Physics – Quantum Physics
Scientific paper
2009-02-09
Phys. Rev. A 79, 042335 (2009)
Physics
Quantum Physics
11 pages, 8 figures, errors are corrected, Journal information added
Scientific paper
10.1103/PhysRevA.79.042335
We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin orbitals. Each spin orbital is mapped to a qubit: the states $| 1 >$ and $| 0>$ of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of $n$ qubits, which is of dimension $2^{n}$%, $O(2^{n})$ controlled-NOT gates are needed, i.e., the number of gates scales \emph{exponentially} with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most $O(2^{m+1} n^{m}/{m!})$ gates, i.e., scales \emph{polynomially} with the number of qubits $n$, provided $n\gg m$. The algorithm is simulated numerically for the cases of the hydrogen molecule and the water molecule. The numerical simulations show that when additional symmetries of the system are considered, the number of gates to prepare the state can be drastically reduced, in the examples considered in this paper, by several orders of magnitude, from the above estimate.
Ashhab Sahel
Nori Franco
Wang Hefeng
No associations
LandOfFree
Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-176278