13 research outputs found
Quantum-assisted finite-element design optimization
Quantum annealing devices such as the ones produced by D-Wave systems are
typically used for solving optimization and sampling tasks, and in both
academia and industry the characterization of their usefulness is subject to
active research. Any problem that can naturally be described as a weighted,
undirected graph may be a particularly interesting candidate, since such a
problem may be formulated a as quadratic unconstrained binary optimization
(QUBO) instance, which is solvable on D-Wave's Chimera graph architecture. In
this paper, we introduce a quantum-assisted finite-element method for design
optimization. We show that we can minimize a shape-specific quantity, in our
case a ray approximation of sound pressure at a specific position around an
object, by manipulating the shape of this object. Our algorithm belongs to the
class of quantum-assisted algorithms, as the optimization task runs iteratively
on a D-Wave 2000Q quantum processing unit (QPU), whereby the evaluation and
interpretation of the results happens classically. Our first and foremost aim
is to explain how to represent and solve parts of these problems with the help
of a QPU, and not to prove supremacy over existing classical finite-element
algorithms for design optimization.Comment: 17 pages, 5 figure
Quantum simulation of battery materials using ionic pseudopotentials
Ionic pseudopotentials are widely used in classical simulations of materials
to model the effective potential due to the nucleus and the core electrons.
Modeling fewer electrons explicitly results in a reduction in the number of
plane waves needed to accurately represent the states of a system. In this
work, we introduce a quantum algorithm that uses pseudopotentials to reduce the
cost of simulating periodic materials on a quantum computer. We use a
qubitization-based quantum phase estimation algorithm that employs a
first-quantization representation of the Hamiltonian in a plane-wave basis. We
address the challenge of incorporating the complexity of pseudopotentials into
quantum simulations by developing highly-optimized compilation strategies for
the qubitization of the Hamiltonian. This includes a linear combination of
unitaries decomposition that leverages the form of separable pseudopotentials.
Our strategies make use of quantum read-only memory subroutines as a more
efficient alternative to quantum arithmetic. We estimate the computational cost
of applying our algorithm to simulating lithium-excess cathode materials for
batteries, where more accurate simulations are needed to inform strategies for
gaining reversible access to the excess capacity they offer. We estimate the
number of qubits and Toffoli gates required to perform sufficiently accurate
simulations with our algorithm for three materials: lithium manganese oxide,
lithium nickel-manganese oxide, and lithium manganese oxyfluoride. Our
optimized compilation strategies result in a pseudopotential-based quantum
algorithm with a total runtime four orders of magnitude lower than the previous
state of the art for a fixed target accuracy
Initial state preparation for quantum chemistry on quantum computers
Quantum algorithms for ground-state energy estimation of chemical systems
require a high-quality initial state. However, initial state preparation is
commonly either neglected entirely, or assumed to be solved by a simple product
state like Hartree-Fock. Even if a nontrivial state is prepared, strong
correlations render ground state overlap inadequate for quality assessment. In
this work, we address the initial state preparation problem with an end-to-end
algorithm that prepares and quantifies the quality of initial states,
accomplishing the latter with a new metric -- the energy distribution. To be
able to prepare more complicated initial states, we introduce an implementation
technique for states in the form of a sum of Slater determinants that exhibits
significantly better scaling than all prior approaches. We also propose
low-precision quantum phase estimation (QPE) for further state quality
refinement. The complete algorithm is capable of generating high-quality states
for energy estimation, and is shown in select cases to lower the overall
estimation cost by several orders of magnitude when compared with the best
single product state ansatz. More broadly, the energy distribution picture
suggests that the goal of QPE should be reinterpreted as generating
improvements compared to the energy of the initial state and other classical
estimates, which can still be achieved even if QPE does not project directly
onto the ground state. Finally, we show how the energy distribution can help in
identifying potential quantum advantage
How to simulate key properties of lithium-ion batteries with a fault-tolerant quantum computer
There is a pressing need to develop new rechargeable battery technologies
that can offer higher energy storage, faster charging, and lower costs. Despite
the success of existing methods for the simulation of battery materials, they
can sometimes fall short of delivering accurate and reliable results. Quantum
computing has been discussed as an avenue to overcome these issues, but only
limited work has been done to outline how they may impact battery simulations.
In this work, we provide a detailed answer to the following question: how can a
quantum computer be used to simulate key properties of a lithium-ion battery?
Based on recently-introduced first-quantization techniques, we lay out an
end-to-end quantum algorithm for calculating equilibrium cell voltages, ionic
mobility, and thermal stability. These can be obtained from ground-state
energies of materials, which is the core calculation executed by the quantum
computer using qubitization-based quantum phase estimation. The algorithm
includes explicit methods for preparing approximate ground states of periodic
materials in first quantization. We bring these insights together to perform
the first estimation of the resources required to implement a quantum algorithm
for simulating a realistic cathode material, dilithium iron silicate.Comment: 31 pages, 14 figure
Non-Standard Errors
In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants