Noise Spectroscopy Using Correlations of Single-Shot Qubit Readout

A better understanding of the noise causing qubit decoherence is crucial for improving qubit performance. The noise spectrum affecting the qubit may be extracted by measuring dephasing under the application of pulse sequences but requires accurate qubit control and sufficiently long relaxation times, which are not always available. Here, we describe an alternative method to extract the spectrum from correlations of single-shot measurement outcomes of successive free induction decays. This method only requires qubit initialization and readout with a moderate fidelity and also allows independent tuning of both the overall sensitivity and the frequency region over which it is sensitive. Thus, it is possible to maintain a good detection contrast over a very wide frequency range. We discuss using our method for measuring both $1/f$ noise and the fluctuation spectrum of the nuclear bath of GaAs spin qubits.Comment: 5 pages, 3 figure

Phenomenological Study of Decoherence in Solid-State Spin Qubits due to Nuclear Spin Diffusion

We present a study of the prospects for coherence preservation in solid-state spin qubits using dynamical decoupling protocols. Recent experiments have provided the first demonstrations of multipulse dynamical decoupling sequences in this qubit system, but quantitative analyses of potential coherence improvements have been hampered by a lack of concrete knowledge of the relevant noise processes. We present simulations of qubit coherence under the application of arbitrary dynamical decoupling pulse sequences based on an experimentally validated semiclassical model. This phenomenological approach bundles the details of underlying noise processes into a single experimentally relevant noise power spectral density. Our results show that the dominant features of experimental measurements in a two-electron singlet-triplet spin qubit can be replicated using a $1/\omega^{2}$ noise power spectrum associated with nuclear-spin-flips in the host material. Beginning with this validation we address the effects of nuclear programming, high-frequency nuclear-spin dynamics, and other high-frequency classical noise sources, with conjectures supported by physical arguments and microscopic calculations where relevant. Our results provide expected performance bounds and identify diagnostic metrics that can be measured experimentally in order to better elucidate the underlying nuclear spin dynamics.Comment: Updated References. Related articles at: http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm

Two-Qubit Couplings of Singlet-Triplet Qubits Mediated by One Quantum State

We describe high-fidelity entangling gates between singlet-triplet qubits (STQs) which are coupled via one quantum state (QS). The QS can be provided by a quantum dot itself or by another confined system. The orbital energies of the QS are tunable using an electric gate close to the QS, which changes the interactions between the STQs independent of their single-qubit parameters. Short gating sequences exist for the controlled NOT (CNOT) operations. We show that realistic quantum dot setups permit excellent entangling operations with gate infidelities below $10^{-3}$, which is lower than the quantum error correction threshold of the surface code. We consider limitations from fabrication errors, hyperfine interactions, spin-orbit interactions, and charge noise in GaAs and Si heterostructures.Comment: 12 pages, 6 figure

Automated Synthesis of Dynamically Corrected Quantum Gates

We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotations subject to realistic timing and pulse-shaping constraints are provided, which can deliver substantially improved gate fidelity for state-of-the-art experimental capabilities.Comment: 5 pages; further restructure and expansio

Magnetic fields above the surface of a superconductor with internal magnetism

The author presents a method for calculating the magnetic fields near a planar surface of a superconductor with a given intrinsic magnetization in the London limit. He computes solutions for various magnetic domain boundary configurations and derives relations between the spectral densities of the magnetization and the resulting field in the vacuum half space, which are useful if the magnetization can be considered as a statistical quantity and its features are too small to be resolved individually. The results are useful for analyzing and designing magnetic scanning experiments. Application to existing data from such experiments on Sr$_2$RuO$_4$ show that a domain wall would have been detectable, but the magnetic field of randomly oriented small domains and small defects may have been smaller than the experimental noise level.Comment: 8 pages, 2 figures. Journal version. Added one figure, some discussion. A few typos correcte

Charge-noise tolerant exchange gates of singlet-triplet qubits in asymmetric double quantum dots

In the semi-conductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle in the way towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose singlet-triplet qubits based on two quantum dots of different sizes. Such asymmetric double dot systems allow the implementation of exchange gates with controllable exchange splitting $J$ operated in the doubly occupied charge region of the larger dot, where the qubit has high resilience to charge noise. In the larger dot, $J$ can be quenched to a value smaller than the intra-dot tunneling using magnetic fields, while the smaller dot and its larger splitting can be used in the projective readout of the qubit

Roadmap for gallium arsenide spin qubits

Gate-defined quantum dots in gallium arsenide (GaAs) have been used extensively for pioneering spin qubit devices due to the relative simplicity of fabrication and favourable electronic properties such as a single conduction band valley, a small effective mass, and stable dopants. GaAs spin qubits are readily produced in many labs and are currently studied for various applications, including entanglement, quantum non-demolition measurements, automatic tuning, multi-dot arrays, coherent exchange coupling, and teleportation. Even while much attention is shifting to other materials, GaAs devices will likely remain a workhorse for proof-of-concept quantum information processing and solid-state experiments.Comment: This section is part of a roadmap on quantum technologies and comprises 4 pages with 2 figure

Enhancing the Coherence of a Spin Qubit by Operating it as a Feedback Loop That Controls its Nuclear Spin Bath

In many realizations of electron spin qubits the dominant source of decoherence is the fluctuating nuclear spin bath of the host material. The slowness of this bath lends itself to a promising mitigation strategy where the nuclear spin bath is prepared in a narrowed state with suppressed fluctuations. Here, this approach is realized for a two-electron spin qubit in a GaAs double quantum dot and a nearly ten-fold increase in the inhomogeneous dephasing time $T_2^*$ is demonstrated. Between subsequent measurements, the bath is prepared by using the qubit as a feedback loop that first measures its nuclear environment by coherent precession, and then polarizes it depending on the final state. This procedure results in a stable fixed point at a nonzero polarization gradient between the two dots, which enables fast universal qubit control.Comment: Journal version. Improved clarity of presentation and more concise terminology. 4 pages, 3 figures. Supplementary document included as ancillary fil