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- Julia Kempe, Alexei Y. Kitaev, Oded Regev
- FSTTCS
- 2004

The k-LOCAL HAMILTONIAN problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k ≥ 2. It was known that the problem is QMA-complete for any k ≥ 3. On the other hand 1-LOCAL HAMILTONIAN is in P, and hence not believed to be QMA-complete. The complexity of… (More)

We set the ground for a theory of quantum walks on graphs-the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by suitably relaxing the definition, we can obtain a measure of how fast the quantum walk spreads or how confined… (More)

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speed-up over classical algorithms. In this paper, we present a quantum search algorithm based… (More)

- Andris Ambainis, Julia Kempe, Alexander Rivosh
- SODA
- 2005

We show how to search <i>N</i> items arranged on a √<i>N</i> × √<i>N</i> grid in time <i>O</i>(√<i>N</i> log <i>N</i>), using a discrete time quantum walk. This result for the first time exhibits a significant difference between discrete time and continuous time walks without coin degrees of freedom. since it has been shown recently… (More)

- Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, Oded Regev
- 45th Annual IEEE Symposium on Foundations of…
- 2004

The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown. We settle this question and describe an efficient adiabatic simulation of any given quantum algorithm. This implies that the adiabatic computation model and the standard quantum… (More)

- Julia Kempe
- ArXiv
- 2002

We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum random walks. We provide the framework for quantum hitting time and give two alternative definitions to set the ground… (More)

- Julia Kempe, Oded Regev
- Quantum Information & Computation
- 2003

It has been shown by Kitaev that the 5-local Hamiltonian problem is QMA-complete. Here we reduce the locality of the problem by showing that 3-local Hamiltonian is already QMA-complete.

- Dorit Aharonov, Daniel Gottesman, Sandy Irani, Julia Kempe
- 48th Annual IEEE Symposium on Foundations of…
- 2007

We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). Building on the same construction, but with some additional technical effort and 12 states per… (More)

We give an exponential separation between one-way quantum and classical communication protocols for twopartial Boolean functions, both of which are variants of the Boolean Hidden Matching Problem of Bar-Yossef et al. Earlier such an exponential separation was known only for a relational version of the Hidden Matching Problem. Our proofs use the Fourier… (More)

- D P DiVincenzo, D Bacon, J Kempe, G Burkard, K B Whaley
- Nature
- 2000

Various physical implementations of quantum computers are being investigated, although the requirements that must be met to make such devices a reality in the laboratory at present involve capabilities well beyond the state of the art. Recent solid-state approaches have used quantum dots, donor-atom nuclear spins or electron spins; in these architectures,… (More)