Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near-and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better quantum advantage than for search. We uncover two general mechanisms that provide the quantum advantage: matching the driver Hamiltonian to the encoding in the problem Hamiltonian, and an energy redistribution principle that ensures a quantum walk will find a lower energy state in a short timescale. This makes it practical to use quantum walks for solving hard problems, and opens the door for a range of applications on suitable quantum hardware.
Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already been performed. In this perspective, we discuss in a very broad sense what it means for an algorithm to be hybrid quantum-classical. We first explore this concept very directly, by building a definition based on previous work in abstraction-representation theory, arguing that what makes an algorithm hybrid is not directly how it is run (or how many classical resources it consumes), but whether classical components are crucial to an underlying model of the computation. We then take a broader view of this question, reviewing a number of hybrid algorithms and discussing what makes them hybrid, as well as the history of how they emerged and considerations related to hardware. This leads into a natural discussion of what the future holds for these algorithms. To answer this question, we turn to the use of specialized processors in classical computing. The classical trend is not for new technology to completely replace the old, but to augment it. We argue that the evolution of quantum computing is unlikely to be different: Hybrid algorithms are likely here to stay well past the NISQ era and even into full fault tolerance, with the quantum processors augmenting the already powerful classical processors which exist by performing specialized tasks.
Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardized for the postquantum 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 2 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 shows that the more qubit-efficient variant will outperform in the long run, while the other variant is more suitable for near-term implementation.
Articles you may be interested inCross-nucleation between clathrate hydrate polymorphs: Assessing the role of stability, growth rate, and structure matching J. Chem. Phys. 140, 084506 (2014) We present results of computer simulations of homogeneous crystal nucleation in the Gaussian core model. In our simulations, we study the competition between the body-centered-cubic (bcc), face-centered-cubic (fcc), and hexagonal-close-packed crystal phases. We find that the crystal nuclei that form from the metastable fluid phase are typically "mixed"; they do not consist of a single crystal polymorph. Furthermore, when the fcc phase is stable or fcc and bcc phases are equally stable, this mixed nature is found to persist far beyond the size at the top of the nucleation barrier, that is, far into what would be considered the growth (rather than nucleation) regime. In this region, the polymorph that forms is therefore selected long after nucleation. This has implications. When nucleation is slow, it will be the rate-limiting step for crystallization. Then, the step that determines the time scale for crystallisation is different from the step that controls which polymorph forms. This means that they can be independently controlled. Also between nucleation and polymorph selection, there is a growing phase that is clearly crystalline not fluid, but this phase cannot be assigned to any one polymorph. C 2015 AIP Publishing LLC. [http://dx
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