scholarly journals Finding Hadamard Matrices by a Quantum Annealing Machine

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Andriyan Bayu Suksmono ◽  
Yuichiro Minato
Keyword(s):  
Quantum Computing ◽  
Simulated Annealing ◽  
Hadamard Matrix ◽  
Higher Order ◽  
Hard Problem ◽  
Quantum Annealing ◽  
Matrix Problem ◽  
Binary Vectors ◽  
Symbolic Computing ◽  
Binary Matrices

Abstract Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix problem and address its implementation limitation on existing quantum annealing machine (QAM) that allows up to quadratic terms, whereas the problem naturally introduces higher order ones. For an M-order H-matrix, such a limitation increases the number of variables from M2 to (M3 + M2 − M)/2, which makes the formulation of the Hamiltonian too exhaustive to do by hand. We use symbolic computing techniques to manage this problem. Three related cases are discussed: (1) finding N < M orthogonal binary vectors, (2) finding M-orthogonal binary vectors, which is equivalent to finding a H-matrix, and (3) finding N-deleted vectors of an M-order H-matrix. Solutions of the problems by a 2-body simulated annealing software and by an actual quantum annealing hardware are also discussed.

scholarly journals Quantum computing formulation of some classical Hadamard matrix searching methods and its implementation on a quantum computer

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Andriyan Bayu Suksmono ◽  
Yuichiro Minato
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Hadamard Matrix ◽  
Computing Methods ◽  
Previous Method ◽  
Mainframe Computer ◽  
Binary Matrices ◽  
Hard Problems ◽  
Classical Quantum ◽  
Near Future

AbstractFinding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order is a hard problem that can be solved by a quantum computer. Due to the limitation on the number of qubits and connections in current quantum processors, only low order H-matrix search of orders 2 and 4 were implementable by previous method. In this paper, we show that by adopting classical searching techniques of the H-matrices, we can formulate new quantum computing methods for finding higher order ones. We present some results of finding H-matrices of order up to more than one hundred and a prototypical experiment of the classical-quantum resource balancing method that yields a 92-order H-matrix previously found by Jet Propulsion Laboratory researchers in 1961 using a mainframe computer. Since the exactness of the solutions can be verified by an orthogonality test performed in polynomial time; which is untypical for optimization of hard problems, the proposed method can potentially be used for demonstrating practical quantum supremacy in the near future.

scholarly journals Benchmarking Quantum Annealing Against “Hard” Instances of the Bipartite Matching Problem

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Daniel Vert ◽  
Renaud Sirdey ◽  
Stéphane Louise
Keyword(s):  
Simulated Annealing ◽  
Polynomial Time ◽  
Optimal Solution ◽  
Quantum Computers ◽  
Quantum Annealing ◽  
Maximum Cardinality ◽  
Matching Problem ◽  
Bipartite Matching ◽  
Wave Device ◽  
D Wave

AbstractThis paper experimentally investigates the behavior of analog quantum computers as commercialized by D-Wave when confronted to instances of the maximum cardinality matching problem which is specifically designed to be hard to solve by means of simulated annealing. We benchmark a D-Wave “Washington” (2X) with 1098 operational qubits on various sizes of such instances and observe that for all but the most trivially small of these it fails to obtain an optimal solution. Thus, our results suggest that quantum annealing, at least as implemented in a D-Wave device, falls in the same pitfalls as simulated annealing and hence provides additional evidences suggesting that there exist polynomial-time problems that such a machine cannot solve efficiently to optimality. Additionally, we investigate the extent to which the qubits interconnection topologies explains these latter experimental results. In particular, we provide evidences that the sparsity of these topologies which, as such, lead to QUBO problems of artificially inflated sizes can partly explain the aforementioned disappointing observations. Therefore, this paper hints that denser interconnection topologies are necessary to unleash the potential of the quantum annealing approach.

scholarly journals Quantum annealing algorithms for track pattern recognition

2020 ◽  
Vol 245 ◽  
pp. 10006
Author(s):  
Masahiko Saito ◽  
Paolo Calafiura ◽  
Heather Gray ◽  
Wim Lavrijsen ◽  
Lucy Linder ◽  
...  
Keyword(s):  
Pattern Recognition ◽  
Simulated Annealing ◽  
Hadron Collider ◽  
Recognition Algorithm ◽  
Quantum Annealing ◽  
Discovery Potential ◽  
Energy Frontier ◽  
Track Pattern ◽  
Annealing Algorithms ◽  
D Wave

The High-Luminosity Large Hadron Collider (HL-LHC) starts from 2027 to extend the physics discovery potential at the energy frontier. The HL-LHC produces experimental data with a much higher luminosity, requiring a large amount of computing resources mainly due to the complexity of a track pattern recognition algorithm. Quantum annealing might be a solution for an efficient track pattern recognition in the HL-LHC environment. We demonstrated to perform the track pattern recognition by using the D-Wave annealing machine and the Fujitsu Digital Annealer. The tracking efficiency and purity for the D-Wave quantum annealer are comparable with those for a classical simulated annealing at a low pileup condition, while a drop in performance is found at a high pileup condition, corresponding to the HL-LHC pileup environment. The tracking efficiency and purity for the Fujitsu Digital Annealer are nearly the same as the classical simulated annealing.

scholarly journals Finding a Hadamard Matrix by Simulated Quantum Annealing

Entropy ◽  
2018 ◽  
Vol 20 (2) ◽  
pp. 141 ◽  
Author(s):  
Andriyan Suksmono
Keyword(s):  
Hadamard Matrix ◽  
Quantum Annealing

Explaining the “hard” problem

2019 ◽  
pp. 116-139
Author(s):  
Peter Carruthers
Keyword(s):  
Phenomenal Consciousness ◽  
Higher Order ◽  
Hard Problem ◽  
Explanatory Gap ◽  
Phenomenal Concepts ◽  
Reductive Explanation ◽  
David Chalmers ◽  
Global Workspace ◽  
The Hard Problem ◽  
Global Workspace Theory

This chapter shows that global-workspace theory can be developed into a satisfying, fully reductive explanation of phenomenal consciousness. It shows how globally broadcast nonconceptual content enables higher-order thoughts about that content, where those thoughts can lack conceptual connections with physical, functional, or representational facts. As a result, zombies are conceivable and an (epistemic) explanatory gap is opened up. But the thoughts in question can themselves be given a fully naturalistic explanation. Hence all of the facts involved in consciousness can be fully explained. The chapter defends the reality of the phenomenal concepts needed to make this account work, and replies to a dilemma for the account proposed by David Chalmers.

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