Quantum computers are expected to break today’s public key cryptography within a few decades. New cryptosystems are being designed and standardized for the post-quantum era, and a significant proportion of these rely on the hardness of problems like the Shortest Vector Problem to a quantum adversary. In this paper, we describe two variants of a quantum Ising algorithm to solve this problem. One variant is spatially efficient, requiring only O(N log N) qubits where N is the lattice dimension, while the other variant is more robust to noise. Analysis of the algorithms’ performance on a quantum annealer and in numerical simulations show that the more qubit-efficient variant will outperform in the long run, while the other variant is more suitable for near-term implementation.
Scientific Publications
D-Wave is the world’s first commercial supplier of quantum computers. Learn more about the science behind our cutting-edge quantum technology and the use cases it can be applied to. Visit our resource library to read our technical white papers.
2021
![Publications Thumb 7](/media/dl2cs2kn/publications-thumb-7.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865741200000)
Publication
Community Detection in Electrical Grids Using Quantum Annealing
![Publications Thumb 9](/media/1p0apij1/publications-thumb-9.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865777000000)
Publication
Quantum Permutation Synchronization
![Publications Thumb 30](/media/5thdpugy/publications-thumb-30.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865805500000)
Publication
Multi-qubit Correction for Quantum Annealers
![Publications Thumb 29](/media/u0adpjmm/publications-thumb-29.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865782170000)
Publication
Computing Molecular Excited States on a D-Wave Quantum Annealer
![Publications Thumb 23](/media/fnmjmm12/publications-thumb-23.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865691170000)
Publication
Quantum Computing in Green Energy Production
![Publications Thumb 19](/media/anshe3ii/publications-thumb-19.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865743830000)
Publication
Two Quantum Ising Algorithms for the Shortest Vector Problem: One for Now and One for Later
2020
![Publications Thumb 31](/media/zn0nqx15/publications-thumb-31.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865724170000)
Publication
De-Signing Hamiltonians for Quantum Adiabatic Optimization
![Publications Thumb 20](/media/iitf2mpl/publications-thumb-20.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865687900000)
Publication
Coupler-Induced Errors for Flux-qubit Quantum Annealer: Measurements for One-Dimensional Ising Model with Twisted Boundary Fields
![Publications Thumb 1](/media/dwglqyit/publications-thumb-1.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865727000000)
Publication
Hybrid Quantum Annealing via Molecular Dynamics
![Publications Thumb 21](/media/pakkdhpf/publications-thumb-21.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865769730000)
Publication
Accuracy and Minor Embedding in Subqubo Decomposition with Fully Connected Large Problems
![Publications Thumb 12](/media/t4umjft4/publications-thumb-12.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865765100000)
Publication
Traffic Signal Optimization on a Square Lattice using the D-Wave Quantum Annealer
![Publications Thumb 14](/media/aznfzh40/publications-thumb-14.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865771030000)
Publication
Designing Metamaterials with Quantum Annealing and Factorization Machines
![Publications Thumb 30](/media/5thdpugy/publications-thumb-30.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865805500000)
Publication
Reinforcement Quantum Annealing: A Quantum-Assisted Learning Automata Approach
2019
![Publications Thumb 13](/media/ujpjr1iv/publications-thumb-13.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865823300000)
Publication
Unconventional Machine Learning of Genome-Wide Human Cancer Data
2018
![Publications Thumb 32](/media/jgyjsrxg/publications-thumb-32.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865707100000)
Publication