up to T₂=28 ms, single qubit control fidelities of 99.96%, and two-qubit control fidelities of 98%.

In my presentation, I will give an introduction to the SiMOS quantum dot spin qubits that we employ at UNSW Sydney. I will showcase some of the key experiments of the last years related to the experimental challenge of operating silicon spin qubits at temperatures above 1 K. High temperature operation is important for the integration of conventional CMOS control electronics with the qubit system, required for scaling to the millions of qubits that will be required for fault-tolerant quantum computing. In particular, I will describe the operation of a double-island single electron transistor (DISET) for charge readout. Using a DISET, we exploit the tunneling between two quantized states to achieve a highly improved insensitivity to temperature and a single-shot charge readout fidelity >99% at 8 K and a bandwidth of 100 kHz.   

High-fidelity single spin-qubit control with an Intel-developed AWG

Quantum computing promises to tackle exciting and computationally difficult problems. Intel is leveraging 50 years of experience in semiconductor manufacturing to develop silicon-based spin qubit devices. Whereas the electrons, whose spin states are used as qubit states, are all identical, their surroundings are not. Hence, precise calibration of the signals controlling the qubits is required. Moreover, spin qubits require multiple voltage control lines per qubit, plus potentially shared microwave control lines. To orchestrate these increasingly complex setups, we use an in-house developed control and calibration software. It allows us to produce hardware agnostic pulse sequences that are interpreted by the control electronics. In particular, we demonstrate that an in-house developed arbitrary waveform generator (AWG), which relies on direct digital synthesis to translate instructions into precisely timesd pulses (arbitrary waveforms), is a useful tool for coherent qubit control. Leveraging the AWG’s high instruction bandwidth (upload speed), coupled with a large memory, we achieve single-qubit randomized benchmarking fidelities approaching 99.9% in a natural Silicon sample.   

Impact of phonon-meditated back-action in SiGe spin qubits

Phonons emitted by semiconducting spin qubit read out devices, such as quantum point contacts or single electron transistors, can be coherently absorbed by the qubit leading to back-action effects. For example, it was experimentally demonstrated that phonons emitted by a quantum point contact can modify the charge stability diagram of a GaAs spin qubit [1]. More specifically, the absorption of the phonons lead to oscillations in the probability of being in different charge states, which produced observable ripples in the charge stability diagram. In this work, we theoretically extend the work of Ref. [1] to a SiGe spin qubit which is readout by a single electron transistor. Using various analytical methods, including Keldysh field theory, we discuss how the charge stability diagram is impacted by the coherent absorption of phonons emitted by the single electron transistor and similarities and differences with the results presented in Ref. [1] for GaAs. We then move beyond a single qubit and investigate how two-qubit gate fidelity is impacted by this phonon-mediated back-action process.

 

[1] G. Granger, et al. Nature Physics 8, 522 (2012)   

Dispersive RF Measurement of a Tip Induced Quantum Dot in a mK-STM

The development of device-based semiconductor spin qubits is an inherently challenging, multi-faceted effort. Such an endeavor requires significant materials overhead coupled with complex, multi-layered fabrication processes before any measurement can even take place. This workflow is further complicated when exploring new materials with the goal of determining suitability for implementation in devices. Here, we seek to circumvent the barriers imposed by device fabrication and instead probe semiconducting materials directly via radio frequency (RF) reflectometry combined with a millikelvin scanning tunneling microscope (mK-STM). In this configuration, STM tip induced band bending gives rise to the formation of a quantum dot which can be scanned across a sample surface as a means to study interactions with surrounding defects. Meanwhile, the dispersive RF measurement provided by an integrated LC-tank circuit permits the determination of specific dot properties, including charge occupation and size. As a demonstration of this capability, we present spectroscopic measurements on chlorine-terminated silicon wafers of various doping levels, in which the STM tip-sample bias is swept while small shifts in the tank circuit resonance, due to changes in quantum capacitance, are recorded. The techniques described herein will be extended to more complicated heterostructure materials, while also providing a pathway for non-destructive characterization of semiconductor materials for quantum information science applications.

    

Hybrid academic/industrial silicon spin qubit devices for spin readout and manipulation

Silicon based spin qubits are among the leading candidates for a scalable quantum computer. To unveil their full potential regarding scalability and co-integration with classical electronics, these devices have to be fabricated in a Complementary-Metal-Oxide-Semiconductor (CMOS) process.

Even though qubits made with industrial CMOS processes have made impressive progress recently, the development cycles of a CMOS based qubit device remain long and the fabrication is restricted to a limited set of materials and processes. Hybrid qubit devices combining the advantages of CMOS fabrication and academic clean room fabrication can bridge this gap.

In this presentation we show the fabrication of hybrid qubit devices made with an industrial CMOS process and post-processed in an academic clean room. This approach allows us to integrate micro-magnets or superconducting resonators and strip lines in close proximity to the qubit devices.

Furthermore, we will characterize the spin physics of these hybrid devices, exploring different approaches for spin readout and manipulation.   

High Fidelity Spin Readout in a CMOS Device

Following Moore’s law, CMOS electronics is approaching feature sizes of a few nm. At this size, quantum effects become important, posing challenges to classical computer architecture, while creating new research opportunities for quantum information processing.

One quantum system of strong interest are electron spins in semiconductor quantum dots (QD) used as qubits. Silicon is replacing GaAs as the host material of choice due to its industrial compatibility and superior properties for qubits (small spin orbit coupling and low nuclear spin density). After demonstration of high fidelity quantum gates for such qubits, small spin qubit arrays are the next step towards large scale quantum architectures.

In this presentation, we will show single spin detection in an array of CMOS quantum dots. Reflectometry on a single lead QD, operated at its charge degeneracy point, yields an on-off signal when the charge distribution in neighboring QDs changes. First, we probe charge stability diagrams of different double QD configurations.[i] Second, we perform single shot measurements of spin in a double QD with an avg. readout fidelity of 99% at 100kHz. This result is of prime importance towards the realization of a fast and efficient spin readout required for quantum error correction protocols.

Electrostatic coupling control of two-gate metal levels CMOS-based quantum dots

Recent demonstrations of high-fidelity gates using CMOS-based silicon quantum dots (QDs) have boosted the interest of the semiconductor industry to extend their applications to quantum computing. The importance of having individual control of the QD chemical potential and its coupling interactions (QD-QD and QD-reservoir) motivated the development of different architectures with increased number of metal levels.

In this presentation we show the versatility of QD arrays designed with two gate layers, and fabricated in a industry-compatible CMOS process. In order to show that such architectures can achieve the desired electrostatic coupling control and requested tunability, we demonstrate that we can control the transition from single to double QD regimes. Results are obtained through transport characterization. When the two QDs are tuned into a weakly-coupled regime, bias triangles are observed, as well as their excited states. Finally, we show that the tunnel-coupling control is effective in accumulation mode, where the QDs can be formed at the back interface of the silicon channel. The demonstration of high electrostatic control over the coupling between the QDs is an important step towards successful manipulation of spins for qubit applications.   

Dispersively Probed Microwave Spectroscopy of a Silicon Hole Double Quantum Dot

Owing to ever increasing gate fidelities and to a potential transferability to industrial CMOS technology, silicon spin qubits have become a compelling option in the strive for quantum computation. In a scalable architecture, each spin qubit will have to be finely tuned and its operating conditions accurately determined. In view of this, spectroscopic tools compatible with a scalable device layout are of primary importance.

Here we report on a two-tone spectroscopy technique providing access to the spin-dependent energy-level spectrum of a hole double quantum dot defined in a split-gate silicon device. A first gigahertz-frequency tone drives electric dipole spin resonance enabled by the valence-band spin-orbit coupling. A second lower-frequency tone (approximately 500 MHz) allows for dispersive readout via rf-gate reflectometry.

We compare the measured dispersive response to the linear response calculated in an extended Jaynes-Cummings model and we obtain characteristic parameters such as g factors and tunnel and spin-orbit couplings for both even and odd charge occupation.   

Dispersive Sensing of Holes in Silicon Fin Field-Effect Transistors

Silicon is a promising host material for quantum dot (QD) spin qubits, offering long coherence and short gate times. Moreover, a scalable array of densely packed qubits can be envisaged by leveraging well-established industry standard fin-field-effect transistor (FinFET) technology. Recently, a hole spin qubit in FinFETs operating at 4.2K was demonstrated, showcasing fast, all-electrical qubit control [Camenzind et al. arXiv:2103.07369]. The small device footprint and high operation temperature are crucial for future scaling. Here, we report on gate-based reflectometry of hole-charge transitions in QDs formed in FinFET devices. For this purpose, a tank circuit on a dot-defining gate is probed resonantly. Tunnelling of holes in the vicinity of the gate alters the gate admittance that causes a dispersive shift of the reflected signal. Varactor diodes are integrated to tune impedance matching [Ares et al. PRA 5, 034011 (2016)]. We benchmark the resonator performance of commercial inductors as well as superconducting thin-film NbTiN inductors. Our results pave the way towards fast, single-shot readout of FinFET hole spin qubits at few-kelvin temperatures.