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arXiv:1501.05833 · Quantum Information Processing

Effective Hamiltonian for two interacting double-dot exchange-only qubits and their controlled-NOT operations

Elena Ferraro, Marco De Michielis, Marco Fanciulli, Enrico Prati

Published Oct 30, 2014• 20 citations
arXivHTMLPDF
DOI
10.1007/s11128-014-0864-1

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We consider a model of two interacting always-on, exchange-only qubits for which controlled phase (CPHASE), controlled NOT (CNOT), quantum Fourier transform (QFT) and SWAP operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the CPHASE gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: CNOT, QFT and SWAP. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations.
We study controllable exchange coupling between two singlet-triplet qubits. We start from the original second quantized Hamiltonian of a quadruple quantum dot system and obtain the effective spin-spin interaction between the two qubits using the projection operator method. Under a strong uniform external magnetic field and an inhomogeneous local micromagnetic field, the effective interqubit coupling is of the Ising type, and the coupling strength can be expressed in terms of quantum dot parameters. Finally, we discuss how to generate various two-qubit operations using this controllable coupling, such as entanglement generation, and a controlled-not gate.
Abstract Robust two-qubit gates are essential for scalable silicon spin qubits, but their fidelities are limited by microwave-control imperfections and charge-noise-induced exchange fluctuations. We propose a practical scheme for robust controlled-Z (CZ) and controlled-NOT (CNOT) gates in a silicon double quantum dot. By applying a transverse microwave drive, the effective Hamiltonian can be decomposed into two driven subspaces. In the subspace mainly controlled by the microwave field, a Broadband 1 (BB1) composite pulse is used to suppress errors in the microwave amplitude. In the exchange-assisted subspace, the microwave phases and durations are kept fixed, while a few piecewise-constant exchange amplitudes are optimized by a GRAPE-like procedure. This design reduces the sensitivity to both microwave-amplitude and exchange-amplitude errors while keeping the control waveform simple and experimentally friendly. Numerical simulations show that the optimized CNOT gate reaches a fidelity above 99.99% under experimentally relevant noise strengths, and the CZ gate also maintains a fidelity above 99.9%. These results indicate that combining composite pulses with optimized exchange control provides an experimentally feasible route to robust two-qubit gates in silicon spin qubits.