Session J33: Dynamical Decoupling and Bath Engineering for Quantum Control

Live

The protection of spin coherence is an essential task in order to manipulate, store and read quantum information. It has been proposed to dynamically decouple (DD) qubits from their surroundings by applying a series of distinct pulses¹. For nitrogen vacancy centers, such protection was achieved by using concatenated DD up to the second order of dressing². We go beyond their specific case and demonstrate T2~T1 with a new pulse protocol, independent of qubit initial state, in a number of materials with different spin Hamiltonians and environments³. The protocol uses two coherent microwave pulses: one drives the Rabi precession while a low-power, circularly polarized (image) pulse continuously sustains the spin motion. The initial phase of the image drive allows tuning the spin dynamics by altering the Floquet modes. The technical implementation is simple and can be generalized to any type of qubit, such as superconducting circuits or spin systems.
1. L. Viola, S. Lloyd, PRA 58, 2733 (1998).
2. D. Farfurnik, et al, PRA 96, 013850 (2017).
3. S. Bertaina et al, arXiv:2001.02417, to appear.   

Live

Open quantum systems interacting with an environment can be described by Lindblad density matrix equation that encodes their approach to a steady state. When the quantum trajectories of this decoherence-inducing dynamics are restricted to those with no quantum jumps, the resulting evolution is described by effective non-Hermitian Hamiltonians. The presence of a special kind of degeneracy known as an exceptional point (EP) plays an important role in the unique topology of these non-Hermitian systems. Such an EP occurs when both the eigenvalues and eigenstates of the system coalesce. We demonstrate real-time control over a single dissipative qubit described by an effective non-Hermitian Hamiltonian. We reveal how quasistatic tuning of the system parameters results in coherent quantum gates enabled by the complex energy topology. Leaving the quasistatic limit, an effective Floquet Hamiltonian enables rapid quantum gates. Finally, we characterize the geometric phases accumulated from quantum state transport around the EP, revealing the chirality of the transport. Our work demonstrates a new method for control over quantum state, highlighting new facets of quantum bath engineering enabled through time-periodic non-Hermitian control.   

Live

Cleverly designed pulse sequences in NMR can decouple the strong dipolar interaction in dense solid-state spin systems. These decoupling sequences were originally designed to narrow spectral lines and improve resolution in NMR spectroscopy. The effective extension of coherence times using these sequences is also important for quantum control, simulation and sensing applications. In this work, we study the effectiveness of different dipolar decoupling sequences for a variety of uncorrelated single-spin and correlated multi-spin states in different samples. We explore the sensitivity of these sequences to different errors and examine potential error mitigation strategies.   

Live

Dissipative protocols for state preparation provide the ability to stabilize complex entangled states which are inherently robust to decoherence, though they typically exhibit a tradeoff between the preparation rate and the fidelity of the prepared state. In this talk I will describe a scheme for Bell state preparation employing only parametric qubit-qubit and qubit-resonator couplings, which afford a large degree of flexibility and control over the stabilized state. Both the amplitudes and phases of these couplings are tunable in situ, providing a natural avenue to implement time-dependent control of the state preparation dynamics. Such control, here implemented through engineered dissipation, can circumvent the tradeoffs inherent in the scheme by first rapidly preparing a product state then adiabatically tuning to the desired Bell state. I will present analytical and numerical results which show that large speedups are possible with this approach even in the weak-dissipation regime. To understand the achievable speedup, I will examine the adiabaticity criteria in this driven-dissipative system and provide estimates of the resulting bounds on the state preparation time.   

Live

A formalism based on Pontryagin's maximum principle is applied to determine the time-optimal protocol that drives a general initial state to a target state by a Hamiltonian with limited control, i.e., there is a single control field with bounded amplitude. The coupling between the bath and the qubit is modeled by a Lindblad master equation. Dissipation typically drives the system to the maximally mixed state, consequently there generally exists an optimal evolution time beyond which the decoherence prevents the system from getting closer to the target state. For some specific dissipation channel, however, the optimal control can keep the system from the maximum entropy state for infinitely long. The conditions under which this specific situation arises are discussed in detail. The numerical procedure to construct the time-optimal protocol is described. In particular, the formalism adopted here can efficiently evaluate the time-dependent singular control which turns out to be crucial in controlling either an isolated or a dissipative qubit.   

Live

We study the dynamics of a dissipative transmon superconducting qubit whose dissipation comes into two parts: a fast coherent nonunitary dissipation (energy loss) and a slow decoherence due to quantum jumps within the qubit. We observe that the coherence damping rate is enhanced near the exceptional point. Together with the effect of non-Hermitian gain/loss, the decoherence also leads to breakdown of adiabatic evolution under the slow-driving limit. Our study shows the critical role of quantum jumps in generalizing the applications of classical non-Hermitian systems to open quantum systems from sensing to control.   

Live

While robust dynamical decoupling and Hamiltonian engineering techniques are well-developed and highly successful for qubit systems, extensions to qudits involving more than two levels are much less explored. However, the development of such techniques for qudit systems may enable the engineering of novel classes of Hamiltonians for many-body physics, or the development of quantum sensors with higher sensitivity. In this talk, we outline extensions of robust Hamiltonian engineering techniques to qudit systems. We develop general design techniques for pulse sequences that decouple spin-1 dipolar interactions and disorder, while remaining robust against finite pulse duration imperfections, and show their applications in dynamical decoupling, quantum sensing, and the creation of exotic many-body states such as quantum many-body scars. While we illustrate our results in a dense ensemble of NV centers, our methodology and pulse sequences apply to any quantum information platform that obeys the rotating wave approximation, such as superconducting qubits, trapped atoms and quantum dots.   

Live

Future technologies such as quantum computing, sensing and communication demand the ability to control microscopic quantum systems with unprecedented accuracy. This task is particularly daunting due to unwanted and unavoidable interactions with noisy environments that destroy quantum information through decoherence. I will present a new theoretical framework for deriving control waveforms that dynamically combat decoherence by driving qubits in such a way that noise effects destructively interfere and cancel out. This theory exploits a rich geometrical structure hidden within the time-dependent Schrödinger equation in which quantum evolution is mapped to geometric curves. Control waveforms that suppress noise can be obtained by drawing closed curves and computing their curvatures. I will show how this can be done for single- and multi-qubit systems.   

Live

Ultra-subharmonic (USH) bifurcation refers to a broad class of dynamical transitions wherein a driven nonlinear oscillator is resonantly excited to one of q equiprobable stable states by some p/q-th USH of a drive, for naturals p and q. In circuit quantum electrodynamics (cQED), particular USH processes have been employed in quantum devices such as amplifiers based on bifurcation thresholds and qubits based on Schrodinger Cat-like manifolds of degenerate driven-dissipative states. While these instances are well documented, mapping out where in parameter space generic USH processes occur in cQED experiments is of increasing importance. This is especially relevant in cases where unexpected bifurcations plague the driven-dissipative operations employed in quantum information processing. Moreover, controlled USH processes could lead to novel nonlinear interactions, like those involved in stabilizing higher-dimensional cat states. In this talk, basing ourselves on Part 1, we will discuss different experimental manifestations of USH processes. Their comprehensive map in parameter space will be shown. Finally, we will discuss how to mitigate the undesired side-effects of USH bifurcation and to harness it for quantum operations.   

Live

Ultra-subharmonic (USH) bifurcation refers to a broad class of dynamical transitions wherein a driven nonlinear oscillator is resonantly excited to one of q equiprobable stable states by some p/q-th USH of a drive, for naturals p and q. Historically, this bifurcation class has attracted mostly theoretical interest due to the intricate topology of phase space trajectories and its connections to chaos. Recently, particular instances of USH processes have been revisited experimentally in Josephson circuits, specifically in the novel low-dissipation quantum regime, for the purpose of processing quantum information. However, the general physical structure of USH processes — their perturbative order and time-averaged dynamics, remains unexamined, particularly for bridging the classical and quantum regimes. We show that the time-averaged dissipative dynamics governing any USH process in the low-dissipation regime, whether classical or quantum, can always be represented as motion on an effective static Hamiltonian surface endowed with discrete q-fold symmetry. Moreover, semiclassically, this so-called metapotential unifies two distinct quantum manifestations of USH bifurcation: multiphoton nonlinear resonances and protected multistability.   

Live

The spinful nuclei around a controllable color center, such as the NV center in diamond, are promising candidates for a quantum memory. Experiments have demonstrated control of nuclear spins through CPMG-like dynamical decoupling of the NV in diamond and the divacancy in SiC. In this work, we show that the Uhrig decoupling sequence and a hybrid protocol we introduce improve these entangling gates in terms of fidelity, spin control range, and spin selectivity. We numerically show our method's efficacy on NV centers in diamond, but our results are general and applicable to other types of defects in solids.   

Live

Dynamical decoupling and Hamiltonian engineering lie at the cornerstone of modern quantum science and engineering. For qubits, conditions that determine whether a given pulse sequence transforms a native interaction into a desired form are straightforward to obtain due to the intimate connection between single qubit gates and rotations in three dimensions. In this talk, we extend this characterization to generic qudit systems with strongly anharmonic level structures. Utilizing results from group theory we show how the Clebsch-Gordon coefficients of particular irreducible representations of SU(d) lead to simple analytic conditions for the cancellation of generic qudit interactions. We further use them to give a natural parameterization of engineerable Hamiltonians. Lastly, we analytically construct experimentally robust pulse sequences satisfying our cancellation conditions, leveraging the algebraic properties of the generalized Clifford group. Motivated by the prominence of modern qutrit quantum simulation and computation experiments, special attention will be given to this d=3 special case. These results offer an efficient, analytical design tool for modern quantum simulators, opening the door to exotic many-body physics lacking any analog in qubit systems.   

On Demand

Quantum technology requires full manipulation quantum systems, i.e. arbitrary quantum operations (AQuOs) for all possible physical process of an open quantum system. However, this goal demands great extra physical resources and hence is difficult to realize. In this talk, I will show our recent experiments about demonstrating a universal approach of AQuO on a superconducting photonic qudit with only a two-level ancilla and a log₂d-scale circuit depth for a d-dimensional system. Specifically, I will show the AQuO can be applied in quantum trajectory simulations for quantum subspace stabilization and quantum Zeno dynamics, and incoherent manipulation of the qudit. Furthermore, rank-d² positive operator-valued measures are also obtained, which outperform conventional tomography technique in practice. The demonstrated AQuOs in this talk for complete quantum control would play an important role in quantum information science.
Reference:
[1] W. Cai, and et al., arXiv: 2010.11427 (2020).