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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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Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer
We present a new hybrid quantum algorithm to estimate molecular excited and charged states on near-term quantum computers following any VQE-based ground state estimation.
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- Award ID(s):
- 1839136
- PAR ID:
- 10475600
- Publisher / Repository:
- Chemical Science
- Date Published:
- Journal Name:
- Chemical Science
- Volume:
- 14
- Issue:
- 9
- ISSN:
- 2041-6520
- Page Range / eLocation ID:
- 2405 to 2418
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Quantum neuromorphic computing (QNC) is a sub-field of quantum machine learning (QML) that capitalizes on inherent system dynamics. As a result, QNC can run on contemporary, noisy quantum hardware and is poised to realize challenging algorithms in the near term. One key issue in QNC is the characterization of the requisite dynamics for ensuring expressive quantum neuromorphic computation. We address this issue by proposing a building block for QNC architectures, what we call quantum perceptrons (QPs). Our proposed QPs compute based on the analog dynamics of interacting qubits with tunable coupling constants. We show that QPs are, with restricted resources, a quantum equivalent to the classical perceptron, a simple mathematical model for a neuron that is the building block of various machine learning architectures. \framing{Moreover, we show that QPs are theoretically capable of producing any unitary operation.} Thus, QPs are computationally more expressive than their classical counterparts. As a result, QNC architectures built our of QPs are, theoretically, universal. We introduce a technique for mitigating barren plateaus in QPs called entanglement thinning. We demonstrate QPs' effectiveness by applying them to numerous QML problems, including calculating the inner products between quantum states, entanglement witnessing, and quantum metrology. Finally, we discuss potential implementations of QPs and how they can be used to build more complex QNC architectures.more » « less
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/d2sc05371c
