Session DD03: V: Quantum Control

A graph-theoretical approach to analyze controllability and its application to qubit systemsMonika Leibscher

The ability to implement any quantum logic gate in a system of coupled qubits is equivalent to evolution-operator controllability of the qubit system. Controllability analysis can thus be utilized to determine the minimal number of external controls and qubit-qubit couplings required for universal quantum computing in a given qubit array [1]. Analyzing controllability of qubit systems faces two main challenges, the exponential scaling of the Hilbert space dimension with the number of qubits and the inherent existence of multiple transitions with equal energy gaps. We present a graphical method that is suitable to handle both challenges [2,3]. As a working example, we apply this graph test to arrays of five qubits, inspired by the ibmq_quito architecture. We find that the number of controls can be reduced from five to one for complex qubit–qubit couplings and to two for standard qubit–qubit couplings [1].

 

[1] F. Gago-Encinas, M. Leibscher, C. P. Koch, Quantum Sci. Technol. 8 045002 (2023)

[2] E. Pozzoli, M. Leibscher, M. Sigalotti, U. Boscain and C. P. Koch, J. Phys. A: Math. Theor. 55, 215301 (2022).

[3] M. Leibscher, E. Pozzoli, C. Pérez, M. Schnell, M. Sigalotti, U. Boscain, C. P. Koch, Commun. Phys. 5, 110 (2022).   

Quantum Optimal Control from a Robotics Perspective

We are presenting our work applying ideas from robotic control to quantum optimal control (QOC).  In our recent paper, Direct Collocation for Quantum Optimal Control, we showed how one of these ideas can be applied with state-of-the-art results to several systems in simulation and also on an experimental 3D circuit cavity quantum electrodynamics system.  We have also developed easy-to-use software for these methods available as an open-source Julia package.  To fully bridge the gap between simulation and experiment, and allow for automated calibration of pulses, we have embedded our direct collocation method within an iterative learning control algorithm, which has the potential to lower calibration time for complex control pulses.   

Decoherence-Free Subspaces for Spontaneous Emission modeled by Continuous Spontaneous Localization

Practical quantum information processing depends on long coherence times and fast and accurate quantum control. Understanding the boundaries of quantum system control is crucial to improving quantum processor design. One common challenge of quantum system control is the undetected spontaneous decay of excited states through spontaneous emission. The framework of continuous spontaneous localization can model spontaneous emission. Continuous spontaneous localization is a modification of quantum mechanics that addresses the measurement problem. It suggests that all particles have a constant and random localization process, which leads to an exponential suppression of superposition states with an increasing number of particles. This theory proposes that localization occurs continuously rather than due to a measurement or environmental interaction. In this study, we investigate the compatibility and realizability of decoherence-free subspaces to protect against spontaneous emission modeled by continuous spontaneous localization. Decoherence-free subspaces are quantum subspaces resistant to certain types of noise and decoherence, resulting in non-unitary dynamics due to system-bath couplings. By encoding quantum information in a decoherence-free subspace, the information can be protected from environmental disturbances and remain coherent for extended periods of time.   

Characterization and Calibration of Quantum Processors using Machine Learning

The effort required for quantum system control, particularly in terms of measurements during calibration, needs to be low enough to compensate for system parameter changes or fast enough to allow for periodic re-calibration. Complete system characterization can provide accurate numerical models for gate calibration. On the other hand, model-free learning control, although costly and laborious, represents a data-driven calibration technique. As quantum systems increase in size, these methods become more measurement-intensive. Here, we use a technique to extract the quantum processor dynamics and map them to a known Hamiltonian and a neural network capturing the unknown dynamics. This combined approach, known as residual modeling, allows for a comprehensive representation of the experimentally observed dynamics with minimal effort. This characterization technique enables low-effort calibration of the closed-system model. Subsequently, a reinforcement-learning gate-calibration agent is equipped with the acquired model and initiated using a numerically derived guess. Such a low-resource approach could enable scaling up quantum processors calibrated by reinforcement learning agents and sidestep the looming bottleneck of quantum control.   

Fast quantum logic gates using nonadiabatic Landau-Zener-Stückelberg-Majorana transitions

A conventional realization of quantum logic gates and control is based on resonant driving, which causes periodic resonant Rabi oscillations of the occupation probability of the quantum system. We study an alternative paradigm for implementing quantum logic gates based on Landau-Zener-Stückelberg-Majorana (LZSM) interferometry with non-resonant driving and the alternation of adiabatic evolution and non-adiabatic transitions. Compared to the Rabi oscillations method, the main differences are a non-resonant frequency, large amplitude, and a small number of periods in the external driving.

We explore the dynamics of a multilevel quantum system under LZSM drives, demonstrate the implementation of single-qubit X, Y, H, and two-qubit iSWAP, CNOT gates, explore optimization of the parameters for increasing the gate speed and fidelity, and compare the theoretical error rates between the conventional Rabi-based and considered LZSM-based gates. The parameters of the external driving required for implementing a specific gate are defined using the adiabatic-impulse model. The LZSM approach can be applied to a large variety of multi-level quantum systems and external driving, providing a method to control the dynamics and implement quantum logic gates on them.

[1] A.I. Ryzhov, et.al., Alternative fast quantum logic gates using nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, arXiv:2310.17932.   

Control Optimization Landscape Analysis of Interacting Quantum Systems

Fine-tuning quantum processors is labor-intensive, typically relying on intricate experimental approaches, complicated models, and computationally intensive simulations. Constraints of computational resources restrict existing methods from simultaneously calibrating individual quantum gates. Consequently, sequential gate calibration techniques typically neglect the impact of undesired crosstalk and system interactions and, thus, limit the performance of simultaneous gate operations. These interactions and interferences between discrete components of quantum processors and control signals represent a substantial obstacle in calibrating ever-larger quantum information processors. Here, we numerically investigate the effects of quantum interactions on quantum gate optimization, particularly its optimization landscape. Prior research has shown that under ideal assumptions, such as controllability, almost all closed, finite-dimensional quantum systems have trap-free optimization landscapes, meaning, during gate calibration, the global optimum is almost always reached. We explore how the suboptimal nature of optimization landscapes changes based on the selection of the loss function and the undesired strengths of interactions between qubits. Identifying limits on interaction strengths can inform the feasibility of simultaneous gate calibration routines and thus significantly reduce the calibration effort.   

Algorithmic cooling with N qubits

Quantum computers offer massive advantages over classical computers in terms of execution time and memory efficiency for a subset of problems. While a variety of physical implementations of quantum computers are still being explored, all must fulfill a fundamental set of requirements, one of which is the ability to initialize the qubits into a pure, fiducial quantum state. Such purified, or cooled, qubits are needed for both the initialization of qubits for the computation, as well as for ancillary qubits required throughout the computation for quantum error correction. Thus, a key hurdle in the success of quantum computers is developing methods to generate extremely cold qubits. Algorithmic cooling, a promising technique for purifying qubits, lowers the temperature of a subset of qubits by applying certain logic gates to the entire system of qubits. Here we investigate both optimal and practical algorithmic cooling of a single target qubit using N total qubits in both closed and open systems. We single out the family of algorithms that achieves the minimum temperature for the target qubit in a closed system and find its analytical expression. Within this family, we single out the sub-family of algorithms that achieves maximal cooling with minimal work cost. We also show how changing from a closed to an open system allows for further cooling of the target qubit. When implemented on real devices, distinct cooling algorithms will display distinct performance depending on their complexity. We illustrate the tradeoff between cooling, work cost, and complexity when implementing various N-qubit algorithmic cooling methods on noisy quantum computers. Exploring methods for cooling qubits below levels that physical cooling techniques can practically achieve will bring us one step closer to successful computation with quantum computers in both the near term and the future.