Browsing by Author "Mayhall, Nicholas J."

Now showing 1 - 9 of 9
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    Adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer
    Zhu, Linghua; Tang, Ho Lun; Barron, George S.; Calderon-Vargas, F. A.; Mayhall, Nicholas J.; Barnes, Edwin Fleming; Economou, Sophia E. (American Physical Society, 2022-07-11)
    The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA Ansatz is not optimal, there is no systematic approach for finding better Ansatze. We address this problem by developing an iterative version of QAOA that is problem tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity.
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    An adaptive variational algorithm for exact molecular simulations on a quantum computer
    Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin Fleming; Mayhall, Nicholas J. (Springer Nature, 2019-07-08)
    Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.
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    Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
    Gard, Bryan T.; Zhu, Linghua; Barron, George S.; Mayhall, Nicholas J.; Economou, Sophia E.; Barnes, Edwin Fleming (2020-01-28)
    The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multiqubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. We test our circuits in quantum simulations of the H2 and LiH molecules and find that they outperform standard state preparation methods in terms of both accuracy and circuit depth.
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    Explicitly correlated Green's function methods for calculating electron binding energies
    Teke, Nakul Kushabhau (Virginia Tech, 2019-07-29)
    Single-particle Green's function method is a direct way of calculating electron binding energy, which relies on expanding the Fock subspace in a finite single-particle basis. However, these methods suffer from slow asymptotic decay of basis set incompleteness error. An energy-dependent explicitly correlated (F12) formalism for Green's function is presented that achieves faster convergence to the basis set limit. The renormalized second-order Green's function method (NR2-F12) scales as iterative N^5 where N is the system size. These methods are tested on a set of small (O21) and medium-sized (OAM24) organic molecules. The basis set incompleteness error in ionization potential (IP) obtained from the NR2-F12 method and aug-cc-pVDZ basis for OAM24 is 0.033 eV compared to 0.067 eV for NR2 method and aug-cc-pVQZ basis. Hence, accurate electron binding energies can be calculated at a lower cost using NR2-F12 method. For aug-cc-pVDZ basis, the electron binding energies obtained from NR2-F12 are comparable to EOM-IP-CCSD method that uses a CCSD reference and scales as iterative N^6.
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    Gate-free state preparation for fast variational quantum eigensolver simulations
    Meitei, Oinam Romesh; Gard, Bryan T.; Barron, George S.; Pappas, David P.; Economou, Sophia E.; Barnes, Edwin Fleming; Mayhall, Nicholas J. (Springer Nature, 2021-10-27)
    The variational quantum eigensolver is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state, and then measuring the molecular energy. Due to finite coherence times and gate errors, the number of gates that can be implemented remains limited. In this work, we propose an alternative algorithm where device-level pulse shapes are variationally optimized for the state preparation rather than using an abstract-level quantum circuit. In doing so, the coherence time required for the state preparation is drastically reduced. We numerically demonstrate this by directly optimizing pulse shapes which accurately model the dissociation of H2 and HeH+, and we compute the ground state energy for LiH with four transmons where we see reductions in state preparation times of roughly three orders of magnitude compared to gate-based strategies.
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    Preparing Bethe Ansatz Eigenstates on a Quantum Computer
    Van Dyke, John S.; Barron, George S.; Mayhall, Nicholas J.; Barnes, Edwin Fleming; Economou, Sophia E. (2021-11-09)
    Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for which analytic results are unavailable and which are also not well described by approximate numerical methods. Preparing Bethe ansatz eigenstates directly on a quantum computer would allow straightforward extraction of these quantities via measurement. We present a quantum algorithm for preparing Bethe ansatz eigenstates of the spin-1/2 XXZ spin chain that correspond to real-valued solutions of the Bethe equations. The algorithm is polynomial in the number of T gates and the circuit depth, with modest constant prefactors. Although the algorithm is probabilistic, with a success rate that decreases with increasing eigenstate energy, we employ amplitude amplification to boost the success probability. The resource requirements for our approach are lower than for other state-of-the-art quantum simulation algorithms for small error-corrected devices and thus may offer an alternative and computationally less demanding demonstration of quantum advantage for physically relevant problems.
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    Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer
    Asthana, Ayush; Kumar, Ashutosh; Abraham, Vibin; Grimsley, Harper; Zhang, Yu; Cincio, Lukasz; Tretiak, Sergei; Dub, Pavel A.; Economou, Sophia E.; Barnes, Edwin Fleming; Mayhall, Nicholas J. (Royal Society Chemistry, 2023-01-27)
    Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H-2, H-4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.
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    Synthesis and Characterization of pure-phase Zr-MOFs Based on meso-Tetra(4-carboxyphenyl)porphine
    Shaikh, Shaunak Mehboob (Virginia Tech, 2019-05-02)
    Chapter 1: The unique chemical and biological properties of porphyrins have led to increased interest in the development of porphyrin-based materials. Metal organic frameworks (MOFs) can act as a scaffold for the immobilization of porphyrins in desired arrangements. The crystalline nature of MOFs allows for control over spatial arrangement of porphyrins and the local environment of the porphyrin molecules. This opens up the possibility of conducting systematic studies aimed at exploring structure-property relationships. Several strategies for the design and synthesis of porphyrin-based frameworks have been developed over the last two decades, such as, the pillared-layer strategy, construction of nanoscopic metal-organic polyhedrals (MOPs), post-synthetic modification, etc. These strategies provide an opportunity to engineer porphyrin-based MOFs that can target a specific application or serve as multi-functional assemblies. Porphyrin-based MOFs provide a tunable platform to perform a wide variety of functions ranging from gas adsorption, catalysis and light harvesting. The versatile nature of these frameworks can be exploited by incorporating them in multi-functional assemblies that mimic biological and enzymatic systems. Nano-thin film fabrication of porphyrin-based MOFs broadens their application range, making it possible to use them in the construction of photovoltaic and electronic devices. Chapter 2: The reaction of zirconium salts with meso-tetracarboxyphenylporphyrin (TCPP) in the presence of different modulators results in the formation of a diverse set of metal-organic frameworks (MOFs), each displaying distinct crystalline topologies. However, synthesis of phase-pure crystalline frameworks is challenging due to the concurrent formation of polymorphs. The acidity and concentration of modulator greatly influence the outcome of the MOF synthesis. By systematically varying these two parameters, selective framework formation can be achieved. In the present study, we aimed to elucidate the effect of modulator on the synthesis of zirconium-based TCPP MOFs. With the help of powder X-ray diffraction (PXRD) and scanning electron microscopy (SEM), modulator candidates and the optimal synthetic conditions yielding phase-pure PCN-222, PCN-223 and MOF-525 were identified. 1H NMR analysis, TGA and N2 gas adsorption measurements were performed on select MOFs to gain insight into the relationship between their defectivity and modulator properties. Chapter 3: Singlet-singlet energy transfer in PCN-223(free-base), a highly stable Zr-MOF based on meso-tetrakis(4-carboxyphenyl)porphyrin was investigated, using diffuse reflectance spectroscopy, steady-state emission spectroscopy, time-correlated single photon counting (TCSPC) spectroscopy and nanosecond transient absorption spectroscopy. The effects of the surrounding media and temperature on the excited-state properties of PCN-223(fb) were explored to understand the mechanistic aspects of energy transfer. Stern-Volmer photoluminescence quenching of PCN-223(fb) suspensions was performed to extract quenching rate constants and gain insight into the efficiency of energy transfer. Chapter 4: The fourth chapter of this thesis is adapted from chapter 14 of the book "Elaboration and Applications of Metal-Organic Frameworks" authored by Jie Zhu, Shaunak Shaikh, Nicholas J Mayhall and Amanda J Morris. This chapter summarizes the fundamental principles of energy transfer in MOFs and provides an overview of energy transfer in lanthanide-Based luminescent MOFs, Ru/Os-Based MOFs, porphyrin- and metalloporphyrin-based MOF materials, and nonporphyrinic, organic chromophore-based MOFs.
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    Synthesis of New Molecule-Based Magnets using Bridging Organic Radicals
    Houser, Christopher L. (Virginia Tech, 2019-07-12)
    Several new families of organic acceptors that are candidates as building blocks of molecule-based ferrimagnets were synthesized and characterized. These families include fluorodicyanostilbenes, a tetrachlorodicyanostilbene, naphthyltricyanoethylenes, bromophenyltricyanoethylenes, and an anthryltricyanoethylene. The magnetic networks were synthesized by reacting each acceptor with V(CO)6. The magnets synthesized in this study were characterized using a SQUID magnetometer, elemental analysis, and infrared spectroscopy. Although some combinations failed to yield magnetically ordered materials, others exhibited ordering temperatures in the range of 95 K – 260 K. The ordering temperatures and saturation magnetizations were compared among families of acceptors and correlated with individual properties of the acceptors such as reduction potential and structure.