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Quantum algorithms revisited
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum
Limits on the security of coin flips when half the processors are faulty
  • R. Cleve
  • Computer Science
    STOC '86
  • 1 November 1986
TLDR
It is proved that no protocol exists which tolerates faults in at least half of the processors, and protocols which allow an asynchronous network of processors to agree on a r andom (unbiased) bit are opt imal in the sense that few restr ict ions are made on the types of communicat ion allowed between correct processors.
Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H.
Exponential algorithmic speedup by a quantum walk
TLDR
A black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer is constructed and it is proved that no classical algorithm can solve the problem in subexponential time.
HOW TO SHARE A QUANTUM SECRET
We investigate the concept of quantum secret sharing. In a (k,thinspn) threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the
Quantum lower bounds by polynomials
TLDR
This work examines the number of queries to input variables that a quantum algorithm requires to compute Boolean functions on {0,1}N in the black-box model and gives asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings.
Quantum vs. classical communication and computation
TLDR
A simple and general simulation technique is presented that transforms any black-box quantum algorithm to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism, to obtain new positive and negative results.
Simulating Hamiltonian dynamics with a truncated Taylor series.
TLDR
A simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.
Quantum lower bounds by polynomials
TLDR
This work examines the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}/sup N/ in the black-box model and gives asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings.
Quantum fingerprinting.
TLDR
It is shown that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties, implying an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity.
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