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Applied Physics Letters

Individual two-axis control of three singlet-triplet qubits in a micromagnet integrated quantum dot array

Wonjin Jang, Min-Kyun Cho, Jehyun Kim, Hwanchul Chung, V. Umansky, Dohun Kim

Published Dec 7, 2020• 11 citations
Publisher

Abstract

The individual confinement and two-axis qubit operations of two-electron spin qubits in a GaAs gate-defined sextuple quantum dot array with an integrated micromagnet are reported in this study. As a first step toward multiple-qubit operations, we demonstrate coherent manipulations of three singlet-triplet qubits showing underdamped Larmor and Ramsey oscillations in all double dot sites. An accurate measurement of site-dependent field gradients as well as root-mean-squared electric and magnetic noise is provided, which is followed by a discussion of the adequacy of a simple rectangular micromagnet for practical use in multiple quantum dot arrays. Current limitations and possible strategies for achieving simultaneous multi-qubit operations in extended linear arrays are also presented.

DOI
10.1063/5.0031231

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The individual confinement and two-axis qubit operations of two-electron spin qubits in a GaAs gate-defined sextuple quantum dot array with an integrated micromagnet are reported in this study. As a first step toward multiple-qubit operations, we demonstrate coherent manipulations of three singlet-triplet qubits showing underdamped Larmor and Ramsey oscillations in all double dot sites. An accurate measurement of site-dependent field gradients as well as root-mean-squared electric and magnetic noise is provided, which is followed by a discussion of the adequacy of a simple rectangular micromagnet for practical use in multiple quantum dot arrays. Current limitations and possible strategies for achieving simultaneous multi-qubit operations in extended linear arrays are also presented.
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 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 coherent control of interacting spins in semiconductor quantum dots is of strong interest for quantum information processing and for studying quantum magnetism from the bottom up. Here we present a 2 × 4 germanium quantum dot array with full and controllable interactions between nearest-neighbour spins. As a demonstration of the level of control, we define four singlet-triplet qubits in this system and show two-axis single-qubit control of each qubit and SWAP-style two-qubit gates between all neighbouring qubit pairs, yielding average single-qubit gate fidelities of 99.49(8)-99.84(1)% and Bell state fidelities of 73(1)-90(1)%. Combining these operations, we experimentally implement a circuit designed to generate and distribute entanglement across the array. A remote Bell state with a fidelity of 75(2)% and concurrence of 22(4)% is achieved. These results highlight the potential of singlet-triplet qubits as a competing platform for quantum computing and indicate that scaling up the control of quantum dot spins in extended bilinear arrays can be feasible.
Coherent control of quantum operations has previously been demonstrated in singlet-triplet qubits which store information in the relative spin of two electrons occupying two same size quantum dots positioned side by side. Here the authors propose to use two quantum dots differing both in size and out-of-plane magnetic field. This is called an inverted singlet-triplet qubit because the existence of a singlet-triplet inversion differs from other qubits. A comparative advantage is that the strongly confined quantum dot can be used for qubit initialization and readout while the weakly confined one is preferable for qubit manipulations. The authors show that full control could be implemented with electrostatic operations even in the presence of realistic noise.
We use fast gate-voltage pulses and multiplexed RF-reflectometry charge sensing to coherently manipulate and read out multiple singlet-triplet spin qubits, within a 2D array of 12 gate-defined quantum dots in GaAs. By measuring the qubits' responses to precise timing changes of control pulses generated at room temperature, we characterize in situ the synchronization of control pulses with sub-ns resolution. These techniques are useful for calibrating the effective delay in cryogenic transmission lines for silicon quantum processors.
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.