Toward Practical-Scale Quantum Annealing Machine for Prime Factoring

Abstract

We propose a prime factorizer operated in a frame work of quantum annealing (QA). The idea is inverse operation of a multiplier implemented with QA-based Boolean logic circuits. We designed the QA machine on an application-specific-annealing-computing architecture which efficiently increases available hardware budgets at the cost of restricted functionality. The invertible operation of QA logic gates consisting of superconducting flux qubits was confirmed by circuit simulation with classical noise sources. The circuits were implemented and fabricated by using superconducting integrated circuit technologies with Nb/AlO x /Nb Josephson junctions. We also propose a 2.5-dimensional packaging scheme of a qubit-chip / interposer / package-substrate structure for realizing practically large-scale QA systems.

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

“…Recently, proposals have also been made for efficient input formats to Ising machines based on the operation principle of Ising machines [29]. Examples include simulated annealing (SA)-based machines [13]- [17], quantum annealing ma-chines [18]- [20], and photonics-based machines [21]- [24]. The features of the various Ising machines are summarized in [30].…”

“…The same trends are observed for all other values n and c for both types of encoding. Moreover, the values of A necessary to obtain a high FS rate are smaller for unary encoding than binary encoding, except for (n, c) = (20,30). For the problem with (n, c) = (800, 1200), the FS rate approaches 1 around A = 1.6 × 10 3 in binary encoding [Fig.…”

How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins

“…As another type of an annealing machine, quantum annealing machine for prime factoring has been developed [4], [5]. The quantum annealing machine employs an application-specific annealing computing (ASAC) architecture to reduce the hardware overhead and the cost and time for development.…”

“…In general, obtaining an optimal solution from these problems using von Neumann computers may be challenging since these problems have many solutions, including optimal ones and not optimal ones. Non-von Neumann computers called Annealing machines have been developed to challenge these problems, such as quantum annealing machines [1], [2], [3], [4], [5], CMOS Annealing machines [6], [7], [8], Digital Annealers [9], [10], coherent Ising machines [11], [12], and Simulated Bifurcation machine [13].…”

A Fully-Connected Ising Model Embedding Method and Its Evaluation for CMOS Annealing Machines

“…When these problems have a large solution space, solving them just using von Neumann computers may become very difficult. Nonvon Neumann computers, such as CMOS annealing machines [1], [2], Digital Annealer [3], [4], quantum annealing machines [5]- [8], and coherent Ising machines [9], [10], have been developed to tackle these problems.…”