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Physical Review A

Optimizing control fields for diabatic protocols in the presence of noise

Marllos E. F. Fernandes, Emanuel F. de Lima, L. K. Castelano

Published May 17, 2024• 0 citations
Publisher

Abstract

Quantum control techniques are employed to perform quantum algorithms inspired by the adiabatic quantum computing protocols in the presence of noise. First, we analyze the entanglement protocol for two qubits. In this case, we find that this protocol is very robust against noise. The reason behind this fact is related to the chosen Hamiltonians, where the ground state of the initial Hamiltonian is not affected by the noise. The optimal control solution, in this case, is to leave the system in its ground state and apply a fast pulse to entangle the qubits at the end of the time evolution. Second, we probe a system composed of three qubits, where the goal is to teleport the first qubit to the third qubit. In this case, the ground state of the system does not share the same robustness against noise as in the case of the entanglement protocol. To circumvent this problem, we propose the inclusion of a local control field that can drive the system to an intermediate state, which is more robust against noise in comparison to other states. The target state is also achieved by a fast pulse close to the final time. We find that this approach provides a significant gain and promises to improve the realization of quantum computing in the so-called noisy intermediate-scale quantum devices.

DOI
10.1103/physreva.109.052622

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Quantum control techniques are employed to perform quantum algorithms inspired by the adiabatic quantum computing protocols in the presence of noise. First, we analyze the entanglement protocol for two qubits. In this case, we find that this protocol is very robust against noise. The reason behind this fact is related to the chosen Hamiltonians, where the ground state of the initial Hamiltonian is not affected by the noise. The optimal control solution, in this case, is to leave the system in its ground state and apply a fast pulse to entangle the qubits at the end of the time evolution. Second, we probe a system composed of three qubits, where the goal is to teleport the first qubit to the third qubit. In this case, the ground state of the system does not share the same robustness against noise as in the case of the entanglement protocol. To circumvent this problem, we propose the inclusion of a local control field that can drive the system to an intermediate state, which is more robust against noise in comparison to other states. The target state is also achieved by a fast pulse close to the final time. We find that this approach provides a significant gain and promises to improve the realization of quantum computing in the so-called noisy intermediate-scale quantum devices.
Quantum control techniques are employed to perform adiabatic quantum computing in the presence of noise. First, we analyze the adiabatic entanglement protocol (AEP) for two qubits. In this case, we found that this protocol is very robust against noise. The reason behind this fact is related to the chosen Hamiltonians, where the ground state of the initial Hamiltonian is not affected by the noise. The optimal control solution, in this case, is to leave the system in its ground state and apply a fast pulse to entangle the qubits at the end of the time evolution. Secondly, we probe a system composed of three qubits, where the goal is to teleport the first qubit to the third qubit. In this case, the ground state of the system does not share the same robustness against noise as in the case of AEP. To improve the robustness against noise, we propose the inclusion of a local control field that can drive the system to an intermediate state, which is more robust against noise in comparison to other states. The target state is also achieved by a fast pulse at the final time. We found that this approach provides a significant gain in the fidelity and can improve the adiabatic quantum computing in the so-called Noisy Intermediate-Scale Quantum (NISQ) devices in a near future.
Abstract Quantum optimal control plays a vital role in many quantum technologies, including quantum computation. One of the most important control parameters to optimise for is the evolution time (pulse duration). However, most existing works focus on finding the shortest evolution time theoretically possible without offering explicit pulse constructions under practical constraints like noise in the system. This paper addresses these limitations by introducing an efficient method to perform the chopped random basis optimisation in the presence of noise, specifically when the noise commutes with the gate Hamiltonian, i.e. when the unitary and dissipative parts of the Liouvillian commute. This noise-aware approach allows for direct optimisation of the evolution time alongside other control parameters, significantly reducing the computational cost compared to full noisy simulations. The protocol is demonstrated through numerical simulations on state-to-state transfer and gate compilation problems under several noise models. Results show that the optimised fidelity has a strong dependence on evolution time due to noise, drift Hamiltonian, and local traps in optimisation, highlighting the necessity of optimising evolution time in practical settings that can lead to a substantial gain in the fidelity. Our pulse optimisation protocol can consistently escape from many local minima in all of our examples. We hope that our protocol can be the start of many more works on the crucial topic of control pulse time optimisation in practical settings.
Motivation• In adiabatic quantum computation (AQC), the system is kept in the instantaneous ground state |φ 0 (t) of a slowly varying Hamiltonian H(t), which provides inherent protection against dephasing and relaxation in the energy eigenstate basis.• However, this protection does not guarantee full fault tolerance, since there still exist some types of noise, which can drive undesirable transitions out of the ground state.• Therefore, it would be desirable to try decreasing the accumulation of errors by performing a computation in a shorter time.However, how to reconcile faster evolution with the requirement of adiabaticity?• Our approach: (1) consider Hamiltonians containing multiple control functions and (2) use quantum optimal control theory (QOCT) to find control sets which achieve the target state with a high fidelity while simultaneously maximizing the degree of adiabaticity.• Exploring properties of optimal adiabatic trajectories in few-qubit model systems elucidates the dynamic mechanisms which suppress unwanted excitations from the ground state.
The development of efficient algorithms that generate robust quantum controls is crucial for the realization of quantum technologies. The commonly used gradient-based optimization algorithms are limited by their sensitivity to the initial guess, which affects their performance. Here we propose combining the gradient method with the simulated annealing technique to formulate a hybrid algorithm. Our numerical analysis confirms its superior convergence rate. Using the hybrid algorithm, we generate spin-selective $\ensuremath{\pi}$ pulses and employ them for experimental measurement of local noise spectra in a three-qubit nuclear magnetic resonance system. Moreover, here we describe a general method to construct noise-resilient quantum controls by incorporating noisy fields within the optimization routine of the hybrid algorithm. Upon experimental comparison with similar sequences obtained from standard algorithms, we find remarkable robustness of the hybrid sequences against dephasing errors.
Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.
In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of non-Abelian quasiparticles, such as Majorana zero modes, and are protected from local environmental perturbations. In the adiabatic regime, with timescales set by the inverse gap of the system, the errors can be made arbitrarily small by performing the process more slowly. To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-based qubits. While we sacrifice complete topological protection, we impose constraints on the optimal protocol to take advantage of the nonlocal nature of topological information and increase the robustness of our gates. By using the Pontryagin's maximum principle, we show that robust equivalent gates to perfect adiabatic braiding can be implemented in finite times through optimal pulses. In our implementation, modifications to the device Hamiltonian are avoided. Focusing on thermally isolated systems, we study the effects of calibration errors and external white and 1/f1/f1/f (pink) noise on Majorana-based gates. While a noise-induced antiadiabatic behavior, where a slower process creates more diabatic excitations, prohibits indefinite enhancement of the robustness of the adiabatic scheme, our fast optimal protocols exhibit remarkable stability to noise and have the potential to significantly enhance the practical performance of Majorana-based information processing.