| NSF Org: |
PHY Division Of Physics |
| Recipient: |
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| Initial Amendment Date: | September 3, 2014 |
| Latest Amendment Date: | September 3, 2014 |
| Award Number: | 1416578 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Alexander Cronin
acronin@nsf.gov (703)292-5302 PHY Division Of Physics MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 15, 2014 |
| End Date: | November 30, 2018 (Estimated) |
| Total Intended Award Amount: | $285,000.00 |
| Total Awarded Amount to Date: | $285,000.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
200 UNIVERSTY OFC BUILDING RIVERSIDE CA US 92521-0001 (951)827-5535 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Department of Physics & Astronom Riverside CA US 92521-0001 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
OFFICE OF MULTIDISCIPLINARY AC, CONDENSED MATTER & MAT THEORY, QIS - Quantum Information Scie, Algorithmic Foundations |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
The main challenge for building a quantum computer is that quantum components are prone to error. Error correction can be used to overcome this challenge but it places stringent requirements on future quantum computer hardware. One promising method of quantum error correction is the so-called Quantum Low-Density-Parity-Check (LDPC) codes. If successful, using these codes a large quantum computer could in principle be built. Compared to other existing schemes, it would be much more efficient, requiring fewer redundant quantum bits, called qubits. Studying these codes will improve our understanding of the quantum theoretical problems related to quantum computation. This project will provide excellent opportunities for graduate students.
The award supports theoretical research on physics of non-local discrete and continuous statistical-mechanical models associated with quantum error correcting codes. An important feature of such codes is the existence of the decoding threshold, where a sufficiently large code can deal effectively with any noise level below the threshold, but not above it. Disordered spin models associated with decoding transition (these models have exact Wegner's self-duality), related models with large gauge groups associated with fault-tolerant decoding, as well as models with extensive ground state entropy, including U(1) gauge theories which generalize Wen's mutual Chern-Simons theory describing the ground state of Kitaev's toric code will be constructed and studied. Models associated with quantum LDPC codes are expected to be particularly interesting since their interaction terms involve a limited number of participating particles. The low-energy sectors of these models are expected to be dominated by non-trivial extended defects that generalize the notion of topological defects like domain walls, vortices, etc. New physics includes a phase transition driven by an extensive entropy of defect classes, coming from the exponentially large number of dimensions describing the original quantum code. Results will be relevant to several established fields of physics traditionally dealing with similar models: statistical mechanics of spin glasses, phase transition theory, etc., with potential applications extending to many other fields.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Scalable quantum computation requires quantum error correction (QEC)
or other method of coherence protection. The requirements to
implement QEC are stringent. Currently, our best hopes are associated
with the surface codes invented by Kitaev. These codes have the
weakest set of requirements (highest threshold), and a number of other
nice properties which make them easier to implement. One drawback of
the surface codes is their asymptotically zero rate: to work, they
require a large overhead in the number of qubits.
The focus of the conducted research was on quantum LDPC codes, so far
the only family of codes known to combine finite rates and non-zero
fault-tolerant thresholds to scalable quantum computation, and on
related statistical-mechanical models which characterize the
error-correcting properties of the codes. While in the case of
surface codes the related model is the well-studied square-lattice
random-bond Ising model, finite-rate codes lead to models that are
necessarily non-local. For example, hyperbolic codes produce models
on hyperbolic graphs; while these are locally planar, they cannot be
embedded in any finite-dimensional space without large distortions.
Compared to physical models local in D dimensions, we know relatively
little about non-local models. One exception is percolation
transition, which corresponds to the erasure channel (some known set
of qubits fail). Percolation theory (percolation on graphs) has
experienced a revival in recent years, as an important tool for
various network theory and big data applications.
The most important results include (i) a number of lower (existence)
and upper bounds for the decodable region of parameters and for the
phase transitions in associated models, (ii) detailed numerical
simulations of two families of quantum LDPC codes and related models,
(iii) a numerical algorithm for computing the distance of quantum and
classical LDPC codes, and (iv) a new algebraic construction for
finite-rate quantum LDPC codes with explicitly known distances.
Last Modified: 03/01/2019
Modified by: Leonid P Pryadko
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