488 research outputs found
Resource-Optimized Fermionic Local-Hamiltonian Simulation on Quantum Computer for Quantum Chemistry
The ability to simulate a fermionic system on a quantum computer is expected
to revolutionize chemical engineering, materials design, nuclear physics, to
name a few. Thus, optimizing the simulation circuits is of significance in
harnessing the power of quantum computers. Here, we address this problem in two
aspects. In the fault-tolerant regime, we optimize the \rzgate and \tgate
gate counts along with the ancilla qubit counts required, assuming the use of a
product-formula algorithm for implementation. We obtain a savings ratio of two
in the gate counts and a savings ratio of eleven in the number of ancilla
qubits required over the state of the art. In the pre-fault tolerant regime, we
optimize the two-qubit gate counts, assuming the use of the variational quantum
eigensolver (VQE) approach. Specific to the latter, we present a framework that
enables bootstrapping the VQE progression towards the convergence of the
ground-state energy of the fermionic system. This framework, based on
perturbation theory, is capable of improving the energy estimate at each cycle
of the VQE progression, by about a factor of three closer to the known
ground-state energy compared to the standard VQE approach in the test-bed,
classically-accessible system of the water molecule. The improved energy
estimate in turn results in a commensurate level of savings of quantum
resources, such as the number of qubits and quantum gates, required to be
within a pre-specified tolerance from the known ground-state energy. We also
explore a suite of generalized transformations of fermion to qubit operators
and show that resource-requirement savings of up to more than , in small
instances, is possible
Efficient quantum simulation of fermionic and bosonic models in trapped ions
We analyze the efficiency of quantum simulations of fermionic and bosonic
models in trapped ions. In particular, we study the optimal time of entangling
gates and the required number of total elementary gates. Furthermore, we
exemplify these estimations in the light of quantum simulations of quantum
field theories, condensed-matter physics, and quantum chemistry. Finally, we
show that trapped-ion technologies are a suitable platform for implementing
quantum simulations involving interacting fermionic and bosonic modes, paving
the way for overcoming classical computers in the near future.Comment: 13 pages, 3 figures. Published in EPJ Quantum Technolog
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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