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Scientific Reports

Magnetically tunable singlet-triplet spin qubit in a four-electron InGaAs coupled quantum dot

K. M. Weiss, Javier Miguel-Sanchez, J. M. Elzerman

Published Nov 1, 2013• 10 citations
Publisher

Abstract

A pair of self-assembled InGaAs quantum dots filled with two electrons can act as a singlet-triplet spin qubit that is robust against nuclear spin fluctuations as well as charge noise. This results in a T2* coherence time two orders of magnitude longer than that of a single electron, provided the qubit is operated at a particular "sweet spot" in gate voltage. However, at this fixed operating point the ground-state splitting can no longer be tuned into resonance with e.g. another qubit, limiting the options for coupling multiple qubits. Here, we propose using a four-electron coupled quantum dot to implement a singlet-triplet qubit that features a magnetically tunable level splitting. As a first step towards full experimental realization of this qubit design, we use optical spectroscopy to demonstrate the tunability of the four-electron singlet-triplet splitting in a moderate magnetic field.

DOI
10.1038/srep03121

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A pair of self-assembled InGaAs quantum dots filled with two electrons can act as a singlet-triplet spin qubit that is robust against nuclear spin fluctuations as well as charge noise. This results in a T2* coherence time two orders of magnitude longer than that of a single electron, provided the qubit is operated at a particular "sweet spot" in gate voltage. However, at this fixed operating point the ground-state splitting can no longer be tuned into resonance with e.g. another qubit, limiting the options for coupling multiple qubits. Here, we propose using a four-electron coupled quantum dot to implement a singlet-triplet qubit that features a magnetically tunable level splitting. As a first step towards full experimental realization of this qubit design, we use optical spectroscopy to demonstrate the tunability of the four-electron singlet-triplet splitting in a moderate magnetic field.
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.
The exchange interaction in a singlet-triplet qubit defined by two-electron states in the double-quantum-dot system (``two-electron singlet-triplet qubit'') typically varies monotonically with the exchange interaction and thus carries no sweet spot. Here we study a singlet-triplet qubit defined by four-electron states in the double-quantum-dot system (``four-electron singlet-triplet qubit''). We demonstrate, using configuration-interaction calculations, that in the four-electron singlet-triplet qubit the exchange energy as a function of detuning can be nonmonotonic, suggesting existence of sweet spots. We further show that the tuning of the sweet spot and the corresponding exchange energy by perpendicular magnetic field can be related to the variation of orbital splitting. Our results suggest that a singlet-triplet qubit with more than two electrons can have advantages in the realization of quantum computing.
Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. owever, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations.\n\n\n\nThe focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*.\n\n\n\nWe probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency- dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled.\n\n\n\nThis work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor.
The qubit is the fundamental building block of a quantum computer. We fabricate a qubit in a silicon double-quantum dot with an integrated micromagnet in which the qubit basis states are the singlet state and the spin-zero triplet state of two electrons. Because of the micromagnet, the magnetic field difference ΔB between the two sides of the double dot is large enough to enable the achievement of coherent rotation of the qubit's Bloch vector around two different axes of the Bloch sphere. By measuring the decay of the quantum oscillations, the inhomogeneous spin coherence time T2* is determined. By measuring T2* at many different values of the exchange coupling J and at two different values of ΔB, we provide evidence that the micromagnet does not limit decoherence, with the dominant limits on T2* arising from charge noise and from coupling to nuclear spins.
A logical qubit based on electron-spin singlet-triplet states in a semiconductor double dot has emerged as one of the promising candidates for quantum information processing. Here we propose a systematic method to implement rapid quantum gates in the nanosecond time scale for both a single qubit and multiqubits, by applying adiabatic driving pulses with tunable velocity. This yields considerable high-fidelity gate operations reaching 99.999.9%99.9 which are crucial to scalable quantum computation in a semiconductor-based architecture, even considering the demanding experimental constraints and realistic spin and charge noises.