Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement

We study how the spontaneous relaxation of a qubit affects a continuous quantum non-demolition measurement of the initial state of the qubit. Given some noisy measurement record $\Psi$, we seek an estimate of whether the qubit was initially in the ground or excited state. We investigate four different measurement protocols, three of which use a linear filter (with different weighting factors) and a fourth which uses a full non-linear filter that gives the theoretically optimal estimate of the initial state of the qubit. We find that relaxation of the qubit at rate $1/T_1$ strongly influences the fidelity of any measurement protocol. To avoid errors due to this decay, the measurement must be completed in a time that decrease linearly with the desired fidelity while maintaining an adequate signal to noise ratio. We find that for the non-linear filter the predicted fidelity, as expected, is always better than the linear filters and that the fidelity is a monotone increasing function of the measurement time. For example, to achieve a fidelity of 90%, the box car linear filter requires a signal to noise ratio of $\sim 30$ in a time $T_1$ whereas the non-linear filter only requires a signal to noise ratio of $\sim 18$.Comment: 12 pages, 6 figure

Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits