Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Topologically protected Grover's oracle for the partition problem

Journal Article · · Physical Review A
 [1];  [1]
  1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations
The number partitioning problem (NPP) is one of the NP-complete (nondeterministic polynomial-time complete) computational problems. Its definite exact solution generally requires a check of all $$N$$ solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in $$\sqrt{N}$$ quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with $$N$$ only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time dependence of the physical parameters or the choice of the annealing protocol. In conclusion, we also argue that our approach can solve many other famous NP-complete computational problems in $$\sqrt{N}$$ steps.
Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1997183
Report Number(s):
LA-UR-23-24130
Journal Information:
Physical Review A, Journal Name: Physical Review A Journal Issue: 2 Vol. 108; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (19)

Teoria Relativistica di Particelle Con Momento Intrinseco Arbitrario journal December 1932
Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian journal April 2022
Adiabatic approximation with exponential accuracy for many-body systems and quantum computation journal October 2009
Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation journal January 2023
A geometric phase for m=0 spins journal June 1994
Quantum amplitude amplification and estimation book January 2002
Number Partitioning With Grover’s Algorithm in Central Spin Systems journal May 2021
Quantum Algorithm for Linear Systems of Equations journal October 2009
Quantum Speedup by Quantum Annealing journal July 2012
High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit journal November 2014
Rapid Adiabatic Preparation of Injective Projected Entangled Pair States and Gibbs States journal February 2016
Revealing the Emergence of Classicality Using Nitrogen-Vacancy Centers journal October 2019
Quantum Mechanics Helps in Searching for a Needle in a Haystack journal July 1997
Phase Transition in the Number Partitioning Problem journal November 1998
Quantum computation and Shor's factoring algorithm journal July 1996
Adiabatic quantum computation journal January 2018
A $T = O(2^{n/2} )$, $S = O(2^{n/4} )$ Algorithm for Certain NP-Complete Problems journal August 1981
Period finding with adiabatic quantum computation journal March 2014
The Easiest Hard Problem journal January 2002

Similar Records

Grover Search and the No-Signaling Principle
Journal Article · Tue Sep 13 20:00:00 EDT 2016 · Physical Review Letters · OSTI ID:1600495
Grover-algorithm-like operator using only single-qubit gates
Journal Article · Thu Sep 15 00:00:00 EDT 2005 · Physical Review. A · OSTI ID:20718505
The Boolean Isomorphism problem
Conference · Mon Dec 30 23:00:00 EST 1996 · OSTI ID:457672

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Quantum computation
Quantum information