Quantum control for time-dependent noise

Kabytayev, Chingiz

Title:

Quantum control for time-dependent noise

dc.contributor.advisor	Brown, Kenneth R.
dc.contributor.advisor	Orlando, Thomas M.
dc.contributor.author	Kabytayev, Chingiz
dc.contributor.committeeMember	Chapman, Michael S.
dc.contributor.committeeMember	Kennedy, Brian T. A.
dc.contributor.committeeMember	Pustilnik, Michael
dc.contributor.department	Physics
dc.date.accessioned	2016-08-22T12:19:54Z
dc.date.available	2016-08-22T12:19:54Z
dc.date.created	2015-08
dc.date.issued	2015-05-15
dc.date.submitted	August 2015
dc.date.updated	2016-08-22T12:19:54Z
dc.description.abstract	The main obstacles to implementing ideal quantum operations are unwanted interactions of quantum systems with the environment and noise in control fields. This problem can be tackled by methods of quantum control. Among these methods are composite pulse (CP) sequences which have long been employed in nuclear magnetic resonance (NMR) to mitigate the effects of systematic errors in the control. CP sequences have been initially developed to correct for static but otherwise unknown errors in the amplitude or frequency of the driving field. One of the challenges to the systematic incorporation of these control protocols into practical quantum information systems remains the limited understanding of CP performance in the presence of time-dependent noise. Treating the influence of time-dependent noise processes on quantum control operations has been facilitated by recent advances in dynamical error suppression based on open-loop Hamiltonian engineering. These approaches provide a general framework for understanding and mitigating non-Markovian time- dependent noise in a finite-dimensional open quantum system. Particularly, arbitrary single-qubit control characteristics may be captured quantitatively in filter-transfer functions (FF) using methods of spectral overlap in the frequency domain. In this thesis work, we present a systematic study of control pulse sequences in the presence of time-dependent noise. We use a combination of analytic formulations based on FFs and numerical simulations to demonstrate that CPs are able to effectively suppress control errors caused by time-dependent processes possessing realistic noise power spectra. We provide a geometric interpretation of CP performance under time-dependent amplitude noise, further linking the FF formalism with known techniques in CP construction. We also develop new optimized pulse sequences that act as notch filters for time-dependent noise. These high-fidelity control protocols effectively sup- press errors from the noise sources with sharp features in spectral densities and can be used practically on various quantum architectures. We also present our work on simulation of randomized benchmarking protocols and CPs that have been used experimentally by our collaborators to measure gate errors.
dc.description.degree	Ph.D.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1853/55497
dc.language.iso	en_US
dc.publisher	Georgia Institute of Technology
dc.subject	Quantum control
dc.subject	Time-dependent noise
dc.subject	Quantum information
dc.subject	Quantum computing
dc.subject	Filter-transfer functions
dc.subject	Composite pulses
dc.subject	Optimal control
dc.title	Quantum control for time-dependent noise
dc.type	Text
dc.type.genre	Dissertation
dspace.entity.type	Publication
local.contributor.advisor	Orlando, Thomas M.
local.contributor.advisor	Brown, Kenneth R.
local.contributor.corporatename	College of Sciences
local.contributor.corporatename	School of Physics
relation.isAdvisorOfPublication	fa8c3886-9348-4bc0-ba36-27aa4f9296f6
relation.isAdvisorOfPublication	f47855b9-eee7-44e0-8a7b-fd2c17563fc1
relation.isOrgUnitOfPublication	85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication	2ba39017-11f1-40f4-9bc5-66f17b8f1539
thesis.degree.level	Doctoral