Fighting noise with noise: a stochastic projective quantum eigensolver

Quantum Monte Carlo (QMC) algorithms have proven extremely effective at lowering the computational overhead of electronic structure calculations in a classical setting. In the current noisy intermediate scale quantum (NISQ) era of quantum computation, there are several limitations on the available hardware resources, such as low qubit counts, short decoherence times and high gate noise, which preclude the application of many current hybrid quantum-classical algorithms to non-trivial quantum chemistry problems. Here, we propose combining some of the fundamental elements of conventional QMC algorithms -- stochastic sampling of both the wavefunction and the Hamiltonian of interest -- with an imaginary-time propagation based projective quantum eigensolver. At the cost of increased noise, which can be easily averaged over in a classical Monte Carlo estimation, we obtain a method with quantum computational requirements that are both generally low and highly tunable.Comment: 16 pages, 13 figures, 5 table

A stochastic approach to unitary coupled cluster.

Unitary coupled cluster (UCC), originally developed as a variational alternative to the popular traditional coupled cluster method, has seen a resurgence as a functional form for use on quantum computers. However, the number of excitors present in the Ansatz often presents a barrier to implementation on quantum computers. Given the natural sparsity of wavefunctions obtained from quantum Monte Carlo methods, we consider here a stochastic solution to the UCC problem. Using the coupled cluster Monte Carlo framework, we develop cluster selection schemes that capture the structure of the UCC wavefunction, as well as its Trotterized approximation, and use these to solve the corresponding projected equations. Due to the fast convergence of the equations with order in the cluster expansion, this approach scales polynomially with the size of the system. Unlike traditional UCC implementations, our approach naturally produces a non-variational estimator for the energy in the form of the projected energy. For unitary coupled cluster singles and doubles (UCCSD) in small systems, we find that this agrees well with the expectation value of the energy and, in the case of two electrons, with full configuration interaction results. For the larger N2 system, the two estimators diverge, with the projected energy approaching the coupled cluster result, while the expectation value is close to results from traditional UCCSD

A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems

The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multi-configurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper we explore the potential of incorporating ideas from conventional MRCC - namely the treatment of the strongly correlated space in a configuration interaction formalism - to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations.Comment: 13 pages, 10 figures, 3 table

Multireference Stochastic Coupled Cluster.

We describe a modification of the stochastic coupled cluster algorithm that allows the use of multiple reference determinants. By considering the secondary references as excitations of the primary reference and using them to change the acceptance criteria for selection and spawning, we obtain a simple form of stochastic multireference coupled cluster which preserves the appealing aspects of the single reference approach. The method is able to successfully describe strongly correlated molecular systems using few references and low cluster truncation levels, showing promise as a tool to tackle strong correlation in more general systems. Moreover, it allows simple and comprehensive control of the included references and excitorsthereof, and this flexibility can be taken advantage of to gain insight into some of the inner workings of established electronic structure methods

Multireference Stochastic Coupled Cluster.

We describe a modification of the stochastic coupled cluster algorithm that allows the use of multiple reference determinants. By considering the secondary references as excitations of the primary reference and using them to change the acceptance criteria for selection and spawning, we obtain a simple form of stochastic multireference coupled cluster which preserves the appealing aspects of the single-reference approach. The method is able to successfully describe strongly correlated molecular systems using few references and low cluster truncation levels, showing promise as a tool to tackle strong correlation in more general systems. Moreover, it allows simple and comprehensive control of the included references and excitors thereof, and this flexibility can be taken advantage of to gain insight into some of the inner workings of established electronic structure methods

Variational Phase Estimation with Variational Fast Forwarding

Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained by a quantum computer. The recently proposed Variational Quantum Phase Estimation (VQPE) algorithm uses a basis of real time-evolved states, for which the energy eigenvalues can be obtained directly from the unitary matrix $U=e^{-iH{\Delta}t}$, which can be computed with cost linear in the number of states used. In this paper, we report a circuit-based implementation of VQPE for arbitrary molecular systems and assess its performance and costs for the $H_2$, $H_3^+$ and $H_6$ molecules. We also propose using Variational Fast Forwarding (VFF) to decrease to quantum depth of time-evolution circuits for use in VQPE. We show that the approximation provides a good basis for Hamiltonian diagonalisation even when its fidelity to the true time evolved states is low. In the high fidelity case, we show that the approximate unitary U can be diagonalised instead, preserving the linear cost of exact VQPE

The role of CT and biopsy in the assessment of nasopharyngeal carcinoma

Introduction: Nasopharyngeal carcinoma is the most common cancer originating in the nasopharynx. However, the lack of symptoms makes it difficult to diagnose. It is most frequent in males and when it occurs in women, viral and genetic factors are involved. Methods: We present the case of a female patient who was admitted to the hospital with severe headache and tinnitus. Symptoms started 3 months prior to hospitalization, but without response to analgesics. She was diagnosed in March 2011 with mild hypertension, but she did not follow any treatment. We performed a complete examination of the patient .Except for high blood pressure (180 mmHg/ 70mmHg) and increased VSH the analyses were normal. In June 2011 the patient came to our clinic complaining of the same symptoms. During physical examination we discovered a latero-cervical nodular formation, not as a result of a number of diagnostic modalities were used in order to evaluate and determine the diagnosis: thyroid echography, barium examination of esophagus, stomach and duodenum, abdominal echography, CT. Results: CT and the biopsy of the formation confirmed the diagnosis: nasopharyngeal carcinoma. Conclusion: The paraclinical examination is fundamental and most valuable step in order to put the right diagnosis in this particular case

Multimodal Biosensing on Paper-Based Platform Fabricated by Plasmonic Calligraphy Using Gold Nanobypiramids Ink

In this work, we design new plasmonic paper-based nanoplatforms with interesting capabilities in terms of sensitivity, efficiency, and reproducibility for promoting multimodal biodetection via Localized Surface Plasmon Resonance (LSPR), Surface Enhanced Raman Spectroscopy (SERS), and Metal Enhanced Fluorescence (MEF). To succeed, we exploit the unique optical properties of gold nanobipyramids (AuBPs) deposited onto the cellulose fibers via plasmonic calligraphy using a commercial pen. The first step of the biosensing protocol was to precisely graft the previously chemically-formed p-aminothiophenol@Biotin system, as active recognition element for target streptavidin detection, onto the plasmonic nanoplatform. The specific capture of the target protein was successfully demonstrated using three complementary sensing techniques. As a result, while the LSPR based sensing capabilities of the nanoplatform were proved by successive 13–18 nm red shifts of the longitudinal LSPR associated with the change of the surface RI after each step. By employing the ultrasensitive SERS technique, we were able to indirectly confirm the molecular identification of the biotin-streptavidin interaction due to the protein fingerprint bands assigned to amide I, amide III, and Trp vibrations. Additionally, the formed biotin-streptavidin complex acted as a spacer to ensure an optimal distance between the AuBP surface and the Alexa 680 fluorophore for achieving a 2-fold fluorescence emission enhancement of streptavidin@Alexa 680 on the biotinylated nanoplatform compared to the same complex on bare paper (near the plasmonic lines), implementing thus a novel MEF sensing nanoplatform. Finally, by integrating multiple LSPR, SERS, and MEF nanosensors with multiplex capability into a single flexible and portable plasmonic nanoplatform, we could overcome important limits in the field of portable point-of-care diagnostics

Skeletal Muscle Stem Cell Niche from Birth to Old Age

Stem cells are defined as undifferentiated cells that are able to unlimitedly renew themselves within controlled conditions and to differentiate into a multitude of mature cell types. Skeletal muscle stem cells, represented predominantly by satellite cells, show a variable capability of self-renewal and myogenic differentiation. They were found to be involved not only in the growth of myofibers during neonatal and juvenile life but also in the regeneration of skeletal muscles after an injury. The microenvironment in which stem cells are nourished and maintained dormant preceding division and differentiation is known as “niche.” The niche consists of myofibers, which are believed to modulate the active/inactive state of the stem cells, extracellular matrix, neural networks, blood vessels, and a multitude of soluble molecules. It was observed that changes in the composition of the niche have an impact on the stem cell functions and hierarchy. Furthermore, it seems that its layout is variable throughout the entire life, translating into a decrease in the regenerative capacity of satellite cells in aged tissues. The scope of this chapter is to provide a detailed view of the changes that occur in the skeletal stem cell niche during life and to analyze their implications on tissue regeneration. Future studies should focus on developing new therapeutic tools for diseases involving muscle atrophy