8,759 research outputs found
Quantum Chemistry in the Age of Quantum Computing
Practical challenges in simulating quantum systems on classical computers
have been widely recognized in the quantum physics and quantum chemistry
communities over the past century. Although many approximation methods have
been introduced, the complexity of quantum mechanics remains hard to appease.
The advent of quantum computation brings new pathways to navigate this
challenging complexity landscape. By manipulating quantum states of matter and
taking advantage of their unique features such as superposition and
entanglement, quantum computers promise to efficiently deliver accurate results
for many important problems in quantum chemistry such as the electronic
structure of molecules. In the past two decades significant advances have been
made in developing algorithms and physical hardware for quantum computing,
heralding a revolution in simulation of quantum systems. This article is an
overview of the algorithms and results that are relevant for quantum chemistry.
The intended audience is both quantum chemists who seek to learn more about
quantum computing, and quantum computing researchers who would like to explore
applications in quantum chemistry.Comment: 194 pages, 13 figures, 5 tables and 404 references. Fixed formatting
issues from the previous version. Comments welcom
Compact wavefunctions from compressed imaginary time evolution
Simulation of quantum systems promises to deliver physical and chemical
predictions for the frontiers of technology. Unfortunately, the exact
representation of these systems is plagued by the exponential growth of
dimension with the number of particles, or colloquially, the curse of
dimensionality. The success of approximation methods has hinged on the relative
simplicity of physical systems with respect to the exponentially complex worst
case. Exploiting this relative simplicity has required detailed knowledge of
the physical system under study. In this work, we introduce a general and
efficient black box method for many-body quantum systems that utilizes
technology from compressed sensing to find the most compact wavefunction
possible without detailed knowledge of the system. It is a Multicomponent
Adaptive Greedy Iterative Compression (MAGIC) scheme. No knowledge is assumed
in the structure of the problem other than correct particle statistics. This
method can be applied to many quantum systems such as spins, qubits,
oscillators, or electronic systems. As an application, we use this technique to
compute ground state electronic wavefunctions of hydrogen fluoride and recover
98% of the basis set correlation energy or equivalently 99.996% of the total
energy with configurations out of a possible . Building from this
compactness, we introduce the idea of nuclear union configuration interaction
for improving the description of reaction coordinates and use it to study the
dissociation of hydrogen fluoride and the helium dimer
Hypercomputability of quantum adiabatic processes: Fact versus Prejudices
We give an overview of a quantum adiabatic algorithm for Hilbert's tenth
problem, including some discussions on its fundamental aspects and the emphasis
on the probabilistic correctness of its findings. For the purpose of
illustration, the numerical simulation results of some simple Diophantine
equations are presented. We also discuss some prejudicial misunderstandings as
well as some plausible difficulties faced by the algorithm in its physical
implementation.Comment: 25 pages, 4 figures. Invited paper for a special issue of the Journal
of Applied Mathematics and Computatio
Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function
Including finite-temperature effects from the electronic degrees of freedom
in electronic structure calculations of semiconductors and metals is desired;
however, in practice it remains exceedingly difficult when using
zero-temperature methods, since these methods require an explicit evaluation of
multiple excited states in order to account for any finite-temperature effects.
Using a Matsubara Green's function formalism remains a viable alternative,
since in this formalism it is easier to include thermal effects and to connect
the dynamic quantities such as the self-energy with static thermodynamic
quantities such as the Helmholtz energy, entropy, and internal energy. However,
despite the promising properties of this formalism, little is know about the
multiple solutions of the non-linear equations present in the self-consistent
Matsubara formalism and only a few cases involving a full Coulomb Hamiltonian
were investigated in the past. Here, to shed some light onto the iterative
nature of the Green's function solutions, we self-consistently evaluate the
thermodynamic quantities for a one-dimensional (1D) hydrogen solid at various
interatomic separations and temperatures using the self-energy approximated to
second-order (GF2). At many points in the phase diagram of this system,
multiple phases such as a metal and an insulator exist, and we are able to
determine the most stable phase from the analysis of Helmholtz energies.
Additionally, we show the evolution of the spectrum of 1D boron nitride (BN) to
demonstrate that GF2 is capable of qualitatively describing the temperature
effects influencing the size of the band gap
Ultrafast ab-initio Quantum Chemistry Using Matrix Product States
Ultrafast dynamics in chemical systems provide a unique access to fundamental
processes at the molecular scale. A proper description of such systems is often
very challenging because of the quantum nature of the problem. The concept of
matrix product states (MPS), however, has proven its performance in describing
such correlated quantum system in recent years for a wide range of
applications. In this work, we continue the development of the MPS approach to
study ultrafast electron dynamics in quantum chemical systems. The method
combines time evolution schemes, such as fourth-order Runge-Kutta and Krylov
space time evolution, with MPS, in order to solve the time-dependent
Schr\"odinger equation efficiently. This allows for describing electron
dynamics in molecules on a full configurational interaction (CI) level for a
few femtoseconds after excitation. As a benchmark, we compare MPS based
calculations to full CI calculations for a chain of hydrogen atoms and for the
water molecule. Krylov space time evolution is in particular suited for the MPS
approach, as it provides a wide range of opportunities to be adjusted to the
reduced MPS dimension case. Finally, we apply the MPS approach to describe
charge migration effects in iodoacetylene and find direct agreement between our
results and experimental observations
Computational Theory of a splitting BEC using a Generalized Wannier basis I: Theory and Statics
We investigate the behavior of a Bose-Einstein Condensate (BEC) under the
influence of a central barrier as the particle number trends towards the
thermodynamic limit. In order to perform these studies, we present a novel
method which is tractable in the large- limit. This method employs what may
be considered to be a generalized Wannier basis, which successfully
incorporates features of previous theoretical and computational assays to the
splitting problem, including mean field effects, and has access to the
dimensionality, trap parameters, and particle numbers relevant to recent
experiments. At any barrier height we are able to discern between a two-mode
state and a state which is described sufficiently by mean field theory and,
further, give a criterion and technique for matching the two-mode theory to the
zero-barrier state. We compare the basis used in this model to the de-localized
basis functions underlying alternate models used in recent theoretical work on
the double-well splitting problem and show that only the generalized Wannier
basis displays the level crossing and emergence of two complex order parameters
with overall symmetry as expected from a large- analogue
of the Superfluid to Mott insulator transition. Using this model, we identify a
universal structure, independent of , in this phase transition. We also
present an analytic and model-independent description of this universal
structure and discuss its consequences for realizing true two-mode physics with
a BEC which trends towards the thermodynamic limit.Comment: 29 pages, 8 figure
Electron-pair densities with time-dependent quantum Monte-Carlo
In this paper we use sets of de Broglie-Bohm trajectories to describe the
quantum correlation effects which take place between the electrons in helium
atom due to exchange and Coulomb interactions. A short-range screening of the
Coulomb potential is used to modify the repulsion between the same spin
electrons in physical space in order to comply with the Pauli's exclusion
principle. By calculating the electron-pair density for ortho-helium we found
that the shape of the exchange hole can be controlled uniquely by a simple
screening parameter. For para-helium the inter-electronic distance, and hence
the Coulomb hole, results from the combined action of the Coulomb repulsion and
the non-local quantum correlations. In this way a robust and
self-interaction-free approach is presented to find both the ground state and
the time evolution of non-relativistic quantum systems.Comment: 18 pages, 4 figure
Many-body state engineering using measurements and fixed unitary dynamics
We develop a scheme to prepare a desired state or subspace in
high-dimensional Hilbert-spaces using repeated applications of a single static
projection operator onto the desired target and fixed unitary dynamics.
Benchmarks against other control schemes, performed on generic Hamiltonians and
on Bose-Hubbard systems, establish the competitiveness of the method. As a
concrete application of the control of mesoscopic atomic samples in optical
lattices we demonstrate the near deterministic preparation of Schr\"{o}dinger
cat states of all atoms residing on either the odd or the even sites.Comment: 5 pages, 4 figures, New revised version with new title, added
references, corrected typos and unclaritie
Q# and NWChem: Tools for Scalable Quantum Chemistry on Quantum Computers
Fault-tolerant quantum computation promises to solve outstanding problems in
quantum chemistry within the next decade. Realizing this promise requires
scalable tools that allow users to translate descriptions of electronic
structure problems to optimized quantum gate sequences executed on physical
hardware, without requiring specialized quantum computing knowledge. To this
end, we present a quantum chemistry library, under the open-source MIT license,
that implements and enables straightforward use of state-of-art quantum
simulation algorithms. The library is implemented in Q#, a language designed to
express quantum algorithms at scale, and interfaces with NWChem, a leading
electronic structure package. We define a standardized schema for this
interface, Broombridge, that describes second-quantized Hamiltonians, along
with metadata required for effective quantum simulation, such as trial
wavefunction ansatzes. This schema is generated for arbitrary molecules by
NWChem, conveniently accessible, for instance, through Docker containers and a
recently developed web interface EMSL Arrows. We illustrate use of the library
with various examples, including ground- and excited-state calculations for
LiH, H, and C with an active-space simplification, and
automatically obtain resource estimates for classically intractable examples.Comment: 36 pages, 5 figures. Examples and data in ancillary files folde
Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
In classical computational chemistry, the coupled-cluster ansatz is one of
the most commonly used methods, which is critically limited by its
non-unitary nature. The unitary modification as an ideal solution to the
problem is, however, extremely inefficient in classical conventional
computation. Here, we provide the first experimental evidence that indeed the
unitary version of the coupled cluster ansatz can be reliably performed in
physical quantum system, a trapped ion system. We perform a simulation on the
electronic structure of a molecular ion (HeH), where the ground-state
energy surface curve is probed, energies of excited-states are studied and the
bond-dissociation is simulated non-perturbatively. Our simulation takes
advantages from quantum computation to overcome the intrinsic limitations in
classical computation and our experimental results indicate that the method is
promising for preparing molecular ground-states for quantum simulation.Comment: 6 pages, 4 figure
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