Publications

2022

1. Generalized quantum similarity learning Radha, Santosh Kumar, and Jao, Casey 2022 [Abs] [arXiv]

   The similarity between objects is significant in a broad range of areas. While similarity can be measured using off-the-shelf distance functions, they may fail to capture the inherent meaning of similarity, which tends to depend on the underlying data and task. Moreover, conventional distance functions limit the space of similarity measures to be symmetric and do not directly allow comparing objects from different spaces. We propose using quantum networks (GQSim) for learning task-dependent (a)symmetric similarity between data that need not have the same dimensionality. We analyze the properties of such similarity function analytically (for a simple case) and numerically (for a complex case) and showthat these similarity measures can extract salient features of the data. We also demonstrate that the similarity measure derived using this technique is (eps,gamma,tau)-good, resulting in theoretically guaranteed performance. Finally, we conclude by applying this technique for three relevant applications - Classification, Graph Completion, Generative modeling.

2. Wasserstein Solution Quality and the Quantum Approximate Optimization Algorithm: A Portfolio Optimization Case Study Baker, Jack S., and Radha, Santosh Kumar 2022 [Abs] [arXiv]

   Optimizing of a portfolio of financial assets is a critical industrial problem which can be approximately solved using algorithms suitable for quantum processing units (QPUs). We benchmark the success of this approach using the Quantum Approximate Optimization Algorithm (QAOA); an algorithm targeting gate-model QPUs. Our focus is on the quality of solutions achieved as determined by the Normalized and Complementary Wasserstein Distance, η, which we present in a manner to expose the QAOA as a transporter of probability. Using η as an application specific benchmark of performance, we measure it on selection of QPUs as a function of QAOA circuit depth p. At n=2 (2 qubits) we find peak solution quality at p=5 for most systems and for n=3 this peak is at p=4 on a trapped ion QPU. Increasing solution quality with p is also observed using variants of the more general Quantum Alternating Operator Ansätz at p=2 for n=2 and 3 which has not been previously reported. In identical measurements, η is observed to be variable at a level exceeding the noise produced from the finite number of shots. This suggests that variability itself should be regarded as a QPU performance benchmark for given applications. While studying the ideal execution of QAOA, we find that p=1 solution quality degrades when the portfolio budget B approaches n/2 and increases when B≈1 or n−1. This trend directly corresponds to the binomial coefficient nCB and is connected with the recently reported phenomenon of reachability deficits. Derivative-requiring and derivative-free classical optimizers are benchmarked on the basis of the achieved η beyond p=1 to find that derivative-free optimizers are generally more effective for the given computational resources, problem sizes and circuit depths.

3. A quantum generative model for multi-dimensional time series using Hamiltonian learning Haim Horowitz, Pooja Rao, and Radha, Santosh Kumar 2022 [Abs] [arXiv]

   Synthetic data generation has proven to be a promising solution for addressing data availability issues in various domains. Even more challenging is the generation of synthetic time series data, where one has to preserve temporal dynamics, i.e., the generated time series must respect the original relationships between variables across time. Recently proposed techniques such as generative adversarial networks (GANs) and quantum-GANs lack the ability to attend to the time series specific temporal correlations adequately. We propose using the inherent nature of quantum computers to simulate quantum dynamics as a technique to encode such features. We start by assuming that a given time series can be generated by a quantum process, after which we proceed to learn that quantum process using quantum machine learning. We then use the learned model to generate out-of-sample time series and show that it captures unique and complex features of the learned time series. We also study the class of time series that can be modeled using this technique. Finally, we experimentally demonstrate the proposed algorithm on an 11-qubit trapped-ion quantum machine.

2021

1. Quantum constraint learning for quantum approximate optimization algorithm Radha, Santosh Kumar 2021 [Abs] [arXiv]

   The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm which offers the potential to handle combinatorial optimization problems. Introducing constraints in such combinatorial optimization problems poses a major challenge in the extensions of QAOA to support relevant larger scale problems. In this paper, we introduce a quantum machine learning approach to learn the mixer Hamiltonian that is required to hard constrain the search subspace. We show that this method can be used for encoding any general form of constraints. By using a form of an adaptable ansatz, one can directly plug the learnt unitary into the QAOA framework. This procedure gives the flexibility to control the depth of the circuit at the cost of accuracy of enforcing the constraint, thus having immediate application in the Noisy Intermediate Scale Quantum (NISQ) era. We also develop an intuitive metric that uses Wasserstein distance to assess the performance of general approximate optimization algorithms with/without constrains. Finally using this metric, we evaluate the performance of the proposed algorithm.

2. Quantum option pricing using Wick rotated imaginary time evolution Radha, Santosh Kumar 2021 [Abs] [arXiv]

   In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation algorithms. This way of pricing options boils down to mapping an initial option price to a quantum state and then simulating the time dependence in Wick’s imaginary time space. We numerically verify our algorithm for European options using a particular imaginary time evolution algorithm as proof of concept and show how it can be extended to path dependent options like Asian options. As the proposed method uses a hybrid variational algorithm, it is bound to be relevant for near-term quantum computers.

3. Calculated phonon modes, infrared and Raman spectra in orthorhombic α-MoO₃ and monolayer MoO₃ Ratnaparkhe, Amol, Radha, Santosh Kumar, and Lambrecht, Walter R. L. 2021 [Abs] [arXiv]

   Orhorhombic α-MoO₃ is a layered oxide with various applications and with excellent potential to be exfoliated as a 2D ultrathin film or monolayer. In this paper, we present a first-principles computational study of its vibrational properties. Our focus is on the zone center modes which can be measured by a combination of infared and Raman spectroscopy. The polarization dependent spectra are simulated. Calculations are also performed for a monolayer form in which "double layers" of Mo2O6 which are weakly van der Waals bonded in the α-structure are isolated. Shift in phonon frequencies are analyzed.

4. Optical response and band structure of LiCoO2 including electron-hole interaction effects Radha, Santosh Kumar, Lambrecht, Walter R. L., Cunningham, Brian, Grüning, Myrta, Pashov, Dimitar, and Schilfgaarde, Mark 2021
5. Ultrathin 2D-oxides: A perspective on fabrication, structure, defect, transport, electron, and phonon properties Radha, Santosh Kumar, Crowley, Kyle, Holler, Brian A., Gao, Xuan P. A., Lambrecht, Walter R. L., Volkova, Halyna, Berger, Marie-Hélène, Pentzer, Emily, Pachuta, Kevin G., and Sehirlioglu, Alp Journal of Applied Physics 2021

2020

1. Topological obstructed atomic limit by annihilating Dirac fermions Radha, Santosh Kumar, and Lambrecht, Walter RL arXiv preprint arXiv:2011.04098 2020 [Abs] [arXiv]

   We show that annihilating a pair of Dirac fermions implies a topological transition from the critical semi-metallic phase to an Obstructed Atomic Limit (OAL) insulator phase instead of a trivial insulator. This is shown to happen because of branch-cuts in the phase of the wave functions, leading to non trivial Zak phase along certain directions. To this end, we study their Z2 invariant and also study the phase transition using Entanglement Entropy. We use low energy Hamiltonians and numerical result from model systems to show this effect. These transitions are observed in realistic materials including strained graphene and buckled honeycomb group-V (Sb/As).

2. Buckled honeycomb antimony: Higher order topological insulator and its relation to the Kekule lattice Radha, Santosh Kumar, and Lambrecht, Walter RL Physical Review B 2020
3. Quantum topological switch and controllable quasi 1D wires in antimonene Radha, Santosh Kumar, and Lambrecht, Walter R. L. 2020 [Abs] [arXiv]

   Based on the recently found non-trivial topology of buckled antimonene, we propose the conceptual design of a quantized switch that is protected by topology and a mechanism to create configurable 1D wire channels. We show that the topologically required edge states in this system can be turned on and off by breaking the inversion symmetry (reducing the symmetry from S₆ to C₃), which can be achieved by gating the system. This is shown to create a field-effect quantum switch projected by topology. Secondly we show that by locally gating the system with different polarity in different areas, a soliton-like domain wall is created at their interface, which hosts a protected electronic state, in which transport could be accessed by gated doping.

4. Electron microscopy and spectroscopic study of structural changes, electronic properties and conductivity in annealed Li _x CoO _2 Volkova, Halyna, Pachuta, Kevin, Crowley, Kyle, Radha, Santosh Kumar, Pentzer, Emily, Gao, Xuan, Lambrecht, Walter RL, Sehirlioglu, Alp, and Berger, Marie-Hélène arXiv preprint arXiv:2010.06769 2020 [arXiv]
5. Quasiparticle self-consistent GW band structures and high-pressure phase transitions of LiGaO2 and NaGaO2 Radha, Santosh Kumar, Ratnaparkhe, Amol, and Lambrecht, Walter RL arXiv preprint arXiv:2010.15934 2020 [arXiv]
6. Spin-polarized two-dimensional electron/hole gases on LiCoO₂ layers Radha, Santosh Kumar, and Lambrecht, Walter R. L. 2020 [Abs] [arXiv]

   First-principles calculations show the formation of a 2D spin polarized electron (hole) gas on the Li (CoO₂) terminated surfaces of finite slabs down to a monolayer of LiCoO2 in remarkable contrast with the bulk band structure stabilized by Li donating its electron to the CoO2 layer forming a Co-d−t^2g insulator. By mapping the first-principles computational results to a minimal tight-binding models corresponding to a non-chiral 3D generalization of the quadripartite Su-Schriefer-Heeger (SSH4) model, we show that these surface states have topological origin.

7. Buckled honeycomb group-V-S₆ symmetric (d-2) higher order topological insulators Radha, Santosh Kumar, and Lambrecht, Walter R. L. 2020 [Abs] [arXiv]

   Higher Order Topological Insulators (HOTI) are d-spatial dimensional systems featuring topologically protected gap-less states at their (d−n)-dimensional boundaries. With the help of ab-initio calculations and tight binding models along with symmetry considerations we show that monolayer buckled honeycomb structures of group-V elements (Sb,As), which have already been synthesized, belong in this category and have a charge fractionalization of e/2 at the corner states as well as weak topological edge states, all protected by their properties under the inversion operation which classify this system as a quadrupole topological insulator.

8. pyQuestaal: An python interface or Questaal quantum codes. Radha, Santosh Kumar 2020
9. Electrical Characterization and Charge Transport in Chemically Exfoliated 2D LixCoO2 Nanoflakes Gao, Kyle Crowley Kevin Pachuta Santosh Kumar Radha Halyna Volkova Alp Sehirlioglu Emily B. Pentzer Marie-Helene Berger Walter R. L. Lambrecht Xuan P.A. 2020 [Abs]

   Transition metal oxides often possess complex interactions between charge, spin, lattice, and orbital degrees of freedom, resulting in correlated electronic and magnetic phases. LixCoO2 is one such material. One of the most commonly used cathode choices in rechargeable batteries, this oxide also evidences numerous correlated effects, evolving as a function of lithium content (x). Due to the strong electrostatic forces which govern the layered nature of this material, however, most investigations of these behaviors have been on bulk forms (>0.1mm). In the 2D limit, correlated effects are more easily tuned and studied, therefore it is of fundamental importance to develop an experimental basis for investigation. Herein, a two-step process is utilized to chemically delithiate and exfoliate LiCoO2 single crystals and study nanoflakes 10-60nm thick, with 0.37 < x < 0.8. An initial electrical characterization of this new form reflects bulk conduction properties, verifying the reliability of this new technique: temperature-dependent resistance measurements indicate an insulating 2D variable ranging hopping conduction for samples of x>0.75, and metallic characteristics with a finite residual conductance for x<0.75. However, these thin flakes also exhibit correlated characteristics less commonly observed and understood in LixCoO2. An energy barrier upon contact formation is observed for all conditions, independent of lithium concentration and electrode work function, suggesting enhanced correlated effects due to reduced dimensionality. Additionally, charge ordering phenomena in the temperature-dependent resistance occur under specific preparation conditions. These anomalies are markedly larger in magnitude than previous accounts in bulk systems, and are also found in low-lithium ranges of x<0.5, matching theoretical predictions not commonly observed experimentally. This work utilizes a new approach to gain insight behind the complex transport phenomena inherent in LixCoO2, providing a new opportunity to understand these correlated effects using a 2D, single crystal form.

10. Information flow in political elections: a stochastic perspective Radha, Santosh Kumar 2020 [Abs] [arXiv]

    Often times, a candidate’s attractiveness is directly associated with his clear ideologies and opin- ions on various policies and social issues. Using the ideas of stochastic differential equations and Ornstein-Uhlenbeck Process, we develop a phenomenological model to understand the effect of (un)clearly communicating a candidate’s stance on policies to the voting public. We will show that, counter intuitively, there are quantifiable advantages to be vague on one’s stance.

2019

1. Stochastic differential theory of cricket Radha, Santosh Kumar 2019 [Abs] [arXiv]

   A new formalism for analyzing the progression of cricket game using Stochastic differential equation (SDE) is introduced. This theory enables a quantitative way of representing every team using three key variables which have physical meaning associated with them. This is in contrast with the traditional system of rating/ranking teams based on combination of different statical cumulants. Further more, using this formalism, a new method to calculate the winning probability as a progression of number of balls is given.

2. Understanding the Crystallographic Phase Relations in Alkali‐Trihalogeno‐Germanates in Terms of Ferroelectric or Antiferroelectric Arrangements of the Tetrahedral GeX₃ Units Radha, Santosh Kumar, and Lambrecht, Walter R. L. Advanced Electronic Materials 2019 [Abs]

   The alkali-trihalogeno-germanates AGeX₃ with A a large single positive ion such as Rb, Cs, or organic radicals such as methyl ammonium (MA), and X a halogen (I, Br, Cl, F) along with the corresponding stannates (ASnX3) and plumbates (APbX₃) exhibit a large variety of crystal structures, some of which are of the perovskite type. These materials, better known as "halide perovskites” have recently gained worldwide attention as promising photovoltaic and more broadly opto-electronic materials. But their stability problems relative to the non-perovskite phases is a major issue. Here we show that the phase relations in these materials can be understood in terms of the relative orientation of the GeX3 tetrahedral units, which is ferroelectric in the perovskite phase but antiferroelectric in the competing phases. This suggests that an applied electric field could be used to stabilize the desired phases and trigger a phase transition between two phases of the material with widely different optical and electronic properties.

3. Topological band structure transitions in honeycomb antimonene as function of buckling Radha, Santosh Kumar, and Lambrecht, Walter R. L. 2019 [Abs] [arXiv]

   The electronic band topology of monolayer β-Sb (antimonene) is studied from the flat honeycomb to the equilibrium buckled structure using first-principles calculations and analyzed using a tight-binding model and low energy Hamiltonians. In flat monolayer Sb, the Fermi level occurs near the intersection of two warped Dirac cones, one associated with the pz-orbitals, and one with the px,py-orbitals. The differently oriented threefold warping of these two cones leads to an unusually shaped nodal line, which leads to anisotropic in-plane transport properties and goniopolarity. A slight buckling opens a gap along the nodal line except at six remaining Dirac points, protected by symmetry. Under increasing buckling, pairs of Dirac points of opposite winding number annihilate at a critical buckling angle. At a second critical angle, the remaining Dirac points disappear when the band structure becomes a trivial semiconductor. Spin-orbit coupling and edge states are discussed.

4. Classification and anomaly detection of time series data using latent space Deep Neural-network distance measure Radha, Santosh Kumar 2019
5. Band Gaps and Dynamical Meta-Stability of CsSiX₃ Halides Radha, Santosh K., and Lambrecht, Walter R. L. 2019

2018

1. Ordering in the mixed ZnGeN2-GaN alloy system: Crystal structures and band structures of ZnGeGa2N4 from first principles Jayatunga, Benthara Hewage Dinushi, Lyu, Sai, Radha, Santosh Kumar, Kash, Kathleen, and Lambrecht, Walter R. L. Phys. Rev. Materials 2018
2. Tuning Rashba spin–orbit coupling in gated multilayer InSe Premasiri, Kasun, Radha, Santosh Kumar, Sucharitakul, Sukrit, Kumar, U Rajesh, Sankar, Raman, Chou, Fang-Cheng, Chen, Yit-Tsong, and Gao, Xuan PA Nano letters 2018
3. Distortion modes in halide perovskites: To twist or to stretch, a matter of tolerance and lone pairs Radha, Santosh Kumar, Bhandari, Churna, and Lambrecht, Walter R. L. Phys. Rev. Materials 2018
4. Essence of Quantum Many-Body Perturbation theory Radha, Santosh Kumar In 2018 [Abs]

   We walk through derivation of the ubiquitous Hedin equations using Quantum Many-Body Perturbation theory (QMBPT). QMBPT is full of rich diagrams showing the symmetries of myriad interactions of particles and anti-particles, giving us insights on how to miss-match and add different interactions important to the specific system we are dealing with. This is in contrast with the usual presentation of Hedin’s equations derived using variational principle and quantum linear response theory, where an equivalent but analytic functional approach of probing the system with fictitious infinitesimal field is used.

2017

1. Classical-Gravity as curvature in Manifold Radha, Santosh Kumar 2017