# Quantum Computation

Advances in quantum information processing have opened new avenues for using quantum phenomena to perform computation. Quantum computers have become of great interest, primarily due to their potential of solving certain computationally hard problems such as factoring integers and searching databases. The fact that a quantum computer might be more powerful than an ordinary computer is based on the notion that a quantum system can be in a superposition of states and that this allows exponentially many computations to be done in parallel. The presence of the superposition of states is a direct manifestation of the internal quantum dynamics of the elementary units of the quantum computer, the qubits.

**Ideal Quantum Computers**

Theoretical work on quantum computation usually assumes the existence of units that perform highly idealized unitary operations, the elementary building blocks of an ideal quantum computer. On JUGENE we simulate a 42-qubit ideal quantum computer using 262.144 of its 294.912 CPUs. Simulating a 43-qubit ideal quantum computer requires twice as much CPUs. The simulation software scales nearly perfectly.

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**Adiabatic quantum computing**

An adiabatic quantum computer maintains a system of qubits in the ground state of a slowly (adiabatically) varying Hamiltonian. The initial Hamiltonian is a Hamiltonian with an easy to construct or known ground state. The final Hamiltonian, encoding the problem to be solved, has a computationally-challenging ground state. Problem Hamiltonians of interest are those parametrizing NP-complete problems such as the Boolean- satisfiability problem 3-SAT, the exact cover problem and spin glass systems. Studying the efficiency of adiabatic quantum algorithms solving these NP-complete problems requires a comparison with classical algorithms.

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