Session N50: Quantum Control and Pulse Engineering

Optimally Band-Limited Noise Filtering and Crosstalk Mitigation for Single Qubit Gates in Multi-Qubit Systems

In the NISQ era, accurate and scalable quantum computation is hindered by noise that is often difficult to mitigate. A particularly prevalent source of noise in NISQ devices is quantum crosstalk, where qubits experience always-on or gate-induced parasitic interactions. In this work, we construct optimized control sequences that mitigate temporally correlated noise and quantum crosstalk during the implementation of simultaneous single-qubit gates on multi-qubit systems. We utilize the Filter Function Formalism to define conditions for achieving crosstalk mitigation and filtering system-environment noise. This formalism allows us to analytically derive intuitive initial conditions that are used within the Filter Gradient Ascent in Function Space (F-GRAFS) optimization framework to achieve optimal noise filtering, via slepian based control. We showcase our work on multi-qubit systems with variable topology. In addition, we examine the interplay between control bandwidth, crosstalk mitigation, and system-environment noise filtering, to develop bandwidth conditions for achieving high-fidelity gates.   

Designing Crosstalk Robust Gate Sets using Optimal Control

Crosstalk is a detrimental type of unintended correlated noise that harms the fidelity of quantum computations. One particularly harmful category of crosstalk affecting devices based on fixed frequency superconducting qubits is ZZ-crosstalk. We leverage optimal control to design gate sets that are able to suppress ZZ-crosstalk across entire devices during computations. Previous software approaches have demonstrated ZZ-crosstalk suppression within constrained circuit blocks by combining optimal control and scheduling co-optimization. In our work, we achieve complete and scalable crosstalk suppression by coordinating redundant implementations of basis gates differing in their pulse implementation. We evaluate calibration schemes for achieving our gates on hardware. We report the success of our approach by running dynamical simulations of circuits across a suite of benchmark quantum algorithms.   

Accurate real-time feedback quantum control with reinforcement learning

Reinforcement learning (RL) has been used in recent years to achieve quantum control in complex and counterintuitive nonlinear problems. However, continuous measurement-based feedback control (MBFC) faces a major challenge due to measurement noise, which makes it difficult to accurately and quickly train RL agents and achieve accurate control over noisy measurement data[1]. Here we present a method for real-time stochastic state estimation that overcomes this hurdle and enables noise-resistant tracking of the conditional dynamics, including the full density matrix of the quantum system[2]. This facilitates a faster training process and accurate discovery of control strategies for the RL agent based on any conditional observable means, including the full conditional density matrix, which is usually not readily and accurately determined in practical real-time experiments.

[1]  S. Borah, B. Sarma, M. Kewming, G. Milburn and J. Twamley, Phys. Rev. Lett. 127, 190403 (2021)

[2] S. Borah and B. Sarma, https://arxiv.org/abs/2301.07254   

Quantum gate design with machine learning

Designing of fast and high fidelity quantum gates is crucial for getting the most out of current quantum hardware since detrimental effects of decoherence can in this way be minimised during the operation of the gates. However, achieving fast gates with high-fidelity and desirable efficiency on the state-of-the-art physical hardware platforms remains a formidable task owing to the presence of hardware-level errors and crosstalk. In recent years, machine learning (ML)-based methods have found widespread applications in different domains of science and technology for nontrivial tasks. In this work, we exploit the power of ML to design quantum gates that uses the hardware-level leakage errors to one's advantage. These gates are found to exhibit controlled leakage dynamics in and out of the computational states at appropriate times during the course of the gate that makes these extremely fast.   

Automating the design of robust quantum control using geometric space curves

The realization of fault-tolerant quantum computation requires robust control of the underlying physical setup. Space Curve Quantum Control is a framework that facilitates the design of smooth pulses that implement dynamically corrected gates by mapping the problem to the task of constructing space curves satisfying certain geometric properties. In this talk, we show how to streamline the process of constructing suitable curves by working in the spin vector representation and by leveraging the machinery of control points and Bezier curves. Our work provides a general continuous-pulse gradient-based gate optimization scheme that allows the utilization of the existing machine learning strategies.   

Quantum optimal control of superconducting qubits based on machine-learning characterization

Implementing fast and high-fidelity quantum operations using quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Reinforcement learning eliminates the need for such an accurate quantum model by relying on fast online interactions between a controller and the quantum device. However, these model-free approaches require large data sets and yield no other useful information beyond the specific control task it was designed for. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while explicitly characterizing this quantum system. Specifically, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimental data and then optimize our experimental controls on this trained model. We demonstrate the power and feasibility of this approach by optimizing arbitrary single-qubit operations performed in parallel on superconducting transmon qubits, using both detailed numerical simulations and an experimental realization.   

Title:Invited: Quantum Control Optimization for Near-Term Quantum Simulation and Variational Algorithms

Quantum control optimization is a critical part of quantum computer design that translates quantum algorithms into analog control signals. Near-term simulation of non-trivial many-body systems and different types of variational algorithms can drastically benefit from having access to parametrized quantum gates. I will review various challenges towards designing extremely high-fidelity quantum gates for parameterized single and two-qubit control optimization and the opportunities it brings to the new paradigm of hybrid digital and analog quantum simulations.    

Frequency- and Amplitude- Modulated Pulses for Single- and Two-Qubit Gates

To achieve lower error rates in superconducting qubits, more robust quantum control is becoming increasingly important. We introduce a method of pulse design for single- and two-qubit gates using optimal quantum control schemes in an extended Hilbert space leveraging Floquet theory. In contrast to more traditional pulse design focused solely on amplitude modulation of the pulse envelope, we concentrate on deliberately manipulating both the amplitude and frequency of the pulse with the goal of achieving faster gates while maintaining the robustness and fidelity. We present numerical simulations using our method and progress towards realizing robust high-fidelity gates using the frequency-modulated pulses.   

Frequency patches for high-fidelity quantum control

Analytical solutions for quantum control are physically intuitive and preferable in experiments but difficult to find. We propose a perturbative approach for high-fidelity quantum control, which is based on the Floquet-Magnus expansion of an oscillatory Hamiltonian. The control performance increases with the number of constant driving fields, which is nicknamed as making frequency patches. Numerical examples with one and two superconducting qubits showcase the effectiveness of this method.   

FPGA-based Machine Learning for In-situ Qubit State Discrimination on QubiC

The integration of machine learning based field-programmable gate array (FPGA) control systems holds tremendous potential for advancing quantum computing by enabling real-time analysis and optimization of qubit readout, resulting in enhanced performance and efficiency. Leveraging the capabilities of the QubiC (Qubit Control) system, we deploy a real-time qubit state discrimination machine learning model on an FPGA. This model not only swiftly identifies the current state of the qubit but also delivers an estimation of the readout classification accuracy. This FPGA-based machine learning controller is constructed through a process involving machine learning model training, pruning and quantization, followed by compilation and assembly on an FPGA. This approach leads to minimal latency and exceptional efficiency in discriminating qubit states, paving the way for substantial advancements in the field of quantum computing.   

Suppressing spurious transitions using spectrally balanced derivative pulse

In scalable superconducting quantum computing, spurious transitions due to crosstalk degrade the performance of quantum operations. The Derivative Removal by Adiabatic Gate (DRAG) technique has been widely used for eliminating the leakage to non-computational levels during single-qubit gate operations. In this work, we propose and demonstrate a practical pulse-shaping technique extended from DRAG for suppressing spurious transition between qubits in a superconducting quantum processor. Our pulse features balanced spectral shaping which leads to effective blocking of specific transitions. This method can be extended to the case with multiple unwanted couplings among multiple qubits. It can further be used to suppress the loss resulting from the harmful interactions between the qubits and two-level systems or other undesired parasitic couplings to facilitate the realization of scalable quantum computing.   

Improving algorithmic performance using hardware efficient gates

Useful quantum algorithms which utilize only the standard entangling gates like CNOT, iSWAP, etc. fail to produce meaningful results on the NISQ devices. Superconducting circuits provide a diverse variety of native multi-qubit interactions depending on the device architecture and gate-drive scheme. The calibration of high fidelity parameterized gates and the construction of an efficient circuit compilation scheme that leverages the richer gate set are open problems. In this talk, we present an efficient method for optimizing a selected set of system-wide entangling gates. These gates can be dynamically used online to create short-duration, high-fidelity parametric gates with arbitrary angles, all while demanding minimal calibration resources. To ensure the optimal incorporation of these gates in algorithms, we built a specialized compilation procedure that automatically finds and replaces optimizable patterns in quantum circuits. We demonstrate that our pulse-efficient gate construction and calibration technique enables both a higher fidelity and shorter duration than the standard implementation. This leads to enhanced performance across several key quantum algorithms, including QFT, Trotterized time evolution and QAOA. For instance, when running a 7-qubit MaxCut QAOA, the default circuit execution on a cloud-accessible quantum computer fails to give the correct bit string as the mode of the output distribution while our approach achieves the correct answer with 99% probability. These results signify the importance of both the hardware efficient gates and deterministic error suppression for making quantum devices useful.