Cedric Yen-Yu Lin

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Inspired by the Elitzur-Vaidman bomb testing problem [19], we introduce a new query complexity model, which we call bomb query complexity B(f). We investigate its relationship with the usual quantum query complexity Q(f), and show that B(f) = Θ(Q(f)2). This result gives a new method to upper bound the quantum query complexity: we give a method of finding(More)
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and the case that all of the measurements have low probability of acceptance. The measurements cannot simply be tried in(More)
We give semidefinite program (SDP) quantum solvers with an exponential speed-up over classical ones. Specifically, we consider SDP instances with m constraint matrices of dimension n, each of rank at most r, and assume that the input matrices of the SDP are given as quantum states (after a suitable normalization). Then we show there is a quantum algorithm(More)
This work presents a precise connection between Clifford circuits, Shor’s factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all these different forms of quantum computation belong to a common new restricted model of quantum operations that we call(More)
We give two complete characterizations of unitary quantum space-bounded classes. The first is based on the Matrix Inversion problem for well-conditioned matrices. We show that given the size-n efficient encoding of a 2 ×2O(k(n)) well-conditioned matrix H , approximating a particular entry of H is complete for the class of problems solvable by a quantum(More)
This paper presents a general space-efficient method for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness c and soundness s, either with or without a witness (corresponding to QMA and BQP, respectively). To convert this computation into a new computation with error at most 2−p, the most(More)
Normalizer circuits [1, 2] are generalized Clifford circuits that act on arbitrary finitedimensional systems Hd1 ⊗· · ·⊗Hdn with a standard basis labeled by the elements of a finite Abelian group G = Zd1 × · · · × Zdn . Normalizer gates implement operations associated with the group G and can be of three types: quantum Fourier transforms, group automorphism(More)
We consider constraint satisfaction problems of bounded degree, with a good notion of ”typicality”, e.g. the negation of the variables in each constraint is taken independently at random. Using the quantum approximate optimization algorithm (QAOA), we show that μ + Ω(1/ √ D) fraction of the constraints can be satisfied for typical instances, with the(More)
by Han-Hsuan Lin Submitted to the Department of Physics on May 22, 2015, in partial fulfillment of the requirements for the degree of Ph.D. in Physics In this thesis, I present three results on quantum algorithms and their complexity. The first one is a numerical study on the quantum adiabatic algorithm( QAA) . We tested the performance of the QAA on random(More)