Corpus ID: 233864539

A Grand Unification of Quantum Algorithms

@inproceedings{Martyn2021AGU,
  title={A Grand Unification of Quantum Algorithms},
  author={John Martyn and Zane Rossi and Andrew Tan and Isaac L. Chuang},
  year={2021}
}
John M. Martyn, 2 Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang 4 Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts… Expand
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References

SHOWING 1-10 OF 105 REFERENCES
Quantum computation and quantum information
  • T. Paul
  • Mathematics, Computer Science
  • Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers dealExpand
Quantum Counting
TLDR
This work generalizes the Grover iteration in the light of a concept called amplitude amplification, and shows that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist. Expand
NMR techniques for quantum control and computation
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclearExpand
Quantum supremacy using a programmable superconducting processor
TLDR
Quantum supremacy is demonstrated using a programmable superconducting processor known as Sycamore, taking approximately 200 seconds to sample one instance of a quantum circuit a million times, which would take a state-of-the-art supercomputer around ten thousand years to compute. Expand
Quantum signal processing by single-qubit dynamics
Quantum computation is the most powerful realizable model of computation, and is uniquely positioned to solve specialized problems intractable to classical computers. This quantum advantage arisesExpand
Finding Angles for Quantum Signal Processing with Machine Precision.
TLDR
An algorithm for finding angle sequences in quantum signal processing, with a novel component the authors call halving based on a new algebraic uniqueness theorem, and another they call capitalization that allows us to find sequences of more than 3000 angles within 5 minutes for important applications such as Hamiltonian simulation, all in standard double precision arithmetic. Expand
Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision
TLDR
The algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation, and allows the quantum phase estimation algorithm, whose dependence on $\epsilon$ is prohibitive, to be bypassed. Expand
Fixed-point quantum search with an optimal number of queries.
TLDR
This work provides the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup and incorporates an adjustable bound on the failure probability and guarantees that this bound is satisfied over the broadest possible range of λ. Expand
Quantum measurements and the Abelian Stabilizer Problem
  • A. Kitaev
  • Computer Science, Mathematics
  • Electron. Colloquium Comput. Complex.
  • 1996
TLDR
A polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm is presented, based on a procedure for measuring an eigenvalue of a unitary operator. Expand
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
TLDR
A new “Quantum singular value transformation” algorithm is developed that can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singular values of a block of a unitary operator. Expand
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