Person: Whitfield, James D.
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Whitfield
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James D.
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Whitfield, James D.
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Publication Computational complexity in electronic structure(Royal Society of Chemistry, 2013) Whitfield, James D.; Love, Peter; Aspuru-Guzik, AlanIn quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere shortcomings of the algorithm designers and programmers but could stem from the inherent difficulty of simulating quantum systems. Extensions of computer science and information processing exploiting quantum mechanics has led to new ways of understanding the ultimate limitations of computational power. Interestingly, this perspective helps us understand widely used model chemistries in a new light. In this article, the fundamentals of computational complexity will be reviewed and motivated from the vantage point of chemistry. Then recent results from the computational complexity literature regarding common model chemistries including Hartree–Fock and density functional theory are discussed.Publication Computational Complexity of Time-Dependent Density Functional Theory(IOP Publishing, 2014) Whitfield, James D.; Yung, M-H; Tempel, David; Boixo, S; Aspuru-Guzik, AlanTime-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn–Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn–Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn–Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn–Sham potential with controllable error bounds.Publication Quantum Computing for Molecular Energy Simulations(2010) Whitfield, James D.; Biamonte, Jacob; Aspuru-Guzik, AlanOver the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, to obtain the energy of a molecular system with fixed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adiabatic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule, of how a chemical Hamiltonian can be simulated using a quantum computer.Publication Adiabatic Quantum Simulators(2011) Biamonte, J. D; Bergholm, V.; Whitfield, James D.; Fitzsimons, J.; Aspuru-Guzik, AlanIn his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.Publication Simulation of Classical Thermal States on a Quantum Computer: A Transfer Matrix Approach(2010) Yung, Man-Hong; Nagaj, Daniel; Whitfield, James D.; Aspuru-Guzik, AlanWe present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one at a time. We identify a class of classical models for which our method is efficient and avoids potential exponential overheads encountered by Grover-like or quantum Metropolis schemes. Our algorithm also gives an exponential advantage for 2D Ising models with magnetic field on a square lattice, compared with the previously known Zalka's algorithm.Publication Simulating Chemistry Using Quantum Computers(Annual Reviews, 2011) Kassal, Ivan; Whitfield, James D.; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, AlanThe difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.Publication Towards Quantum Chemistry on a Quantum Computer(Nature Publishing Group, 2010) Lanyon, B. P.; Whitfield, James D.; Gillett, G. G.; Goggin, M. E.; Almeida, M. P.; Kassal, Ivan; Biamonte, J. D.; Mohseni, Masoud; Powell, B. J.; Barbieri, M.; Aspuru-Guzik, Alan; White, Andrew G.Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.Publication Quantum Stochastic Walks: A Generalization of Classical Random Walks and Quantum Walks(American Physical Society, 2010) Whitfield, James D.; Rodríguez-Rosario, César A.; Aspuru-Guzik, AlanWe introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.