Approximating ground and excited state energies on a quantum computer

Approximating ground and excited state energies on a quantum computer Approximating ground and a fixed number of excited state energies, or equivalently low-order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows exponentially with the number of degrees of freedom. Under general conditions, and using a perturbation approach, we provide a quantum algorithm that produces estimates of a constant number $$j$$ j of different low-order eigenvalues. The algorithm relies on a set of trial eigenvectors, whose construction depends on the particular Hamiltonian properties. We illustrate our results by considering a special case of the time-independent Schrödinger equation with $$d$$ d degrees of freedom. Our algorithm computes estimates of a constant number $$j$$ j of different low-order eigenvalues with error $$O(\varepsilon )$$ O ( ε ) and success probability at least $$\frac{3}{4}$$ 3 4 , with cost polynomial in $$\frac{1}{\varepsilon }$$ 1 ε and $$d$$ d . This extends our earlier results on algorithms for estimating the ground state energy. The technique we present is sufficiently general to apply to problems beyond the application studied in this paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Approximating ground and excited state energies on a quantum computer

Loading next page...
 
/lp/springer_journal/approximating-ground-and-excited-state-energies-on-a-quantum-computer-HpIBbT7bWq
Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-0927-y
Publisher site
See Article on Publisher Site

Abstract

Approximating ground and a fixed number of excited state energies, or equivalently low-order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows exponentially with the number of degrees of freedom. Under general conditions, and using a perturbation approach, we provide a quantum algorithm that produces estimates of a constant number $$j$$ j of different low-order eigenvalues. The algorithm relies on a set of trial eigenvectors, whose construction depends on the particular Hamiltonian properties. We illustrate our results by considering a special case of the time-independent Schrödinger equation with $$d$$ d degrees of freedom. Our algorithm computes estimates of a constant number $$j$$ j of different low-order eigenvalues with error $$O(\varepsilon )$$ O ( ε ) and success probability at least $$\frac{3}{4}$$ 3 4 , with cost polynomial in $$\frac{1}{\varepsilon }$$ 1 ε and $$d$$ d . This extends our earlier results on algorithms for estimating the ground state energy. The technique we present is sufficiently general to apply to problems beyond the application studied in this paper.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 28, 2015

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off