We study theoretically the responses of the dynamically corrected gates to time-dependent noises in the exchange-only spin-qubit system. We consider $1/f$ noises having spectra proportional to $1/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$, where the exponent $\ensuremath{\alpha}$ indicates the strength of correlation within the noise. The quantum gate errors due to noises are extracted from a numerical simulation of randomized benchmarking and are compared between the application of uncorrected operations and that of dynamically corrected gates robust against the hyperfine noise. We have found that for $\ensuremath{\alpha}\ensuremath{\gtrsim}1.5$, the dynamically corrected gates offer a considerable reduction in the gate error and such a reduction is approximately two orders of magnitude for the experimentally relevant noise exponent. On the other hand, no improvement of the gate fidelity is provided for $\ensuremath{\alpha}\ensuremath{\lesssim}1.5$. This critical value of ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.5$ is larger than that for the cases for the singlet-triplet qubits. The filter transfer functions corresponding to the dynamically corrected gates are also computed and compared to those derived from uncorrected pulses. Our results suggest that the dynamically corrected gates are useful measures to suppress the hyperfine noise when operating the exchange-only qubits.We study theoretically the responses of the dynamically corrected gates to time-dependent noises in the exchange-only spin-qubit system. We consider $1/f$ noises having spectra proportional to $1/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$, where the exponent $\ensuremath{\alpha}$ indicates the strength of correlation within the noise. The quantum gate errors due to noises are extracted from a numerical simulation of randomized benchmarking and are compared between the application of uncorrected operations and that of dynamically corrected gates robust against the hyperfine noise. We have found that for $\ensuremath{\alpha}\ensuremath{\gtrsim}1.5$, the dynamically corrected gates offer a considerable reduction in the gate error and such a reduction is approximately two orders of magnitude for the experimentally relevant noise exponent. On the other hand, no improvement of the gate fidelity is provided for $\ensuremath{\alpha}\ensuremath{\lesssim}1.5$. This critical value of ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.5$ is larger than that for the cases for the singlet-triplet qubits. The filter transfer functions corresponding to the dynamically corrected gates are also computed and compared to those derived from uncorrected pulses. Our results suggest that the dynamically corrected gates are useful measures to suppress the hyperfine noise when operating the exchange-only qubits.

arXiv:1607.08093Physical Review AOct 17, 20168 citations

High-Fidelity Entangling Gates for Two-Electron Spin Qubits

Pascal Cerfontaine, Sebastian Mehl, David Peter Divincenzo +1 more

Bulletin of the American Physical SocietyMar 16, 20160 citations

Electric nonadiabatic geometric entangling gates on spin qubits

Vahid Azimi Mousolou

Producing and maintaining entanglement reside at the heart of the optimal construction of quantum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that allows the geometric implementation of entangling gates between the register qubits with any arbitrary entangling power. We show this by demonstrating a circuit through a spin chain, which performs universal nonadiabatic holonomic two-qubit entanglers. The proposed gates are all electric and geometric, which would help to realize fast and robust entangling gates on spin qubits. This family of entangling gates contains gates that are as efficient as the cnot gate in quantum algorithms. We examine the robustness of the circuit to some extent.Producing and maintaining entanglement reside at the heart of the optimal construction of quantum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that allows the geometric implementation of entangling gates between the register qubits with any arbitrary entangling power. We show this by demonstrating a circuit through a spin chain, which performs universal nonadiabatic holonomic two-qubit entanglers. The proposed gates are all electric and geometric, which would help to realize fast and robust entangling gates on spin qubits. This family of entangling gates contains gates that are as efficient as the cnot gate in quantum algorithms. We examine the robustness of the circuit to some extent.

arXiv:1612.04500Physical Review AJul 5, 201737 citations

We study theoretically the responses of the dynamically corrected gates to time-dependent noises in the exchange-only spin-qubit system. We consider

1/f

noises having spectra proportional to $1/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$, where the exponent $\ensuremath{\alpha}$ indicates the strength of correlation within the noise. The quantum gate errors due to noises are extracted from a numerical simulation of randomized benchmarking and are compared between the application of uncorrected operations and that of dynamically corrected gates robust against the hyperfine noise. We have found that for $\ensuremath{\alpha}\ensuremath{\gtrsim}1.5$, the dynamically corrected gates offer a considerable reduction in the gate error and such a reduction is approximately two orders of magnitude for the experimentally relevant noise exponent. On the other hand, no improvement of the gate fidelity is provided for $\ensuremath{\alpha}\ensuremath{\lesssim}1.5$. This critical value of ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.5$ is larger than that for the cases for the singlet-triplet qubits. The filter transfer functions corresponding to the dynamically corrected gates are also computed and compared to those derived from uncorrected pulses. Our results suggest that the dynamically corrected gates are useful measures to suppress the hyperfine noise when operating the exchange-only qubits.