Quantum computing promises significant speed-up for certain types of computational problems. However, robust implementations of semiconducting qubits must overcome the effects of charge noise that currently limit coherence during gate operations. Here we describe a scheme for protecting solid-state qubits from uniform electric field fluctuations by generalizing the concept of a decoherence-free subspace for spins, and we propose a specific physical implementation: a quadrupole charge qubit formed in a triple quantum dot. The unique design of the quadrupole qubit enables a particularly simple pulse sequence for suppressing the effects of noise during gate operations. Simulations yield gate fidelities 10-1,000 times better than traditional charge qubits, depending on the magnitude of the environmental noise. Our results suggest that any qubit scheme employing Coulomb interactions (for example, encoded spin qubits or two-qubit gates) could benefit from such a quadrupolar design.
Quantum optimal control is a powerful tool for designing a pulse that executes a specified gate, i.e., a unitary transformation in quantum computation. If we consider qubits characterized by different spectroscopic properties, we may design a pulse that executes a specified gate on a specified qubit (
S qubit) with the inclusion of neighboring qubits (
B qubits) but does not explicitly include the other qubits. In this situation, first we introduce sets of reduced time-evolution operators associated with the
S and
B qubits. Then, we apply quantum optimal control to these sets to design optimal pulses that could selectively execute the specified gate on the
S qubit while actively removing the effects of the pulse on the
B qubits, which would lead to a scalable pulse-design procedure. The present pulse design is applied to the quantum computation proposed by DeMille with the aim of executing the Hadamard and controlled-not gates on the
S qubits while actively suppressing the pulse-induced population transitions of the
B qubit states. The numerical results illustrate high fidelity even after introducing the extra qubits that are not included in the pulse design.
We present a general method to quickly generate high-fidelity control pulses for any continuously-parameterized set of quantum gates after calibrating a small number of reference pulses. We find that interpolating between optimized control pulses for different quantum operations does not immediately yield a high-fidelity intermediate operation. To solve this problem, we propose a method to optimize control pulses specifically to provide good interpolations. We pick several reference operations in the gate family of interest and optimize pulses that implement these operations, then iteratively re-optimize the pulses to guide their shapes to be similar for operations that are closely related. Once this set of reference pulses is calibrated, we can use a straightforward linear interpolation method to instantly obtain high-fidelity pulses for arbitrary gates in the continuous operation space. We demonstrate this procedure on the three-parameter Cartan decomposition of two-qubit gates to obtain control pulses for any arbitrary two-qubit gate (up to single-qubit operations) with consistently high fidelity. Compared to previous neural network approaches, the method is 7.7x more computationally efficient to calibrate the pulse space for the set of all single-qubit gates. Our technique generalizes to any number of gate parameters and could easily be used with advanced pulse optimization algorithms to allow for better translation from simulation to experiment.