arXiv subjects

Ryan Babbush

Publications and source records attributed to Ryan Babbush.

114 records · Page 7Linked to original sources

arXiv2014

Construction of non-convex polynomial loss functions for training a binary classifier with quantum annealing

Quantum annealing is a heuristic quantum algorithm which exploits quantum resources to minimize an objective function embedded as the energy levels of a programmable physical system. To take advantage of a potential quantum advantage, one needs to be able to map the problem of interest to the native hardware with reasonably low overhead. Because experimental considerations constrain our objective function to take the form of a low degree PUBO (polynomial unconstrained binary optimization), we employ non-convex loss functions which are polynomial functions of the margin. We show that these loss functions are robust to label noise and provide a clear advantage over convex methods. These loss functions may also be useful for classical approaches as they compile to regularized risk expressions which can be evaluated in constant time with respect to the number of training examples.

cs.LG↗

arXiv2014

Quantum Simulation of Helium Hydride in a Solid-State Spin Register

\emph{Ab initio} computation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which have the potential to vastly accelerate research throughput in fields ranging from material science to drug discovery. Using a solid-state quantum register realized in a nitrogen-vacancy (NV) defect in diamond, we compute the bond dissociation curve of the minimal basis helium hydride cation, HeH$^+$. Moreover, we report an energy uncertainty (given our model basis) of the order of $10^{-14}$ Hartree, which is ten orders of magnitude below desired chemical precision. As NV centers in diamond provide a robust and straightforward platform for quantum information processing, our work provides several important steps towards a fully scalable solid state implementation of a quantum chemistry simulator.

quant-ph↗

arXiv2013

Adiabatic Quantum Simulation of Quantum Chemistry

We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-local qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-local, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.

quant-ph↗

arXiv2013

Resource Efficient Gadgets for Compiling Adiabatic Quantum Optimization Problems

We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, we optimize methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits. Next, we show a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision. Finally, we present numerics which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.

quant-ph↗

arXiv2013

Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions

Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.

cond-mat.stat-mech↗

arXiv2013

Construction of Energy Functions for Lattice Heteropolymer Models: A Case Study in Constraint Satisfaction Programming and Adiabatic Quantum Optimization

Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as constraint satisfaction problems such as linear programming, maximum satisfiability, and pseudo-boolean optimization. By encoding problems this way, one can leverage substantial insight and powerful solvers from the computer science community which studies constraint programming for diverse applications such as logistics, scheduling, artificial intelligence, and circuit design. We demonstrate how to constrain and embed lattice heteropolymer problems using several strategies. Each strikes a unique balance between number of constraints, complexity of constraints, and number of variables. Finally, we show how to reduce the locality of couplings in these energy functions so they can be realized as Hamiltonians on existing quantum annealing machines. We intend that this review be used as a case study for encoding related combinatorial optimization problems in a form suitable for adiabatic quantum optimization.

quant-ph↗