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Quantum machine learning algorithms promise to deliver near-term, applicable quantum computation on noisy, intermediate-scale systems. While most of these algorithms leverage quantum circuits for generic applications, a recent set of proposals, called analog quantum machine learning (AQML) algorithms, breaks away from circuit-based abstractions and favors leveraging the natural dynamics of quantum systems for computation, promising to be noise-resilient and suited for specific applications such as quantum simulation. Recent AQML studies have called for determining best ansatz selection practices and whether AQML algorithms have trap-free landscapes based on theory from quantum optimal control (QOC). We address this call by systematically studying AQML landscapes on two models: those admitting black-boxed expressivity and those tailored to simulating a specific unitary evolution. Numerically, the first kind exhibits local traps in their landscapes, while the second kind is trap-free. However, both kinds violate QOC theory’s key assumptions for guaranteeing trap-free landscapes. We propose a methodology to co-design AQML algorithms for unitary evolution simulation using the ansatz’s Magnus expansion. Our methodology guarantees the algorithm has an amenable dynamical Lie algebra with independently tunable terms. We show favorable convergence in simulating dynamics with applications to metrology and quantum chemistry. We conclude that such co-design is necessary to ensure the applicability of AQML algorithms.
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A quantum algorithm for evolving open quantum dynamics on quantum computing devices
Abstract Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.
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- Award ID(s):
- 1839191
- PAR ID:
- 10154069
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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