Corpus ID: 233864539

A Grand Unification of Quantum Algorithms

  title={A Grand Unification of Quantum Algorithms},
  author={John Martyn and Zane Rossi and Andrew Tan and Isaac L. Chuang},
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
A Quantum Hamiltonian Simulation Benchmark
Yulong Dong, K. Birgitta Whaley, and Lin Lin3,4,5∗ Berkeley Center for Quantum Information and Computation, Berkeley, California 94720 USA Department of Chemistry, University of California, Berkeley,Expand
Hybridized Methods for Quantum Simulation in the Interaction Picture
1Department of Physics, University of Washington, Seattle, WA 98195, USA 2InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, USAExpand
A comparative study of universal quantum computing models: towards a physical unification
This work carried out a primary attempt to unify UQCM by classifying a few of them as two categories, hence making a table of models, which reveals the importance and feasibility of systematic study of computing models. Expand
Quantum Algorithms based on the Block-Encoding Framework for Matrix Functions by Contour Integrals
The matrix functions can be defined by Cauchy’s integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show aExpand
Quantum diffusion map for nonlinear dimensionality reduction
A quantum algorithm for DM is proposed, termed quantum diffusion map (qDM), which takes as an input N classical data vectors, performs an eigen-decomposition of the Markov transition matrix in time O(logN), and classically constructs the diffusion map via the readout (tomography) of the eigenvectors, giving a total runtime of O(NpolylogN). Expand
Concentration for Random Product Formulas
Quantum simulation has wide applications in quantum chemistry and physics. Recently, scientists have begun exploring the use of randomized methods for accelerating quantum simulation. Among them, aExpand
On the energy landscape of symmetric quantum signal processing
  • Jiasu Wang, Yulong Dong, Lin Lin
  • Physics, Computer Science
  • 2021
It is proved that one particular global minimum belongs to a neighborhood of Φ0, on which the cost function is strongly convex under suitable conditions, which explains the success of optimization algorithms, and solves the open problem of finding phase factors using only standard double precision arithmetic operations. Expand


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
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
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.
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
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.
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
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
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