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New Physics Sae Mulli

Quantum Measurement under the Conditions of an Adiabatic Process on a D-Wave Quantum Annealer

Hayun Park, Hunpyo Lee

Published Nov 30, 2023• 0 citations
Publisher
DOI
10.3938/npsm.73.978

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Abstract We solve the one-dimensional Helmholtz equation in several scenarios using the quantum annealer provided by D-Wave systems within a pseudospectral framework, where the solution is encoded in an appropriate set of basis functions. We evaluate the performance of different encoding strategies based on algebraic conditioning and adiabatic considerations, and benchmark their performance against the classical simulated annealing algorithm. In particular, we analyze the minimum energy gap, the so-called dynamic range, and the mean squared error to assess the numerical stability, consistency, and accuracy of the solutions returned by each strategy. Our work highlights the importance of developing custom embedding techniques ensuring well-conditioned algebraic systems. In particular, we show that encoding strategies producing full-rank matrices with reduced dynamic ranges enhance the performance of the quantum annealer even under polychromatic driving and nontrivial initial conditions. We further discuss the potential of developing hybrid quantum-classical schemes designed to simultaneously satisfy algebraic conditioning and adiabatic requirements.
In this chapter, we discuss the notion of a quantum simulator as a device that emulates a complex quantum many-body Hamiltonian, and a quantum annealer as an extension of such a paradigm that focuses on the preparation of the ground state in those Hamiltonians. Starting from the Landau–Zener processes and the adiabatic theorem, we illustrate how such ground states can be prepared by slow (adiabatic) deformations of a Hamiltonian. We discuss how this results in an adiabatic quantum computing algorithm and how, depending on the Hamiltonian we apply it to, we can solve problems of different classical and quantum complexity. The chapter closes with a thorough discussion of the D-Wave quantum annealer as a real-world superconducting quantum simulator of Ising-type models. This discussion centers both on the design of the superconducting annealers as well as on the conclusion from the literature on how this device works in practice, including how quantum operations are still possible even in the pressence of decoherence. We close the chapter with an outlook on the challenges that need to be overcome for making coherent quantum annealers and universal adiabatic quantum computers.
Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing such signals. Compressive sensing with matrix uncertainty is an extension of the standard compressive sensing problem that appears in various applications including but not limited to cognitive radio sensing, calibration of the antenna, and deconvolution. The original problem of compressive sensing is NP-hard so the traditional techniques, such as convex and nonconvex relaxations and greedy algorithms, apply stringent constraints on the measurement matrix to indirectly handle this problem in the realm of classical computing. We propose well-posed approaches for both binary compressive sensing and binary compressive sensing with matrix uncertainty problems that are tractable by quantum annealers. Our approach formulates an Ising model whose ground state represents a sparse solution for the binary compressive sensing problem and then employs an alternating minimization scheme to tackle the binary compressive sensing with matrix uncertainty problem. This setting only requires the solution uniqueness of the considered problem to have a successful recovery process, and therefore the required conditions on the measurement matrix are notably looser. As a proof of concept, we can demonstrate the applicability of the proposed approach on the D-Wave quantum annealers; however, we can adapt our method to employ other modern computing phenomena -like adiabatic quantum computers (in general), CMOS annealers, optical parametric oscillators, and neuromorphic computing.