Optimized pulses for the control of uncertain qubits

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for \pi/2- and \pi-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from \pi/2- and \pi-pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter, to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, post facto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.Comment: 38 pages, 15 figures, RevTeX 4.1, minor modifications to the previous versio

Optimal combinations of imperfect objects

We address the question of how to make best use of imperfect objects, such as defective analog and digital components. We show that perfect, or near-perfect, devices can be constructed by taking combinations of such defects. Any remaining objects can be recycled efficiently. In addition to its practical applications, our `defect combination problem' provides a novel generalization of classical optimization problems.Comment: 4 pages, 3 figures, minor change

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and the Double Unitary Coupled-Cluster Approach.

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of the molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding preprocessing technique with the variational quantum eigensolver, we solve for the ground-state energy of H2, Li2, and BeH2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations

Dynamic control of Coding in Delay Tolerant Networks

Delay tolerant Networks (DTNs) leverage the mobility of relay nodes to compensate for lack of permanent connectivity and thus enable communication between nodes that are out of range of each other. To decrease message delivery delay, the information to be transmitted is replicated in the network. We study replication mechanisms that include Reed-Solomon type codes as well as network coding in order to improve the probability of successful delivery within a given time limit. We propose an analytical approach that allows us to compute the probability of successful delivery. We study the effect of coding on the performance of the network while optimizing parameters that govern routing

Constrained coordinated distributed control of smart grid with asynchronous information exchange

Smart grid constrained optimal control is a complex issue due to the constant growth of grid complexity and the large volume of data available as input to smart device control. In this context, traditional centralized control paradigms may suffer in terms of the timeliness of optimization results due to the volume of data to be processed and the delayed asynchronous nature of the data transmission. To address these limits of centralized control, this paper presents a coordinated, distributed algorithm based on distributed, local controllers and a central coordinator for exchanging summarized global state information. The proposed model for exchanging global state information is resistant to fluctuations caused by the inherent interdependence between local controllers, and is robust to delays in information exchange. In addition, the algorithm features iterative refinement of local state estimations that is able to improve local controller ability to operate within network constraints. Application of the proposed coordinated, distributed algorithm through simulation shows its effectiveness in optimizing a global goal within a complex distribution system operating under constraints, while ensuring network operation stability under varying levels of information exchange delay, and with a range of network sizes

A general theory of intertemporal decision-making and the perception of time

Animals and humans make decisions based on their expected outcomes. Since relevant outcomes are often delayed, perceiving delays and choosing between earlier versus later rewards (intertemporal decision-making) is an essential component of animal behavior. The myriad observations made in experiments studying intertemporal decision-making and time perception have not yet been rationalized within a single theory. Here we present a theory-Training--Integrated Maximized Estimation of Reinforcement Rate (TIMERR)--that explains a wide variety of behavioral observations made in intertemporal decision-making and the perception of time. Our theory postulates that animals make intertemporal choices to optimize expected reward rates over a limited temporal window; this window includes a past integration interval (over which experienced reward rate is estimated) and the expected delay to future reward. Using this theory, we derive a mathematical expression for the subjective representation of time. A unique contribution of our work is in finding that the past integration interval directly determines the steepness of temporal discounting and the nonlinearity of time perception. In so doing, our theory provides a single framework to understand both intertemporal decision-making and time perception.Comment: 37 pages, 4 main figures, 3 supplementary figure

Sequence of penalties method to study excited states using VQE

We propose an extension of the Variational Quantum Eigensolver (VQE) that leads to more accurate energy estimations and can be used to study excited states. The method is based on the introduction of a sequence of increasing penalties in the cost function. This approach does not require circuit modifications and thus can be applied with no additional depth cost. Through numerical simulations, we show that we are able to produce variational states with desired physical properties, such as total spin and charge. We assess its performance both on classical simulators and on currently available quantum devices, calculating the potential energy curves of small molecular systems in different physical configurations. Finally, we compare our method to the original VQE and to another extension, obtaining a better agreement with exact simulations for both energy and targeted physical quantities.Comment: 11 pages, 9 figures, accepted in IOP Quantum Science and Technolog