128 research outputs found
Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
We introduce a unitary coupled-cluster (UCC) ansatz termed -UpCCGSD that
is based on a family of sparse generalized doubles (D) operators which provides
an affordable and systematically improvable unitary coupled-cluster
wavefunction suitable for implementation on a near-term quantum computer.
-UpCCGSD employs products of the exponential of pair coupled-cluster
double excitation operators (pCCD), together with generalized single (S)
excitation operators. We compare its performance in both efficiency of
implementation and accuracy with that of the generalized UCC ansatz employing
the full generalized SD excitation operators (UCCGSD), as well as with the
standard ansatz employing only SD excitations (UCCSD). -UpCCGSD is found to
show the best scaling for quantum computing applications, requiring a circuit
depth of , compared with for UCCGSD and
for UCCSD where is the number of spin
orbitals and is the number of electrons. We analyzed the accuracy of
these three ans\"atze by making classical benchmark calculations on the ground
state and the first excited state of H (STO-3G, 6-31G), HO (STO-3G),
and N (STO-3G), making additional comparisons to conventional coupled
cluster methods. The results for ground states show that -UpCCGSD offers a
good tradeoff between accuracy and cost, achieving chemical accuracy for lower
cost of implementation on quantum computers than both UCCGSD and UCCSD. Excited
states are calculated with an orthogonally constrained variational quantum
eigensolver approach. This is seen to generally yield less accurate energies
than for the corresponding ground states. We demonstrate that using a
specialized multi-determinantal reference state constructed from classical
linear response calculations allows these excited state energetics to be
improved
Matchgate Shadows for Fermionic Quantum Simulation
"Classical shadows" are estimators of an unknown quantum state, constructed
from suitably distributed random measurements on copies of that state [Nature
Physics 16, 1050-1057]. Here, we analyze classical shadows obtained using
random matchgate circuits, which correspond to fermionic Gaussian unitaries. We
prove that the first three moments of the Haar distribution over the continuous
group of matchgate circuits are equal to those of the discrete uniform
distribution over only the matchgate circuits that are also Clifford unitaries;
thus, the latter forms a "matchgate 3-design." This implies that the classical
shadows resulting from the two ensembles are functionally equivalent. We show
how one can use these matchgate shadows to efficiently estimate inner products
between an arbitrary quantum state and fermionic Gaussian states, as well as
the expectation values of local fermionic operators and various other
quantities, thus surpassing the capabilities of prior work. As a concrete
application, this enables us to apply wavefunction constraints that control the
fermion sign problem in the quantum-classical auxiliary-field quantum Monte
Carlo algorithm (QC-AFQMC) [Nature 603, 416-420], without the exponential
post-processing cost incurred by the original approach.Comment: 53 pages, 1 figur
A principled approach to the measurement of situation awareness in commercial aviation
The issue of how to support situation awareness among crews of modern commercial aircraft is becoming especially important with the introduction of automation in the form of sophisticated flight management computers and expert systems designed to assist the crew. In this paper, cognitive theories are discussed that have relevance for the definition and measurement of situation awareness. These theories suggest that comprehension of the flow of events is an active process that is limited by the modularity of attention and memory constraints, but can be enhanced by expert knowledge and strategies. Three implications of this perspective for assessing and improving situation awareness are considered: (1) Scenario variations are proposed that tax awareness by placing demands on attention; (2) Experimental tasks and probes are described for assessing the cognitive processes that underlie situation awareness; and (3) The use of computer-based human performance models to augment the measures of situation awareness derived from performance data is explored. Finally, two potential example applications of the proposed assessment techniques are described, one concerning spatial awareness using wide field of view displays and the other emphasizing fault management in aircraft systems
A Non-Orthogonal Variational Quantum Eigensolver
Variational algorithms for strongly correlated chemical and materials systems
are one of the most promising applications of near-term quantum computers. We
present an extension to the variational quantum eigensolver that approximates
the ground state of a system by solving a generalized eigenvalue problem in a
subspace spanned by a collection of parametrized quantum states. This allows
for the systematic improvement of a logical wavefunction ansatz without a
significant increase in circuit complexity. To minimize the circuit complexity
of this approach, we propose a strategy for efficiently measuring the
Hamiltonian and overlap matrix elements between states parametrized by circuits
that commute with the total particle number operator. We also propose a
classical Monte Carlo scheme to estimate the uncertainty in the ground state
energy caused by a finite number of measurements of the matrix elements. We
explain how this Monte Carlo procedure can be extended to adaptively schedule
the required measurements, reducing the number of circuit executions necessary
for a given accuracy. We apply these ideas to two model strongly correlated
systems, a square configuration of H and the -system of Hexatriene
(CH)
Accelerating Quantum Algorithms with Precomputation
Real-world applications of computing can be extremely time-sensitive. It would be valuable if we could accelerate such tasks by performing some of the work ahead of time. Motivated by this, we propose a cost model for quantum algorithms that allows quantum precomputation; i.e., for a polynomial amount of ``free'' computation before the input to an algorithm is fully specified, and methods for taking advantage of it. We analyze two families of unitaries that are asymptotically more efficient to implement in this cost model than in the standard one. The first example of quantum precomputation, based on density matrix exponentiation, could offer an exponential advantage under certain conditions. The second example uses a variant of gate teleportation to achieve a quadratic advantage when compared with implementing the unitaries directly. These examples hint that quantum precomputation may offer a new arena in which to seek quantum advantage
On quantum backpropagation, information reuse, and cheating measurement collapse
The success of modern deep learning hinges on the ability to train neural
networks at scale. Through clever reuse of intermediate information,
backpropagation facilitates training through gradient computation at a total
cost roughly proportional to running the function, rather than incurring an
additional factor proportional to the number of parameters - which can now be
in the trillions. Naively, one expects that quantum measurement collapse
entirely rules out the reuse of quantum information as in backpropagation. But
recent developments in shadow tomography, which assumes access to multiple
copies of a quantum state, have challenged that notion. Here, we investigate
whether parameterized quantum models can train as efficiently as classical
neural networks. We show that achieving backpropagation scaling is impossible
without access to multiple copies of a state. With this added ability, we
introduce an algorithm with foundations in shadow tomography that matches
backpropagation scaling in quantum resources while reducing classical auxiliary
computational costs to open problems in shadow tomography. These results
highlight the nuance of reusing quantum information for practical purposes and
clarify the unique difficulties in training large quantum models, which could
alter the course of quantum machine learning.Comment: 29 pages, 2 figure
Can solid body destruction explain abundance discrepancies in planetary nebulae?
In planetary nebulae, abundances of oxygen and other heavy elements derived
from optical recombination lines are systematically higher than those derived
from collisionally excited lines. We investigate the hypothesis that the
destruction of solid bodies may produce pockets of cool, high-metallicity gas
that could explain these abundance discrepancies. Under the assumption of
maximally efficient radiative ablation, we derive two fundamental constraints
that the solid bodies must satisfy in order that their evaporation during the
planetary nebula phase should generate a high enough gas phase metallicity. A
local constraint implies that the bodies must be larger than tens of meters,
while a global constraint implies that the total mass of the solid body
reservoir must exceed a few hundredths of a solar mass. This mass greatly
exceeds the mass of any population of comets or large debris particles expected
to be found orbiting evolved low- to intermediate-mass stars. We therefore
conclude that contemporaneous solid body destruction cannot explain the
observed abundance discrepancies in planetary nebulae. However, similar
arguments applied to the sublimation of solid bodies during the preceding
asymptotic giant branch (AGB) phase do not lead to such a clear-cut conclusion.
In this case, the required reservoir of volatile solids is only one
ten-thousandth of a solar mass, which is comparable to the most massive debris
disks observed around solar-type stars, implying that this mechanism may
contribute to abundance discrepancies in at least some planetary nebulae, so
long as mixing of the high metallicity gas is inefficient.Comment: 8 pages, no figures, ApJ in pres
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