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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Adiabatic Quantum Computation: Noise in the Adiabatic Theorem and Using the Jordan-Wigner Transform to Find Effective Hamiltonians.

Adiabatic Quantum Computation: Noise in the Adiabatic Theorem and Using the Jordan-Wigner Transform to Find Effective Hamiltonians.

O'Hara, Michael James

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Biology

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ISBN10: 1243524170
ISBN13: 9781243524171
Publisher: Proquest Umi Dissertation Pub
Pages: 124
Weight: 0.58
Height: 0.32 Width: 7.99 Depth: 10.00
Language: English
This thesis explores two mathematical aspects of adiabatic quantum computation. Adiabatic quantum computation depends on the adiabatic theorem of quantum mechanics, and (a) we provide a rigorous formulation of the adiabatic theorem with explicit definitions of constants, and (b) we bound error in the adiabatic approximation under conditions of noise and experimental error. We apply the new results to a standard example of violation of the adiabatic approximation, and to a superconducting flux qubit. Further, adiabatic quantum computation requires large ground-state energy gaps throughout a Hamiltonian evolution if it is to solve problems in polynomial time. We identify a class of random Hamiltonians with non-nearest-neighbor interactions and a ground-state energy gap of O(1/ n ), where n is the number of qubits. We also identify two classes of Hamiltonians with non-nearest-neighbor interactions whose ground state can be found in polynomial time with adiabatic quantum computing. We then use the Jordan-Wigner transformation to derive equivalent results for Hamiltonians defined using Pauli operators.

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