2,651 research outputs found
Equivalence is in the Eye of the Beholder
In a recent provocative paper, Lamport points out "the insubstantiality of
processes" by proving the equivalence of two different decompositions of the
same intuitive algorithm by means of temporal formulas. We point out that the
correct equivalence of algorithms is itself in the eye of the beholder. We
discuss a number of related issues and, in particular, whether algorithms can
be proved equivalent directly.Comment: See also the ASM web site at http://www.eecs.umich.edu/gasm
Abstract State Machines 1988-1998: Commented ASM Bibliography
An annotated bibliography of papers which deal with or use Abstract State
Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm
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
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