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arXiv:1403.2910 · Physical Review B

Two-qubit couplings of singlet-triplet qubits mediated by one quantum state

Sebastian Mehl, Hendrik Bluhm, David Peter Divincenzo

Published Jul 9, 2014• 42 citations
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Abstract

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 controlled not (cnot) operations. We show that realistic quantum dot setups permit excellent entangling operations with gate infidelities below ${10}^{\ensuremath{-}3}$, 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.

DOI
10.1103/physrevb.90.045404

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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 controlled not (cnot) operations. We show that realistic quantum dot setups permit excellent entangling operations with gate infidelities below 10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−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.
The search for a sweet spot, the locus in qubit parameters where quantum control is first-order insensitive to noises, is key to achieve high-fidelity quantum gates. Efforts to search for such a sweet spot in conventional double-quantum-dot singlet-triplet qubits where each dot hosts one electron (``two-electron singlet-triplet qubit''), especially for two-qubit operations, have been unsuccessful. Here we consider singlet-triplet qubits allowing each dot to host more than one electron, with a total of four electrons in the double quantum dots (``four-electron singlet-triplet qubit''). We theoretically demonstrate, using configuration interaction calculations, that sweet spots appear in this coupled qubit system. We further demonstrate that, under realistic charge noise and hyperfine noise, a two-qubit operation at the proposed sweet spot could offer gate fidelities ($\ensuremath{\sim}99%$) that are higher than the conventional two-electron singlet-triplet qubit system ($\ensuremath{\sim}90%$). Our results should facilitate realization of high-fidelity two-qubit gates in singlet-triplet qubit systems.
Hybrid systems comprising superconducting and semiconducting materials are promising architectures for quantum computing. Superconductors induce long-range interactions between the spin degrees of freedom of semiconducting quantum dots. These interactions are widely anisotropic when the semiconductor material has strong spin-orbit interactions. We show that this anisotropy is tunable and enables fast and high-fidelity two-qubit gates between singlet-triplet (ST) spin qubits. Our design is immune to leakage of the quantum information into noncomputational states and removes always-on interactions between the qubits, thus resolving key open challenges for these architectures. Our ST qubits do not require additional technologically demanding components nor fine-tuning of parameters. They operate at low magnetic fields of a few millitesla and are fully compatible with superconductors. By suppressing systematic errors in realistic devices, we estimate infidelities below ${10}^{\ensuremath{-}3}$, which could pave the way toward large-scale hybrid superconducting-semiconducting quantum processors.
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.
Several logical qubits and quantum gates have been proposed for semiconductor quantum dots controlled by voltages applied to top gates. The different schemes can be difficult to compare meaningfully. Here we develop a theoretical framework to evaluate disparate qubit-gating schemes on an equal footing. We apply the procedure to two types of double-dot qubits: the singlet-triplet and the semiconducting quantum dot hybrid qubit. We investigate three quantum gates that flip the qubit state: a DC pulsed gate, an AC gate based on logical qubit resonance, and a gate-like process known as stimulated Raman adiabatic passage. These gates are all mediated by an exchange interaction that is controlled experimentally using the interdot tunnel coupling g and the detuning [Symbol: see text], which sets the energy difference between the dots. Our procedure has two steps. First, we optimize the gate fidelity (f) for fixed g as a function of the other control parameters; this yields an f(opt)(g) that is universal for different types of gates. Next, we identify physical constraints on the control parameters; this yields an upper bound f(max) that is specific to the qubit-gate combination. We show that similar gate fidelities (~99:5%) should be attainable for singlet-triplet qubits in isotopically purified Si, and for hybrid qubits in natural Si. Considerably lower fidelities are obtained for GaAs devices, due to the fluctuating magnetic fields ΔB produced by nuclear spins.
Singlet-triplet qubits in lateral quantum dots in semiconductor heterostructures exhibit high-fidelity single-qubit gates via exchange interactions and magnetic field gradients. High-fidelity two-qubit entangling gates are challenging to generate since weak interqubit interactions result in slow gates that accumulate error in the presence of noise. However, the interqubit electrostatic interaction also produces a shift in the local double well detunings, effectively changing the dependence of exchange on the gate voltages. We consider an operating point where the effective exchange is first-order insensitive to charge fluctuations while maintaining nonzero interactions. This ``sweet spot'' exists only in the presence of interactions. We show that working at the interacting sweet spot can directly produce maximally entangling gates, and we simulate the gate evolution under realistic 1/f1/f1/f noise. We report theoretical two-qubit gate fidelities above 99% in GaAs and Si systems.
In order to enable semiconductor-based quantum computing with many qubits, issues like residual interqubit coupling and constraints from scalable control hardware need to be tackled to retain the high gate fidelities demonstrated in current single-qubit devices. Here we focus on two exchange-coupled singlet-triplet spin qubits, considering realistic control hardware as well as Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we optimize realistic control pulses and show that two-qubit (single-qubit) gate fidelities of 99.90% ($\ensuremath{\ge}99.69%$) can be reached in GaAs, while 99.99% ($\ensuremath{\ge}99.95%$) can be achieved in Si.