We study the coupled-qubit oscillation driven by an oscillating field. When the period of the nonresonant mode is commensurate with that of the resonant mode of the Rabi oscillation, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate oscillations, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of oscillating field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and qubit energy gap in experiments.
We study the coupled-qubit oscillation driven by an oscillating field. When the period of the nonresonant mode is commensurate with that of the resonant mode of the Rabi oscillation, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate oscillations, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of oscillating field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and qubit energy gap in experiments.
We study the coupled-qubit oscillation driven by an oscillating field. When the period of the non-resonant mode is commensurate with that of the resonant mode of the Rabi oscillation, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate oscillations, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of oscillating field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and qubit energy gap in experiments.
We establish theoretical bounds on qubit detuning for some of the previously proposed controlled-NOT (CNOT) logic gate implementations with weakly coupled Josephson phase qubits. It is found that in the two-step, iSWAP-based case the value of the detuning during the entangling operations must not exceed 2g, where g is the characteristic coupling constant. In the single-step case we consider two practical, physically distinct implementations, in which one of the qubits is driven by a concurrent rf pulse of fixed frequency. We find that when the local drive is applied to the ``reference'' qubit (with which it is in resonance), the detuning should not exceed g. If the drive is applied to the ``detuned'' qubit, generation of the perfect CNOT gate is possible at any value of detuning provided that the amplitude of the pulse can be made arbitrarily large.
Building on the previous results of the Weyl chamber steering method, we demonstrate how to generate high-fidelity controlled-NOT (CNOT) gates by direct application of certain physically relevant Hamiltonians with fixed coupling constants containing Rabi terms. Such Hamiltonians are often used to describe two superconducting qubits driven by local rf pulses. It is found that in order to achieve 100% fidelity in a system with capacitive coupling of strength g, one Rabi term suffices. We give the exact values of the physical parameters needed to implement such CNOT gates. The gate time and all possible Rabi frequencies are found to be $t=\ensuremath{\pi}∕(2g)$ and ${\ensuremath{\Omega}}_{1}∕g=\sqrt{64{n}^{2}\ensuremath{-}1},n=1,2,3,\dots{}$. Generation of a perfect CNOT gate in a system with inductive coupling, characterized by additional constant k, requires the presence of both Rabi terms. The gate time is again $t=\ensuremath{\pi}∕(2g)$, but now there is an infinite number of solutions, each of which is valid in a certain range of k and is characterized by a pair of integers (n,m), $\frac{{\ensuremath{\Omega}}_{1,2}}{g}=\sqrt{16{n}^{2}\ensuremath{-}{(\frac{k\ensuremath{-}1}{2})}^{2}}\ifmmode\pm\else\textpm\fi{}\sqrt{16{m}^{2}\ensuremath{-}{(\frac{k+1}{2})}^{2}}$. We distinguish two cases, depending on the sign of the coupling constant: (i) the antiferromagnetic case $(k\ensuremath{\geqslant}0)$ with $n\ensuremath{\geqslant}m=0,1,2,\dots{}$ and (ii) the ferromagnetic case $(k\ensuremath{\leqslant}0)$ with n>m=0,1,2,…. We conclude with consideration of fidelity degradation by switching to resonance. Simulation of time evolution based on the fourth-order Magnus expansion reveals characteristics of the gate similar to those found in the exact case, with slightly shorter gate time and shifted values of the Rabi frequencies.
We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterization. Operating the robust CNOT gate in a suitably characterized system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.
Coherent control of two-level quantum systems is typically achieved using resonant driving fields, forming the basis for qubit operations. Here, we report a mechanism for inducing complete Rabi oscillations in monochromatically driven two-level quantum systems, when the drive frequency is much larger than the Larmor frequency of the qubit. This effect$\unicode{x2015}$Rabi oscillations induced by nonresonant gyrating drive (RING)$\unicode{x2015}$requires a gyrating control field, i.e., an elliptic drive trajectory that encloses a nonzero area per cycle. We illustrate the effect with numerical simulations, and provide an analytical understanding via a simple effective Hamiltonian obtained from Floquet theory and perturbation theory. We show that RING enables coherent oscillations without relying on resonant energy exchange, allows for high-pass noise filtering, provides access to non-Abelian phases in finite magnetic fields. We detail a realization in electrically driven spin-orbit qubits and argue that the RING mechanism enables amplification of the Rabi frequency using the same gate voltage amplitudes at higher drive frequencies. Our results broaden the landscape of quantum control techniques, by highlighting a pathway to achieving coherent oscillations under off-resonant driving conditions.
Single-qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. Although high-fidelity single-qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been challenging because of rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities greater than 99%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 nanoseconds. We used the CNOT gate to generate a Bell state with 78% fidelity (corrected for errors in state preparation and measurement). Our quantum dot device architecture enables multi-qubit algorithms in silicon.