# 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

#### 7 Citations

A Quantum Hamiltonian Simulation Benchmark

- Physics
- 2021

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

- Physics
- 2021

1Department of Physics, University of Washington, Seattle, WA 98195, USA 2InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, USA… Expand

A comparative study of universal quantum computing models: towards a physical unification

- Computer Science, Physics
- ArXiv
- 2021

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

- Physics
- 2021

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 a… Expand

Quantum diffusion map for nonlinear dimensionality reduction

- Physics, Computer Science
- ArXiv
- 2021

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

- Physics, Mathematics
- PRX Quantum
- 2021

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, a… Expand

On the energy landscape of symmetric quantum signal processing

- 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

#### References

SHOWING 1-10 OF 105 REFERENCES

Quantum computation and quantum information

- 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 deal… Expand

Quantum Counting

- Computer Science, Physics
- ICALP
- 1998

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

- Physics
- 2005

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 nuclear… Expand

Quantum supremacy using a programmable superconducting processor

- Medicine, Computer Science
- Nature
- 2019

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

- Physics
- 2017

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 arises… Expand

Finding Angles for Quantum Signal Processing with Machine Precision.

- Computer Science, Physics
- 2020

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

- Mathematics, Computer Science
- SIAM J. Comput.
- 2017

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.

- Medicine, Computer Science
- Physical review letters
- 2014

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

- 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

- Computer Science, Mathematics
- STOC
- 2019

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