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PRX Quantum

Complete Readout of Two-Electron Spin States in a Double Quantum Dot

Martin Nurizzo, Baptiste Jadot, Pierre-André Mortemousque, Vivien Thiney, Emmanuel Chanrion, David J. Niegemann, Matthieu Dartiailh, Arne Ludwig, Andreas Dirk Wieck, Christopher Bäuerle, Matias Urdampilleta, Tristan Meunier

Published Mar 20, 2023• 18 citations
Publisher

Abstract

We propose and demonstrate complete spin state readout of a two-electron system in a double quantum dot probed by an electrometer. The protocol is based on repetitive single-shot measurements using Pauli spin blockade and our ability to tune on fast timescales the detuning and the interdot tunnel coupling between the GHz and sub-Hz regime. A sequence of three distinct manipulations and measurements allows establishing if the spins are in S, T_{0}, T_{+}, or T_{−} state. This work points at a procedure to reduce the overhead for spin readout, an important challenge for scaling up spin-qubit platforms.

DOI
10.1103/prxquantum.4.010329

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We propose and demonstrate complete spin state readout of a two-electron system in a double quantum dot probed by an electrometer. The protocol is based on repetitive single-shot measurements using Pauli spin blockade and our ability to tune on fast timescales the detuning and the interdot tunnel coupling between the GHz and sub-Hz regime. A sequence of three distinct manipulations and measurements allows establishing if the spins are in S, T_{0}, T_{+}, or T_{−} state. This work points at a procedure to reduce the overhead for spin readout, an important challenge for scaling up spin-qubit platforms.
Spin qubits in semiconductor quantum circuits have been identified as a compelling platform for large scale quantum computing. Today an ongoing effort of the community is aiming at the scaling of such systems by filling larger and larger arrays. In this context the development of tuning and readout protocols allowing to reduce the inherent complexity of such systems seems to be a necessity.In the first part of my thesis, I demonstrate array partitioning of a linear triple quantum dot defined in a AlGaAs/GaAs heterostructure via a highly tunable interdot tunnel coupling. This allows us to operate independently smaller sections of the array which reduces the number of available charge states for the system and therefore reduces its complexity during the tuning.The second part of my thesis is focused on reducing the hardware overhead necessary to extract information during the readout of the spin qubits. In semiconductor spin qubits, high fidelity read-out is obtained through Pauli spin blockade in a double quantum dot with two electrons probed by a local electrometer. One electron is the qubit, the second is the ancilla and only one bit of information is extracted. To obtain the full two-bit information of the two-electron spin states, more quantum hardware is necessary (either dots, electrometers, or reservoirs).Based on an original protocol, I develop in this thesis a complete single-shot read-out procedure for two-electron spin states in a double quantum dot discriminating between S, T0, T+ and T-. It uses successively three distinct spin-to-charge conversion protocols interleaved with charge configuration measurements. The strategy is based on four novel experimental achievements:First, the control from the GHz to sub-Hz regime of the interdot tunnel coupling at the nanosecond timescale.Second, the separation of the spin-to-charge conversion and the charge read-out in the voltage gate space.Third, the suppression of spin relaxation process during the read-out procedure.Finally, the repetition of three distinct spin-to-charge conversion protocols.The read-out procedure is tested on various initialized populations and implemented in more complex spin manipulation sequences to assess its validity.
Pauli-spin-blockade (PSB) measurements have so far achieved the highest fidelity of spin readout in semiconductor quantum dots, overcoming the 99% threshold. Moreover, in contrast to energy-selective readout, PSB is less error prone to thermal energy, an important feature for large-scale architectures that could be operated at temperatures above a few hundreds of millikelvins. In this work, we use rf reflectometry on a single-lead quantum dot to perform charge sensing and to probe the spin state of a double quantum dot at 0.5 K. At this relatively elevated temperature, we characterize both singlet-triplet and parity readout, which are complementary measurements to perform a complete readout of a two-spin system. We demonstrate high-fidelity spin readout with an average fidelity above 99.9 % for a readout time of 20 μs and 99 % for 4 μs. Finally, we succeed in initializing a singlet state in a single dot with a fidelity higher than 99 % and separate the two electrons while retaining the same spin state with a 95.6 % fidelity
We present efficient methods to reliably characterize and tune gate-defined semiconductor spin qubits. Our methods are developed for double quantum dots in GaAs heterostructures, but they can easily be adapted to other quantum-dot-based qubit systems. These tuning procedures include the characterization of the interdot tunnel coupling, the tunnel coupling to the surrounding leads, and the identification of various fast initialization points for the operation of the qubit. Since semiconductor-based spin qubits are compatible with standard semiconductor process technology and hence promise good prospects of scalability, the challenge of efficiently tuning the dot’s parameters will only grow in the near future, once the multiqubit stage is reached. With the anticipation of being used as the basis for future automated tuning protocols, all measurements presented here are fast-to-execute and easy-to-analyze characterization methods. They result in quantitative measures of the relevant qubit parameters within a couple of seconds and require almost no human interference.
Electron spins in semiconductor quantum dots are a promising platform for qubits. An essential step toward quantum error correction with spin qubits requires the ability to read out states and identify errors in the two-spin logical basis in a fast and high-fidelity way. Here we propose a scheme for spin singlet-triplet readout in a double quantum dot, with a superconducting resonator serving as the detector. Making use of a spin driving pulse sequence, this procedure can read out the spin states with a fidelity of 99.999.9%99.9 in a time 100 ns. Interestingly, this method makes use of the spin driving pulse to adjust the resonator signal field, leading to significant improvement of the spin readout. In addition, this method can be directly applied to multiplexed readout of qubits and repeated readout to identify logical errors. These results pave the way for the implementation of quantum error correction and scalable quantum processor with spin qubits.
We report repeated single-shot measurements of the two-electron spin state in a GaAs double quantum dot. The readout allows measurement with a fidelity above 90% with a approximately 7 micros cycle time. Hyperfine-induced precession between singlet and triplet states of the two-electron system are directly observed, as nuclear Overhauser fields are quasistatic on the time scale of the measurement cycle. Repeated measurements on millisecond to second time scales reveal the evolution of the nuclear environment.
We propose a scheme for full Bell state measurement of spin qubits in a double quantum dot. Our scheme consists of Pauli spin-blockade measurements and biaxial electron-spin resonance. In order to eliminate the average of the Zeeman fields, the double quantum dot is designed so that the Land\'e ggg-factors of first and second dots satisfy ${g}_{1}=\ensuremath{-}{g}_{2}$ with the use of ggg-factor engineering. Thus, we can swap one of the three spin-triplet states for the spin-singlet state without disturbing the other states. Our study shows that the sequential spin-to-charge conversions enable us to implement the full Bell state measurement of electron-spin qubits.