28 research outputs found
Dynamical uncertainty propagation with noisy quantum parameters
Many quantum technologies rely on high-precision dynamics, which raises the
question of how these are influenced by the experimental uncertainties that are
always present in real-life settings. A standard approach in the literature to
assess this is Monte Carlo sampling, which suffers from two major drawbacks.
First, it is computationally expensive. Second, it does not reveal the effect
that each individual uncertainty parameter has on the state of the system. In
this work, we evade both these drawbacks by incorporating propagation of
uncertainty directly into simulations of quantum dynamics, thereby obtaining a
method that is faster than Monte Carlo simulations and directly provides
information on how each uncertainty parameter influence the system dynamics.
Additionally, we compare our method to experimental results obtained using the
IBM quantum computers.Comment: 10 pages, 3 figure
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Shaken Lattice Interferometry
Since the first demonstrations in 1991, atom interferometry has been a burgeoning field of research. The work done in this field is motivated by the potential sensitivity improvements that atom-based devices can have over the current state-of-the-art light- and MEMS-based devices. This dissertation presents a new and unique approach to atom interferometry in that we perform the basic interferometric sequence of splitting, propagation, reflection, reverse-propagation, and recombination with atoms trapped in a phase-modulated (shaken) optical lattice. In both simulation and experiment we demonstrate a one-dimensional shaken lattice interferometer configured as an accelerometer. The interferometry sequence is developed through the use of learning and optimal control algorithms that allow us to implement the desired state-to-state transformations and perform the desired operations, e.g. splitting and recombination of the atoms trapped in the lattice. This device has a sensitivity that scales as the square of the interrogation time and an ability to distinguish both the magnitude and sign of an applied acceleration signal. Furthermore we show that we can tailor the transfer function of the interferometer to be sensitive to a signal of interest, e.g. an AC signal of a given frequency. Finally, we explore the analytics of shaken lattice interferometry and offer some suggestions as to the future of this new technology
Robust Control Performance for Open Quantum Systems
The robustness of quantum control in the presence of uncertainties is
important for practical applications but their quantum nature poses many
challenges for traditional robust control. In addition to uncertainties in the
system and control Hamiltonians and initial state preparation, there is
uncertainty about interactions with the environment leading to decoherence.
This paper investigates the robust performance of control schemes for open
quantum systems subject to such uncertainties. A general formalism is
developed, where performance is measured based on the transmission of a dynamic
perturbation or initial state preparation error to a final density operator
error. This formulation makes it possible to apply tools from classical robust
control, especially structured singular value analysis, to assess robust
performance of controlled, open quantum systems. However, there are additional
difficulties that must be overcome, especially at low frequency ().
For example, at , the Bloch equations for the density operator are
singular, and this causes lack of continuity of the structured singular value.
We address this issue by analyzing the dynamics on invariant subspaces and
defining a pseudo-inverse that enables us to formulate a specialized version of
the matrix inversion lemma. The concepts are demonstrated with an example of
two qubits in a leaky cavity under laser driving fields and spontaneous
emission. In addition, a new performance index is introduced for this system.
Instead of the tracking or transfer fidelity error, performance is measured by
the steady-steady entanglement generated, which is quantified by a non-linear
function of the system state called concurrence. Simulations show that there is
no conflict between this performance index, its log-sensitivity and stability
margin under decoherence, unlike for conventional control problems [...].Comment: 12 pages, 5 figures, 2 table
Sample-efficient Model-based Reinforcement Learning for Quantum Control
We propose a model-based reinforcement learning (RL) approach for noisy
time-dependent gate optimization with improved sample complexity over
model-free RL. Sample complexity is the number of controller interactions with
the physical system. Leveraging an inductive bias, inspired by recent advances
in neural ordinary differential equations (ODEs), we use an auto-differentiable
ODE parametrised by a learnable Hamiltonian ansatz to represent the model
approximating the environment whose time-dependent part, including the control,
is fully known. Control alongside Hamiltonian learning of continuous
time-independent parameters is addressed through interactions with the system.
We demonstrate an order of magnitude advantage in the sample complexity of our
method over standard model-free RL in preparing some standard unitary gates
with closed and open system dynamics, in realistic numerical experiments
incorporating single shot measurements, arbitrary Hilbert space truncations and
uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be
leveraged by existing control methods like GRAPE for further gradient-based
optimization with the controllers found by RL as initializations. Our algorithm
that we apply on nitrogen vacancy (NV) centers and transmons in this paper is
well suited for controlling partially characterised one and two qubit systems.Comment: 14+6 pages, 6+4 figures, comments welcome
Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to non-unitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control
Games for Quantum Physics Education
As the second quantum revolution comes to pass with its potential to revolutionize our lives, it becomes increasingly relevant to educate the public about quantum mechanics. Quantum literacy is also a formidable challenge and opportunity for a massive cultural uplift, since it fosters the possibility for citizens to engender their creativity and practice a new way of thinking. However, quantum theory is highly counterintuitive, manifesting in a reality we have no direct experience of, and represented by mathematically difficult formalisms. Here, we propose that games can provide a playground for engaging forms of experimental and symbolic literacy accessible to anyone. We discuss the theoretical foundations underlying this idea in the framework of a global educational strategy, illustrate existing examples of its implementation along different dimensions related to educational, citizen-science, and age-related contexts, and envision future challenges
Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIM_p) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the p-th order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The RIM_p is the p-th root of the p-th raw moment of the infidelity distribution. Using a metrization argument, we justify why RIM_1 (the average infidelity) is a good practical robustness measure. Based on the RIM_p, an algorithmic robustness-infidelity measure (ARIM) is developed to quantify the expected robustness and fidelity of controllers found by a control algorithm. The utility of the RIM and ARIM is demonstrated on energy landscape controllers of spin-1/2 networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and non-stochastic optimization objectives are considered. Although high fidelity and robustness are often conflicting objectives, some high-fidelity, robust controllers can usually be found, irrespective of the choice of the quantum control algorithm. However, for noisy or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels
Sample-efficient model-based reinforcement learning for quantum control
We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with reduced sample complexity over model-free RL. Sample complexity is defined as the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an autodifferentiable ODE, parametrized by a learnable Hamiltonian ansatz, to represent the model approximating the environment, whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic computational experiments incorporating single-shot measurements, arbitrary Hilbert space truncations, and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE (gradient ascent pulse engineering) for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm, which we apply to nitrogen vacancy (NV) centers and transmons, is well suited for controlling partially characterized one- and two-qubit systems