66 research outputs found
Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analogue of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit
Modes of Foreign Entry under Asymmetric Information about Potential Technology Spillovers
This paper studies the effect of technology spillovers on the entry decision of a multinational enterprise into a foreign market. Two alternative entry modes for a foreign direct investment are considered: Greenfield investment versus acquisition. We find that with quantity competition a spillover makes acquisitions less attractive, while with price competition acquisitions become more attractive. Asymmetric information about potential spillovers always reduces the number of
acquisitions independently of whether the host country or the entrant has private information. Interestingly, we find that asymmetric information always hurts the entrant, while it sometimes is in favor of the host country
Correct quantum chemistry in a minimal basis from effective Hamiltonians
We describe how to create ab-initio effective Hamiltonians that qualitatively
describe correct chemistry even when used with a minimal basis. The
Hamiltonians are obtained by folding correlation down from a large parent basis
into a small, or minimal, target basis, using the machinery of canonical
transformations. We demonstrate the quality of these effective Hamiltonians to
correctly capture a wide range of excited states in water, nitrogen, and
ethylene, and to describe ground and excited state bond-breaking in nitrogen
and the chromium dimer, all in small or minimal basis sets
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