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Numerical Analysis on a Quantum Computer
"... We give a short introduction to quantum computing and its relation to numerical analysis. We survey recent research on quantum algorithms and quantum complexity theory for two basic numerical problems – high dimensional integration and approximation. Having matching upper and lower complexity bound ..."
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We give a short introduction to quantum computing and its relation to numerical analysis. We survey recent research on quantum algorithms and quantum complexity theory for two basic numerical problems – high dimensional integration and approximation. Having matching upper and lower complexity bounds for the quantum setting, we are in a position to compare them with those for the classical deterministic and randomized setting, previously obtained in informationbased complexity theory. This enables us to assess the possible speedups quantum computation could provide over classical deterministic or randomized algorithms for these numerical problems.
An R k Cmax quantum scheduling algorithm
 Quantum Inf. Process
, 2005
"... Many scheduling problems are N P − hard on classical computers. Using quantum parallelism and entanglement, a quantum schedule algorithm may be able to lead to an exponential improvement. The algorithm presented in this paper constructs a superposition of all schedules and a superposition of their m ..."
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Many scheduling problems are N P − hard on classical computers. Using quantum parallelism and entanglement, a quantum schedule algorithm may be able to lead to an exponential improvement. The algorithm presented in this paper constructs a superposition of all schedules and a superposition of their makespans and then amplifies the one that corresponds to the solution. We perform O ( √ 2n+q) Grover iterations. The time complexity of the quantum scheduling algorithm for an RCmax problem is O ( √ 2n+q) while the complexity of a classical algorithm is O(2 m2n 1
Contents
, 2002
"... Abstract. In this paper, we use the methods found in [12] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → C from the reals R to the complex numbers C, where Φ belongs to ..."
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Abstract. In this paper, we use the methods found in [12] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → C from the reals R to the complex numbers C, where Φ belongs to a very general class of functions, called the class of admissible functions. This algorithm gives some insight into the inner workings of Shor’s quantum factoring algorithm.
On a Problem in Quantum Computation
, 2001
"... We consider the computation of the mean of sequences in the quantum model of computation. We determine the query complexity in the case of sequences which satisfy a psummability condition for 1 ≤ p < 2. This settles a problem left open in Heinrich (2001). ..."
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We consider the computation of the mean of sequences in the quantum model of computation. We determine the query complexity in the case of sequences which satisfy a psummability condition for 1 ≤ p < 2. This settles a problem left open in Heinrich (2001).
Automated Test Pattern Generation for Quantum Circuits
"... This work extends a general method used to test classical circuits to quantum circuits. Gate internal errors are address using a discrete fault model. Fault models to represent unwanted nearest neighbor entanglement as well as unwanted qubit rotation are presented. When witnessed, the faults we mode ..."
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This work extends a general method used to test classical circuits to quantum circuits. Gate internal errors are address using a discrete fault model. Fault models to represent unwanted nearest neighbor entanglement as well as unwanted qubit rotation are presented. When witnessed, the faults we model are probabilistic, but there is a set of tests with the highest probability of detecting a discrete repetitive fault. A method of probabilistic set covering to identify the minimal set of tests is introduced. A large part of our work consisted of writing a software package that allows us to compare various fault models and test strategies for quantum networks.