74,839 research outputs found
A Universal Quantum Circuit Scheme For Finding Complex Eigenvalues
We present a general quantum circuit design for finding eigenvalues of
non-unitary matrices on quantum computers using the iterative phase estimation
algorithm. In particular, we show how the method can be used for the simulation
of resonance states for quantum systems
Digital Quantum Rabi and Dicke Models in Superconducting Circuits
We propose the analog-digital quantum simulation of the quantum Rabi and
Dicke models using circuit quantum electrodynamics (QED). We find that all
physical regimes, in particular those which are impossible to realize in
typical cavity QED setups, can be simulated via unitary decomposition into
digital steps. Furthermore, we show the emergence of the Dirac equation
dynamics from the quantum Rabi model when the mode frequency vanishes. Finally,
we analyze the feasibility of this proposal under realistic superconducting
circuit scenarios.Comment: 5 pages, 3 figures. Published in Scientific Report
The Bravyi-Kitaev transformation for quantum computation of electronic structure
Quantum simulation is an important application of future quantum computers
with applications in quantum chemistry, condensed matter, and beyond. Quantum
simulation of fermionic systems presents a specific challenge. The
Jordan-Wigner transformation allows for representation of a fermionic operator
by O(n) qubit operations. Here we develop an alternative method of simulating
fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu.
Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation
cost to O(log n) qubit operations for one fermionic operation. We apply this
new Bravyi-Kitaev transformation to the task of simulating quantum chemical
Hamiltonians, and give a detailed example for the simplest possible case of
molecular hydrogen in a minimal basis. We show that the quantum circuit for
simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian
for H2 requires fewer gate applications than the equivalent circuit derived
from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev
method is asymptotically better than the Jordan-Wigner method, this result for
molecular hydrogen in a minimal basis demonstrates the superior efficiency of
the Bravyi-Kitaev method for all quantum computations of electronic structure
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