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1. Richter, Peter C. (Peter Courtland). Quantum walks and ground state problems.

Degree: PhD, Computer Science, 2007, Rutgers University

URL: http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16768

Since the appearance of Shor's factoring algorithm in 1994, the search for novel quantum computer algorithms has proved surprisingly difficult. Two design approaches that have yielded some progress are quantum walks and adiabatic computing. The former has been shown to speed up algorithms whose complexity is related to the classical hitting time of a symmetric Markov chain, and there is evidence that the latter speeds up simulated annealing algorithms for computing ground states of classical Hamiltonians. In this thesis, we look into the possibility of obtaining a quantum speedup for the mixing time of a symmetric Markov chain. We prove that by subjecting a quantum walk to a small amount of decoherence (typically the adversary of a quantum computer), it can be forced to mix to the correct stationary distribution, often considerably faster than its classical counterpart. A more general theorem to this effect would imply quantum speedups for a variety of approximation algorithms forP-complete problems. We conclude with some observations on adiabatic computing – a time-dependent generalization of the quantum walk framework – and the problem of estimating the ground state energy of a quantum Hamiltonian with local spin interactions.

Subjects/Keywords: Computer algorithms; Quantum field theory; Random walks (Mathematics)

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APA (6^{th} Edition):

Richter, P. C. (. C. (2007). Quantum walks and ground state problems. (Doctoral Dissertation). Rutgers University. Retrieved from http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16768

Chicago Manual of Style (16^{th} Edition):

Richter, Peter C (Peter Courtland). “Quantum walks and ground state problems.” 2007. Doctoral Dissertation, Rutgers University. Accessed September 20, 2020. http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16768.

MLA Handbook (7^{th} Edition):

Richter, Peter C (Peter Courtland). “Quantum walks and ground state problems.” 2007. Web. 20 Sep 2020.

Vancouver:

Richter PC(C. Quantum walks and ground state problems. [Internet] [Doctoral dissertation]. Rutgers University; 2007. [cited 2020 Sep 20]. Available from: http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16768.

Council of Science Editors:

Richter PC(C. Quantum walks and ground state problems. [Doctoral Dissertation]. Rutgers University; 2007. Available from: http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16768