Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session N71: Robust Control in High-Dimensional Hilbert SpacesFocus
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Sponsoring Units: DQI Chair: Frank Schaefer, Massachusetts Institute of Technology Room: Room 407/408 |
Wednesday, March 8, 2023 11:30AM - 11:42AM |
N71.00001: Designing dynamically corrected gates robust to multiple noise sources using geometric space curves: Part 1 Evangelos Piliouras, Hunter T Nelson, Kyle Connelly, Sophia Economou, Edwin Barnes Quantum computation demands high-fidelity control despite the presence of noise, a necessity for reaching the threshold for quantum error correction. A recently developed method named Space Curve Quantum Control (SCQC) maps the entire control problem to a Euclidean curve that dictates the type and degree of error suppression. In this talk, we augment the SCQC framework by deriving the global geometric conditions for pulse error tolerance, completing the picture of noise-robust single qubit control under SCQC. Our work further illuminates the connection between holonomic evolution and pulse error suppression. |
Wednesday, March 8, 2023 11:42AM - 11:54AM |
N71.00002: Designing dynamically corrected gates robust to multiple noise sources using geometric space curves: Part 2 Hunter T Nelson, Evangelos Piliouras, Kyle Connelly, Sophia Economou, Edwin Barnes Quantum processors typically suffer from multiple noise sources that degrade the quality of gates. In this talk, I will present a general technique to design control pulses that simultaneously suppress noise in both qubit energy levels and control fields. This is facilitated through a reverse engineering approach known as the space curve quantum control (SCQC) formalism in which closed curves in Euclidean space map to robust control fields. Constraints on these curves give necessary and sufficient conditions for robust evolution. Several methods for how to build such curves will be presented. |
Wednesday, March 8, 2023 11:54AM - 12:06PM |
N71.00003: Fast and Robust Geometric Two-Qubit Gates for Superconducting Qubits and Beyond Fnu Setiawan, Peter Groszkowski, Aashish A Clerk Quantum protocols based on adiabatic evolution are remarkably robust against imperfections of control pulses and system uncertainties. While adiabatic protocols have been successfully implemented for quantum operations such as quantum state transfer and single-qubit gates, their use for geometric two-qubit gates remains a challenge. In this talk, I will present a general scheme to realize robust geometric two-qubit gates in multi-level qubit systems where the interaction between the qubits is mediated by an auxiliary system (such as a bus or coupler). While our scheme utilizes Stimulated Raman Adiabatic Passage (STIRAP), it is substantially simpler than STIRAP-based gates that have been proposed for atomic platforms, requiring fewer control tones and ancillary states, as well as utilizing only a generic dispersive interaction. I will show how our gate can be accelerated using a shortcuts-to-adiabaticity approach, allowing one to achieve a gate that is both fast and relatively robust. I will present a comprehensive theoretical analysis of the performance of our two-qubit gate in a parametrically-modulated superconducting circuits comprising two fluxonium qubits coupled to an auxiliary system. |
Wednesday, March 8, 2023 12:06PM - 12:18PM |
N71.00004: Robust Quantum Control: Analysis & Synthesis via Averaging — Part 1: Algorithm Robert Kosut, Gaurav Bhole, Benjamin Lienhard, Herschel A Rabitz Robust control over the dynamics of a quantum system is indispensable for realizing useful quantum information processors. Here, we utilize the classical method of averaging to realize an approach for robustness analysis and synthesis of controls for quantum logic gates. By separating the system Hamiltonian into a nominal (uncertainty-free) and interaction (error) Hamiltonian, the robustness measure is defined as the size of the average of the interaction Hamiltonian. The result is a multi-criterion optimization competing uncertainty-free fidelity with the robustness measure. Exploiting the topology of the control landscape at high fidelity (as determined by the null space of the nominal fidelity Hessian), we arrive at a two-stage optimization algorithm: first, improve the nominal fidelity until sufficiently high, and then reduce the robustness measure while maintaining high nominal fidelity. An optimal solution is obtained by approximating the nominal fidelity and robustness measure as quadratics in the control increments. The approximation enables the control increments at each iteration to be solved by a convex optimization. For each iteration, the goal is to keep the nominal fidelity high while reducing the robustness measure. This approach reduces the experimental quantum-system-characterization effort, enabling robust and high-fidelity quantum logic gate design. |
Wednesday, March 8, 2023 12:18PM - 12:30PM |
N71.00005: Robust Quantum Control: Analysis & Synthesis via Averaging — Part 2: Experiment Gaurav Bhole, Robert Kosut, Benjamin Lienhard, Herschel A Rabitz Useful quantum information processors require their control to be robust to the inherent noise and system uncertainties. We propose an approach to design robust quantum operations via a two-stage algorithm. We first improve the control fidelities close to optimality before optimizing for robustness in system uncertainties. The two-stage approach leverages the control landscape topology to enable a computationally efficient method. The algorithm aims to maintain high control fidelities while increasing the robustness. To verify the utility and efficacy of the theoretically and numerically developed approach, we test it on a multi-quit NMR system. We experimentally extract the maximally possible fidelity of single- and multi-qubit gates designed by the algorithm. The algorithm designs the control instances using incomplete knowledge of the quantum system and upper bounds of the system uncertainties, such as the coupling to environmental two-level systems. The algorithm successfully compensates for unknown system couplings and outperforms standard optimal control algorithms. The numerically and experimentally implemented algorithm enables the design of quantum logic gates under realistic circumstances in which only limited knowledge of the accurate and complete system Hamiltonian is available. The proposed robustness approach eases the experimental effort to characterize the quantum system meticulously and enables efficient and high-fidelity quantum logic gate design under these uncertainties. |
Wednesday, March 8, 2023 12:30PM - 12:42PM |
N71.00006: Considerations of the robustness of a control solution and its application in an experimental scenario Marco Rossignolo We report general theoretical considerations concerning the robustness of a quantum optimal control solution. The variation of the noise parameters in the system could be a barrier to employing an efficient and stable operation. |
Wednesday, March 8, 2023 12:42PM - 1:18PM |
N71.00007: Opportunities and challenges in learning how to control high dimensional quantum systems Invited Speaker: Christian Arenz The control of complex quantum system is of paramount importance for quantum technologies. One common approach for controlling quantum systems is through properly tailored electromagnetic pulses. In this talk, I will consider a more general picture where controls are simply given by tunable parameters that enter in the system evolution. Taking this view allows for analyzing the task of finding optimal control solutions for a wide range of applications, including variational quantum algorithms (VQAs). The ease of finding these control solutions is determined by the structure of the underlying optimization landscape, whose study has a long history in optimal control theory. Decades of numerical and experimental evidence, combined with recent analytical work, suggests that the control landscape structure typically favors finding optimal controls, i.e., iterative procedures tend to converge to global optima, provided that some assumptions on the properties of the control pulses are met. I will begin by revisiting these assumptions within the context of this more general control picture. I will then go on to focus on VQAs, where parameters in a quantum circuit serve as the controls for preparing the ground state of a desired Hamiltonian, and will argue that almost all VQAs converge to the ground state almost surely if the quantum circuit is described by sufficiently many control parameters. I will conclude by discussing the trade-off between obtaining convergence guarantees through overparameterization and the appearance of barren plateaus, where regions in the optimization landscape can be become exponentially flat. |
Wednesday, March 8, 2023 1:18PM - 1:30PM |
N71.00008: Universally robust control sequences for high-dimensional superconducting qubits Madeline K Taylor, Kangdi Yu, Murat C Sarihan, Jin Ho Kang, Ananyo Banerjee, Cody S Fan, Daniel A Lidar, Chee Wei Wong Recently superconducting transmon qubits are consistently being implemented as the building blocks of large-scale quantum processors due to their longer coherence times, potential for precise optimal control using microwave electronics, and microelectronics scalability. Working with higher-order Fock states, transmon qubits could be implemented as a d-dimensional Hilbert-space quantum system, or qudit, where quantum information is encoded in the higher Jaynes-Cummings levels of the transmon system which reduces circuit complexity for non-classical gate operations and algorithms. It is necessary for these high-dimensional qudits to hold long coherence times in both relaxation and dephasing pathways so that the transmon logic gates can be implemented with high fidelity. In an effort to suppress decoherence in these qudits, here we demonstrate robust dynamical decoupling (DD) using precise pulse sequences to mediate systematic errors and dephasing that occur in the evolution of these higher-order qudits. We demonstrate the effectiveness of several DD pulse sequences applied on the higher-order transitions of a transmon qudit coupled to a readout microwave resonator during Ramsey measurements. These pulse sequences mediate the dephasing effect in this superposition state which resulted in improved dephasing times (T2) at the microsecond scale. |
Wednesday, March 8, 2023 1:30PM - 1:42PM |
N71.00009: Pulse-level control and dynamics of qudit gates A. Baris Ozguler, Joshua A Job Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler [1]. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. We address this problem by simulating qudit dynamics for circuit quantum electrodynamics (cQED) systems. Our results show that the frequency shifts due to crosstalk yield extremely stringent bounds on interaction parameters and spectator mode occupations. Here, we provide an experimentally relevant fidelity scaling formula that is independent of the gate type and can be used as a bound on the fidelity decay [2]. The estimated scaling of the fidelity matches the scaling calculated using our numerical results. |
Wednesday, March 8, 2023 1:42PM - 1:54PM |
N71.00010: Realizing high-fidelity qudit gates on a transmon via optimal control Lennart Maximilian Seifert, Ziqian Li, Jason Chadwick, Tanay Roy, Andrew Litteken, Jonathan M Baker, David Schuster, Frederic T Chong Many physical quantum architectures have access to a wider range of possible states. Previous theoretical studies [1] have shown that using these higher qudit states can significantly reduce the depth and width of a quantum circuit, increasing the computation volume of quantum computers with limited coherence and size. However, in order to fully investigate the viability of using qudit states for computation, control pulses corresponding to qudit gates have to be designed and their quality evaluated on actual hardware. Using optimal control methods, we explicitly construct short-duration pulses of high theoretical fidelity (>0.999) for single qutrits and ququarts to realize practical gate types that can explore the entire state space. We successfully demonstrate their experimental implementation on a superconducting transmon with four well-characterized energy levels and estimate their fidelity via quantum process tomography. Our findings motivate further research in higher-radix quantum computing architectures and tailored compiler design. |
Wednesday, March 8, 2023 1:54PM - 2:06PM |
N71.00011: Simulating neutrino oscillations with a transmon qutrit. Vinh San Dinh, Jens Koch, Matthew Reagor, Silvia Zorzetti, Alexander Romanenko, Joshua A Job Current cloud quantum processors based on superconducting qubits are primarily set up for employing the two lowest levels of transmon circuits as qubits. Here, we show that functionality made accessible to the user also enables the use of higher levels, turning the transmon into a qudit. As an illustration, we present a qutrit-based quantum simulation of three-flavor neutrino oscillations on a Rigetti cloud-access processor. Single-qutrit unitaries in this simulation are realized by two methods: quantum optimal control and gate decomposition. We discuss advantages and limitations of these schemes. |
Wednesday, March 8, 2023 2:06PM - 2:18PM |
N71.00012: Direct pulse level compilation of arbitrary quantum logic gates on superconducting qutrits Yujin Cho, Kristin M Beck, Alessandro R Castelli, Kyle A Wendt, Bram Evert, Matthew Reagor, Jonathan L DuBois In principle, optimal control techniques can be used to implement any complex many-body unitary on a quantum device without the need to decompose the operation into primitive gates. In addition, the resulting operation can be achieved in a shorter time and with less error than compilation to a fixed gate set. Here, we demonstrate the practical utility of integrating optimal control techniques directly into a quantum compiler toolchain. We will present experimental results for pulse-level compilation of randomly generated unitaries implemented with optimal control on superconducting qutrits. We demonstrate high-fidelity evolution on two different experimental platforms with different qudit architectures, the LLNL QuDIT testbed and Rigetti Aspen-11. Our work shows that optimal control can practically be used to enable more detailed and accurate simulations of complicated quantum phenomena than is possible with the fixed gate set approach on current quantum hardware. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-841474. |
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