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This paper explores the utility of the quantum phase estimation (QPE) in calculating high-energy excited states characterized by promotions of electrons occupying inner energy shells. These states have been intensively studied over the last few decades especially in supporting the experimental effort at light sources. Results obtained with the QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is also discussed.

An isolated system of interacting quantum particles is described by a Hamiltonian operator. Hamiltonian models underpin the study and analysis of physical and chemical processes throughout science and industry, so it is crucial they are faithful to the system they represent. However, formulating and testing Hamiltonian models of quantum systems from experimental data is difficult because it is impossible to directly observe which interactions the quantum system is subject to. Here, we propose and demonstrate an approach to retrieving a Hamiltonian model from experiments, using unsupervised machine learning. We test our methods experimentally on an electron spin in a nitrogen-vacancy interacting with its spin bath environment, and numerically, finding success rates up to 86%. By building agents capable of learning science, which recover meaningful representations, we can gain further insight on the physics of quantum systems., Comment: 27 pages, 8 figures

Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical inference to glean estimates of the eigenvalues from the resulting data. Here, we show a generalization of this framework where each of the steps in the simulation uses a different Hamiltonian. This allows the precision of the Hamiltonian to be changed as the phase estimation precision increases. Additionally, through the use of importance sampling, we can exploit knowledge about the ground state to decide how frequently each Hamiltonian term should appear in the evolution, and minimize the variance of our estimate. We rigorously show, if the Hamiltonian is gapped and the sample variance in the ground state expectation values of the Hamiltonian terms sufficiently small, that this process has a negligible impact on the resultant estimate and the success probability for phase estimation. We demonstrate this process numerically for two chemical Hamiltonians, and observe substantial reductions in the number of terms in the Hamiltonian; in one case, we even observe a reduction in the number of qubits needed for the simulation. Our results are agnostic to the particular simulation algorithm, and we expect these methods to be applicable to a range of approaches., Comment: 17 pages, 2 figures

Fault-tolerant quantum computation promises to solve outstanding problems in quantum chemistry within the next decade. Realizing this promise requires scalable tools that allow users to translate descriptions of electronic structure problems to optimized quantum gate sequences executed on physical hardware, without requiring specialized quantum computing knowledge. To this end, we present a quantum chemistry library, under the open-source MIT license, that implements and enables straightforward use of state-of-art quantum simulation algorithms. The library is implemented in Q#, a language designed to express quantum algorithms at scale, and interfaces with NWChem, a leading electronic structure package. We define a standardized schema for this interface, Broombridge, that describes second-quantized Hamiltonians, along with metadata required for effective quantum simulation, such as trial wavefunction ansatzes. This schema is generated for arbitrary molecules by NWChem, conveniently accessible, for instance, through Docker containers and a recently developed web interface EMSL Arrows. We illustrate use of the library with various examples, including ground- and excited-state calculations for LiH, H$_{10}$, and C$_{20}$ with an active-space simplification, and automatically obtain resource estimates for classically intractable examples., Comment: 36 pages, 5 figures. Examples and data in ancillary files folder

We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the phase directly from experimental data. Our method is highly flexible, recovers from failures, and can be run in the presence of substantial decoherence and other experimental imperfections and is as fast or faster than existing algorithms.

In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide an explicit algorithm for estimating parameters of physical models given access to a simulator which is only capable of producing sample outcomes. Since our algorithm does not require that a simulator be able to efficiently compute exact probabilities, it is able to exponentially outperform standard algorithms based on exact computation. In this way, our algorithm opens the door for the application of new insights and resources to the problem of characterizing large quantum systems, which is exponentially intractable using standard simulation resources., Comment: Significantly revised presentation

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance., Comment: 24 pages, 12 figures; to appear in New Journal of Physics

Understanding fault-tolerant properties of quantum circuits is important for the design of large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the relationships between the noise model, encoding scheme, and threshold value. For general circuits and noise models, these simulations quickly become intractable in the size of the encoded circuit. We introduce methods for approximating a noise process by one which allows for efficient Monte Carlo simulation of properties of encoded circuits. The approximations are as close to the original process as possible without overestimating their ability to preserve quantum information, a key property for obtaining more honest estimates of threshold values. We numerically illustrate the method with various physically relevant noise models., Comment: 6 pages, 1 figure

Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially improved accuracy over offline estimation strategies. To achieve this, we derive an adaptive protocol which finds the optimal experiments based on previous observations. We show that the risk associated with this algorithm is close to the global optimum, given a uniform prior. Additionally, we show that sampling at the Nyquist rate is not optimal., Comment: 8 pages, 3 figures. To appear in Bayesian Inference And Maximum Entropy Methods In Science And Engineering: Proceedings of the 31th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering

Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an important parameter in the Hamiltonian. Here, we explore how to design experiments so as to minimize error in the estimation of this parameter. While it has been shown that useful results may be obtained by minimizing the risk incurred by each experiment, such an approach is computationally intractable in general. Here, we motivate and derive heuristic strategies for experiment design that enjoy the same exponential scaling as fully optimized strategies. We then discuss generalizations to the case of finite relaxation times, T_2 < \infty., Comment: 7 pages, 2 figures, 3 appendices; Quantum Information Processing, Online First, 20 April 2012

We describe a method for coupling disjoint quantum bits (qubits) in different local processing nodes of a distributed node quantum information processor. An effective channel for information transfer between nodes is obtained by moving the system into an interaction frame where all pairs of cross-node qubits are effectively coupled via an exchange interaction between actuator elements of each node. All control is achieved via actuator-only modulation, leading to fast implementations of a universal set of internode quantum gates. The method is expected to be nearly independent of actuator decoherence and may be made insensitive to experimental variations of system parameters by appropriate design of control sequences. We show, in particular, how the induced cross-node coupling channel may be used to swap the complete quantum states of the local processors in parallel., Comment: revtex4-1; 7 pages; 5 figures. New version includes minor changes, with updated Fig. 4 and new supplemental material