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 Q71: Quantum Optimal Control and Gate SynthesisFocus
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Sponsoring Units: DQI Chair: Gaurav Bhole, Princeton University Room: Room 407/408 |
Wednesday, March 8, 2023 3:00PM - 3:12PM |
Q71.00001: More for LESS: Optimal Control of Open Quantum Systems Within the Born approximation Matthew D Grace, Constantin Brif, Herschel A Rabitz, Robert Kosut In the context of the Born approximation, i.e., neglecting system-environment correlations in the composite system state and assuming a time-independent environment state, we develop the dynamics of controlled, time-dependent quantum systems in the presence of irreversible environment-induced decoherence. We show that in the interaction picture, these dynamics separate the time evolution of the system into a sequence of unitary and nonunitary operations exactly. For state-dependent objectives, quantum optimal control is applied to the corresponding dynamical equations, and using a composite system model of interacting spins as an illustrative example, we find that simple and versatile controls are able to discover and use decoherence-free subspaces (when they exist) to optimize the state objectives. Results from several numerical control simulations will be presented and discussed. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. SAND2022-14340 A |
Wednesday, March 8, 2023 3:12PM - 3:24PM |
Q71.00002: Accelerating the Quantum Optimal Control of Large Qubit Systems with Symmetry-based Hamiltonian Transformations and Linear Unitary Propagators Xian Wang, Bryan M Wong, Anshuman Kumar We have developed a novel framework for the quantum optimal control (QOC) of multi-qubit systems. A large family of Hamiltonians satisfies the symmetry of finite groups, e.g., the permutation group Sn and the dihedral group Dn. Using the symmetry of a multi-qubit system, we can decompose the Hilbert space of the system and block diagonalize the Hamiltonian, which enables efficient computations when the transition is limited to a specific subspace. We show that the size of the n-qubit Hamiltonian is reduced from 2n to O(n) under Sn symmetry or O(2n/n) under Dn symmetry. We show that the computational cost for carrying out quantum control of these transformed Hamiltonians is significantly reduced without affecting the fidelity of the output. We also show that the Lie-Trotter-Suzuki decomposition generalizes the application of this technique to a larger number of varieties of multi-qubit systems. |
Wednesday, March 8, 2023 3:24PM - 3:36PM |
Q71.00003: Quantum optimal control in a generalized rotating frame Agustin Di Paolo, William P Banner, Jack Qiu, Jeffrey A Grover, William D Oliver With superconducting-qubit gate operations now routinely approaching their speed limits, strategies for mitigating the impact of coherent errors are increasingly important. In this talk, we introduce a method for quantum optimal control in an extended Hilbert space, where the quantum dynamics becomes exactly differentiable without needing rotating-wave approximations. Our representation exploits an expansion of the quantum controls in a physically motivated basis, which conveniently leads to waveforms with a bounded frequency spectrum. We perform numerical simulations using our optimal-control method and demonstrate improved two-qubit gate fidelities for typical transmon- and fluxonium-qubit architectures. We show, for instance, that our numerical technique rediscovers known pulse schedules for minimizing leakage, e.g., DRAG for single qubits, and generalizes such a strategy to larger systems. We extend our optimal-control approach to Liouville space and discuss the impact of dissipation and finite amplitude and frequency resolution on the two-qubit gate fidelities. |
Wednesday, March 8, 2023 3:36PM - 3:48PM |
Q71.00004: Pontryagin–Optimal Control of a non-Hermitian Qubit Philippe Lewalle, Birgitta Whaley Open-system quantum dynamics described by non-Hermitian effective Hamiltonians have become a subject of considerable interest. Studies of non-Hermitian physics have revealed general principles, including relationships between the topology of the complex eigenvalue space and the breakdown of adiabatic control strategies. We study here the control of a single non-Hermitian qubit, similar to recently realized experimental systems in which the non-Hermiticity arises from an open spontaneous emission channel. We review the topological features of the resulting non-Hermitian Hamiltonian and then present two distinct results. First, we illustrate how to realize any continuous and differentiable pure-state trajectory in the dynamics of a qubit that are conditioned on no emission. This result implicitly provides a workaround for the breakdown of standard adiabatic following in such non-Hermitian systems. Second, we use Pontryagin's maximum principle to derive optimal trajectories connecting boundary states on the Bloch sphere, using a cost function which balances the desired dynamics against the controller energy used to realize them. We demonstrate that the latter approach can effectively find trajectories which maintain high state purity even in the case of inefficient detection. |
Wednesday, March 8, 2023 3:48PM - 4:00PM |
Q71.00005: Application of Pontryagin's Maximum Principle to Quantum Metrology in Dissipative Systems Chungwei Lin Optimal control theory, also known as Pontryagin's Maximum Principle, is applied to the quantum parameter estimation in the presence of decoherence. An efficient procedure is devised to compute the gradient of quantum Fisher information with respect to the control parameters and is used to construct the optimal control protocol. The proposed procedure keeps the control problem in the time-invariant form so that both first-order and second-order optimality conditions derived from Pontryagin's Maximum Principle apply; the second-order condition turns out to be crucial when the optimal control contains singular arcs. Concretely we look for the optimal control that maximizes quantum Fisher information for ``twist and turn'' problem. We find that the optimal control is singular without dissipation but can become unbounded once the quantum decoherence is introduced. An amplitude constraint is needed to guarantee a bounded solution. With quantum decoherence, the maximum quantum Fisher information happens at a finite time due to the decoherence, and the asymptotic value depends on the specific decoherence channel and the control of consideration. |
Wednesday, March 8, 2023 4:00PM - 4:12PM |
Q71.00006: Non-adiabatic Majorana brading protocol in a Y-shaped nanowire Sutapa Samanta, Haylen Gerhard, Armin Rahmani Braiding of Majorana fermions is the primary logical operation of a topological quantum computer. Recently adiabatic Majorana braiding has been studied numerically for a realistic Y-shaped nanowire junction. In this work, we find optimized nonadiabatic braiding protocols on these Y junctions using simulated annealing and Pontryagin's minimum principle. These finite-time optimal protocols provide an advantage over the adiabatic evolution while preserving topological protection. |
Wednesday, March 8, 2023 4:12PM - 4:48PM |
Q71.00007: A globally convergent approach for quantum control and system identification Invited Speaker: Denys I Bondar Numerical optimization methods, collectively referred to as ``optimal control", are an important tool able to determine what is possible in the manipulation of quantum systems when no other method can. Two significant difficulties limit the power of these methods: the need to numerically simulate the evolution of the quantum system many times, and the difficulty in finding near-optimal solutions in the presence of multiple local minima. Here we introduce a formulation of quantum control that removes both of these difficulties. The Magnus expansion and an appropriate representation for the control functions provide an analytic approximation to the evolution of essentially any system that is also polynomial in the control parameters. This approximation both eliminates the need for repeated simulation and allows global optimization with recently-developed optimization methods for polynomials. It greatly reduces the numerical overhead in fixed-time quantum control, minimum-time control, and Hamiltonian identification. |
Wednesday, March 8, 2023 4:48PM - 5:00PM |
Q71.00008: Counterdiabatic Optimised Local Driving Ieva Cepaite, Andrew J Daley, Callum W Duncan, Anatoli S Polkovnikov Counterdiabatic driving protocols provide a way to speed up adiabatic dynamics through the suppression of excitations into unwanted states. However, exact counterdiabatic drives require knowledge of the spectral properties of the instantaneous Hamiltonians, which limits their application. It has recently been shown that this requirement can be removed by using a variational approach which allows one to determine an approximate, localised counterdiabatic drive without requiring access to the wavefunction of the system. We show that when coupled with additional parameterised driving terms, the path of the system can be optimised in a way that enhances the loss-suppressing effects of a chosen local order of the counterdiabatic protocol. Furthermore, this path appears to minimise the total power and maximal driving strength of higher local order terms in the approximate counterdiabatic drive. We show that this can be used in order to perform optimisation of the system path in a way that suppresses non-diabatic losses without requiring access to the system dynamics or experimental results. |
Wednesday, March 8, 2023 5:00PM - 5:12PM |
Q71.00009: Fast-forward scaling theory for nonadiabatic transitions Takuya Hatomura Many quantum technologies are realized by using time-dependent quantum control. Control speed is a very important factor for realizing such quantum technologies since decoherence is inevitable in quantum systems. However, simple speed-up of time-dependent driving changes the amount of nonadiabatic transitions and it results in different measurement outcomes. It is also a problem from the viewpoint of quantum simulation of nonadiabatic phenomena. The fast-forward scaling theory was proposed as a method for changing time scale of given dynamics without changing measurement outcomes. |
Wednesday, March 8, 2023 5:12PM - 5:24PM |
Q71.00010: Assessing the limits of controllability for electron spin qubits through quantum optimal control Paul M Kairys, Jonathan C Marcks, Nazar Delegan, Jiefei Zhang, F. Joseph Heremans, David D Awschalom Evaluating the most optimistic capabilities of quantum devices for specific applications is a nascent use of quantum optimal control theory, where classical numerical simulations estimate essential properties such as quantum speed limits and minimum control times as a function of system parameters and limitations. Here we estimate these quantities for nitrogen-vacancy centers in diamond, a paradigmatic example of an electron spin qubit. Our simulations are performed at high accuracy beyond the rotating wave approximation and through explicit unitary simulation of neighboring nuclear spins. Using the gradient optimization of analytic controls method we identify realistic analytical pulses for unitary control and quantify the relationship between pulse complexity, control time, and fidelity. These simulations provide insight into the throughput of quantum foundries and inform quantum device engineers about the fundamental computational and sensing rates in prospective quantum technologies. |
Wednesday, March 8, 2023 5:24PM - 5:36PM |
Q71.00011: Analytically Realizing Hybrid Boson-Qubit Operations via Hamiltonian Simulation Techniques Christopher Kang, Micheline B Soley, Eleanor Crane, Steven M Girvin, Nathan Wiebe Circuit QED enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson operations are realizable only through optimal control theory (OCT). OCT is oftentimes intractable and uninterpretable, yielding only a pulse which performs the desired operation. This pulse provides no physical intuition and is computationally intensive to produce. In this talk, we introduce an analytic approach for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie-Trotter and Baker-Campbell-Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, i.e., ap a†q for integer p, q. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid boson-qubit devices. |
Wednesday, March 8, 2023 5:36PM - 5:48PM Author not Attending |
Q71.00012: Improving pulse exploration in model predictive quantum control Andy J Goldschmidt Many typical quantum control problems can be solved by local methods for optimal control–relying on exploitation of the model information without fear of becoming trapped at solutions far from the global optimum. Nevertheless, if models of the experiment are inaccurate or the control tasks are sufficiently complex, additional global exploration might become necessary to avoid traps and find good solutions. In this work, we explore the exploitation / exploration tradeoff within model predictive quantum control (MPC). MPC is a local control scheme that utilizes experiment feedback online during the synthesis of the control pulse. With this modest request for data, MPC is able to design pulses which are robust to model uncertainty and system disturbances. In addition, sampling-based MPC algorithms offer a way to improve upon the exploration properties of traditional MPC by leveraging the predictions of a nominal system model or models. By combining model-based exploration with experiment feedback, sampling-based MPC is able to discover robust pulse sequences for hard problems in quantum optimal control. |
Wednesday, March 8, 2023 5:48PM - 6:00PM |
Q71.00013: Quantum Noise Spectroscopy Informed Optimized Gates Andrew J Murphy, Yasuo Oda, Timothy M Sweeney, Kevin Schultz, Leigh M Norris, Gregory Quiroz In recent years, a number of quantum noise spectroscopy (QNS) protocols have been developed to characterize spatio-temporally correlated noise processes. Estimates of the noise power spectral density from QNS protocols are meant to inform optimized control protocols designed to mitigate noise while simultaneously implementing a particular quantum operation. While it is widely accepted that QNS should yield an added advantage to optimized control, there has yet to be an experimental demonstration of QNS-informed optimized control on a non-trivial gate. Here, we demonstrate the utility of QNS-informed control through the design of single qubit operations. Gates are optimized to tailor the frequency response of a fixed frequency transmon using the offline-optimization approach: Filter Gradient Ascent in Function Space (F-GRAFS) [arXiv: 2206.03504 (2022)]. We experimentally verify filter design via the injection of Schrodinger Wave Autoregressive Moving Average (SchWARMA) [Phys. Rev. Res. 4, 013081 (2022)] engineered noise. Controlled noise environments are further employed to evaluate optimized gate performance relative to “noise-uninformed” single qubit operations, and quantify robustness to model uncertainty within the F-GRAFS optimization. Our results convey the significance of noise-informed control and provide experimental insight into the interplay between characterization protocols and optimized control. |
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