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arXiv:1206.2579 · Physical Review B

Exchange-based CNOT gates for singlet-triplet qubits with spin-orbit interaction

Jelena Klinovaja, Dimitrije Stepanenko, Bertrand I. Halperin, Daniel Loss

Published Aug 13, 2012• 53 citations
arXivHTMLPDF

Abstract

We propose a scheme for implementing the CNOT gate over qubits encoded in a pair of electron spins in a double quantum dot. The scheme is based on exchange and spin-orbit interactions and on local gradients in Zeeman fields. We find that the optimal device geometry for this implementation involves effective magnetic fields that are parallel to the symmetry axis of the spin-orbit interaction. We show that the switching times for the CNOT gate can be as fast as a few nanoseconds for realistic parameter values in GaAs semiconductors. Guided by recent advances in surface codes, we also consider the perpendicular geometry. In this case, leakage errors due to spin-orbit interaction occur but can be suppressed in strong magnetic fields.

DOI
10.1103/physrevb.86.085423

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We propose a scheme for implementing the CNOT gate over qubits encoded in a pair of electron spins in a double quantum dot. The scheme is based on exchange and spin-orbit interactions and on local gradients in Zeeman fields. We find that the optimal device geometry for this implementation involves effective magnetic fields that are parallel to the symmetry axis of the spin-orbit interaction. We show that the switching times for the CNOT gate can be as fast as a few nanoseconds for realistic parameter values in GaAs semiconductors. Guided by recent advances in surface codes, we also consider the perpendicular geometry. In this case, leakage errors due to spin-orbit interaction occur but can be suppressed in strong magnetic fields.
We analyze a simple exchange-based two-qubit gate for singlet-triplet qubits in gate-defined semiconductor quantum dots that can be implemented in a single exchange pulse. Excitations from the logical subspace are suppressed by a magnetic field gradient that causes spin-flip transitions to be non-energy-conserving. We show that the use of adiabatic pulses greatly reduces leakage processes comapred to square pulses. We also characterize the effect of charge noise on the entanglement fidelity of the gate both analytically and in simulations; demonstrating high entanglement fidelities for physically realistic experimental parameters. Specifically we find that it is possible to achieve fidelities and gate times that are comparable to single-qubit states using realistic magnetic field gradients.
Hole spin qubits in semiconductors are in the midst of revolutionizing solid-state quantum information processing, and different setups are being investigated to further improve their quality. In this work, the authors demonstrate that the interplay between the spin-orbit interaction and site-dependent ggg tensors of holes confined in a double quantum dot enables all-electrical orthogonal two-axis control of hole singlet-triplet qubits. Remarkably, leakage errors can be strongly suppressed at the same time by choosing an optimal direction of the external magnetic field.
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We propose a set of universal gate operations for the singlet-triplet qubit realized by two-electron spins in a double quantum dot, in the presence of a fixed inhomogeneous magnetic field. All gate operations are achieved by switching the potential offset between the two dots with an electrical bias, and do not require time-dependent control of the tunnel coupling between the dots. We analyze the two-electron dynamics and calculate the effective qubit rotation angle as a function of the applied electric bias. We present explicit gate sequences for single-qubit rotations about two orthogonal axes, and a CNOT gate sequence, completing the universal gate set.
Measurement-based quantum computing (MBQC) promises an alternative approach to quantum computation that has natural compatibility with error-correction codes at the cost of a polynomial increase in physical qubits. MBQC implementations have previously focused on photonic systems where two-qubit gates are difficult. On the other hand, semiconductor spin qubit systems offer fast two-qubit gates via the exchange interaction. To explore the benefits of MBQC on spin systems, two hybrid measurement-exchange schemes for full qubit control with semiconductor double-quantum-dot spin qubits are considered. Protocol 1 fully realizes the cluster-state approach to MBQC but requires singlet-triplet qubits in a magnetic field gradient. Protocol 2 implements a direct measurement-based replacement for more traditional gate-based encoded operations, without need for magnetic field gradients. Both protocols demonstrate full single- and two-qubit control through a combination of interqubit and intraqubit exchange and measurement onto the singlet-triplet basis. We show that both schemes suppress individual qubit spin-state leakage errors and offer fast gate times, up to known phase and Pauli corrections.
Universal quantum computation requires single-qubit control together with at least one entangling two-qubit gate. CNOT and CROT gates are two famous examples of such gates, wherein the state of one qubit (control) dictates the transformation applied to the other (target). By using a simple derivation motivated by symmetry, we show that current device architectures of semiconductor-based quantum dot devices prevent efficient implementation of a CNOT and other asymmetric control-target gates via Heisenberg exchange, Coulomb repulsion, or other interaction that is invariant under spin exchange. Guided by this general principle, we propose a heterogeneous blueprint of double quantum dot devices that enables efficient implementation of the CNOT by breaking the spin exchange symmetry. Crucially, our numerical simulations predict that this novel device blueprint can enable a single-pulse fault-tolerant 100-ns CNOT gate in isotopically purified silicon.