Transversal Clifford gates on folded surface codes

Moussa, Jonathan E.

doi:10.1103/PhysRevA.94.042316

Title: Transversal Clifford gates on folded surface codes

Abstract

Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. Lastly, the specific application of these codes to universal quantum computation based on qubit fusion is also discussed.

Authors:

Moussa, Jonathan E. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Wed Oct 12 00:00:00 EDT 2016

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1333573

Alternate Identifier(s):: OSTI ID: 1328723

Report Number(s):: SAND-2016-2005J
Journal ID: ISSN 2469-9926; PLRAAN; 619860; TRN: US1700128

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review A

Additional Journal Information:: Journal Volume: 94; Journal Issue: 4; Journal ID: ISSN 2469-9926

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

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                    Moussa, Jonathan E. Transversal Clifford gates on folded surface codes.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevA.94.042316.

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                    Moussa, Jonathan E. Transversal Clifford gates on folded surface codes.  United States.  https://doi.org/10.1103/PhysRevA.94.042316

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                    Moussa, Jonathan E. Wed .  
"Transversal Clifford gates on folded surface codes".  United States.  https://doi.org/10.1103/PhysRevA.94.042316.  https://www.osti.gov/servlets/purl/1333573.

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@article{osti_1333573,

  title        = {Transversal Clifford gates on folded surface codes},

  author       = {Moussa, Jonathan E.},

  abstractNote = {Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. Lastly, the specific application of these codes to universal quantum computation based on qubit fusion is also discussed.},

  doi          = {10.1103/PhysRevA.94.042316},

  journal      = {Physical Review A},

  number       = 4,

  volume       = 94,

  place        = {United States},

  year         = {Wed Oct 12 00:00:00 EDT 2016},

  month        = {Wed Oct 12 00:00:00 EDT 2016}

}

Copy to clipboard

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Works referencing / citing this record:

Error rates and resource overheads of encoded three-qubit gates
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Takagi, Ryuji; Yoder, Theodore J.; Chuang, Isaac L.
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Title: Transversal Clifford gates on folded surface codes

Abstract

Citation Formats

Qudit color codes and gauge color codes in all spatial dimensions journal, August 2015

Quantum circuits of T -depth one journal, April 2013

Multilevel distillation of magic states for quantum computing journal, April 2013

Anyons in an exactly solved model and beyond journal, January 2006

Topological quantum memory journal, September 2002

Universal quantum computation with ideal Clifford gates and noisy ancillas journal, February 2005

Restrictions on Transversal Encoded Quantum Gate Sets journal, March 2009

Classification of Topologically Protected Gates for Local Stabilizer Codes journal, April 2013

Optimal resources for topological two-dimensional stabilizer codes: Comparative study journal, July 2007

Topological quantum error correction with optimal encoding rate journal, June 2006

Demonstration of a quantum error detection code using a square lattice of four superconducting qubits journal, April 2015

Magic-state distillation with low overhead journal, November 2012

Phase structure of the random-plaquette gauge model: accuracy threshold for a toric quantum memory journal, October 2004

Architecture for a large-scale ion-trap quantum computer journal, June 2002

Improved HDRG decoders for qudit and non-Abelian quantum error correction journal, March 2015

Topological Quantum Distillation journal, October 2006

An ideal characterization of the Clifford operators journal, July 2014

Theory of fault-tolerant quantum computation journal, January 1998

Quantum measurements and gates by code deformation journal, February 2009

Unfolding the color code journal, August 2015

Surface code quantum computing by lattice surgery journal, December 2012

Optimal and efficient decoding of concatenated quantum block codes journal, November 2006

Fault-tolerant quantum computation by anyons journal, January 2003

Surface code quantum computing with error rates over 1% journal, February 2011

Quantum computations on a topologically encoded qubit journal, June 2014

Fast fault-tolerant decoder for qubit and qudit surface codes journal, September 2015

Low-distance surface codes under realistic quantum noise journal, December 2014

Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes journal, December 2012

Surface codes: Towards practical large-scale quantum computation journal, September 2012

Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions journal, May 2007

Single-spin CCD journal, January 2016

Parafermions in a Kagome Lattice of Qubits for Topological Quantum Computation journal, December 2015

Layered Architecture for Quantum Computing journal, July 2012

The Quantum Double Model with Boundary: Condensations and Symmetries journal, June 2011

Full length article journal, October 1998

Inappropriate sinus tachycardia may be related to an immunologic disorder involving cardiac β andrenergic receptors journal, October 2006

Quantum Measurements and Gates by Code Deformation text, January 2007

Restrictions on Transversal Encoded Quantum Gate Sets text, January 2008

The Quantum Double Model with Boundary: Condensations and Symmetries text, January 2010

Surface code quantum computing by lattice surgery text, January 2011

Classification of topologically protected gates for local stabilizer codes text, January 2012

Magic state distillation with low overhead text, January 2012

Quantum circuits of T-depth one text, January 2012

Multilevel distillation of magic states for quantum computing text, January 2012

Low-distance Surface Codes under Realistic Quantum Noise text, January 2014

A fast fault-tolerant decoder for qubit and qudit surface codes text, January 2014

Parafermions in a Kagome lattice of qubits for topological quantum computation text, January 2015

Anyons in an exactly solved model and beyond text, January 2005

Universal Quantum Computation with ideal Clifford gates and noisy ancillas text, January 2004

Fault-tolerant quantum computation with high threshold in two dimensions text, January 2006

Fault-tolerant quantum computation by anyons text, January 1997

Error rates and resource overheads of encoded three-qubit gates journal, October 2017

The surface code with a twist journal, April 2017

The boundaries and twist defects of the color code and their applications to topological quantum computation journal, October 2018

Error rates and resource overheads of encoded three-qubit gates text, January 2017

The boundaries and twist defects of the color code and their applications to topological quantum computation text, January 2018

Qudit color codes and gauge color codes in all spatial dimensions
journal, August 2015

Quantum circuits of $T$ -depth one
journal, April 2013

Multilevel distillation of magic states for quantum computing
journal, April 2013

Anyons in an exactly solved model and beyond
journal, January 2006

Topological quantum memory
journal, September 2002

Universal quantum computation with ideal Clifford gates and noisy ancillas
journal, February 2005

Restrictions on Transversal Encoded Quantum Gate Sets
journal, March 2009

Classification of Topologically Protected Gates for Local Stabilizer Codes
journal, April 2013

Optimal resources for topological two-dimensional stabilizer codes: Comparative study
journal, July 2007

Topological quantum error correction with optimal encoding rate
journal, June 2006

Demonstration of a quantum error detection code using a square lattice of four superconducting qubits
journal, April 2015

Magic-state distillation with low overhead
journal, November 2012

Phase structure of the random-plaquette gauge model: accuracy threshold for a toric quantum memory
journal, October 2004

Architecture for a large-scale ion-trap quantum computer
journal, June 2002

Improved HDRG decoders for qudit and non-Abelian quantum error correction
journal, March 2015

Topological Quantum Distillation
journal, October 2006

An ideal characterization of the Clifford operators
journal, July 2014

Theory of fault-tolerant quantum computation
journal, January 1998

Quantum measurements and gates by code deformation
journal, February 2009

Unfolding the color code
journal, August 2015

Surface code quantum computing by lattice surgery
journal, December 2012

Optimal and efficient decoding of concatenated quantum block codes
journal, November 2006

Fault-tolerant quantum computation by anyons
journal, January 2003

Surface code quantum computing with error rates over 1%
journal, February 2011

Quantum computations on a topologically encoded qubit
journal, June 2014

Fast fault-tolerant decoder for qubit and qudit surface codes
journal, September 2015

Low-distance surface codes under realistic quantum noise
journal, December 2014

Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes
journal, December 2012

Surface codes: Towards practical large-scale quantum computation
journal, September 2012

Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions
journal, May 2007

Single-spin CCD
journal, January 2016

Parafermions in a Kagome Lattice of Qubits for Topological Quantum Computation
journal, December 2015

Layered Architecture for Quantum Computing
journal, July 2012

The Quantum Double Model with Boundary: Condensations and Symmetries
journal, June 2011

Full length article
journal, October 1998

Inappropriate sinus tachycardia may be related to an immunologic disorder involving cardiac β andrenergic receptors
journal, October 2006

Quantum Measurements and Gates by Code Deformation
text, January 2007

Restrictions on Transversal Encoded Quantum Gate Sets
text, January 2008

The Quantum Double Model with Boundary: Condensations and Symmetries
text, January 2010

Surface code quantum computing by lattice surgery
text, January 2011

Classification of topologically protected gates for local stabilizer codes
text, January 2012

Magic state distillation with low overhead
text, January 2012

Quantum circuits of T-depth one
text, January 2012

Multilevel distillation of magic states for quantum computing
text, January 2012

Low-distance Surface Codes under Realistic Quantum Noise
text, January 2014

A fast fault-tolerant decoder for qubit and qudit surface codes
text, January 2014

Parafermions in a Kagome lattice of qubits for topological quantum computation
text, January 2015

Anyons in an exactly solved model and beyond
text, January 2005

Universal Quantum Computation with ideal Clifford gates and noisy ancillas
text, January 2004

Fault-tolerant quantum computation with high threshold in two dimensions
text, January 2006

Fault-tolerant quantum computation by anyons
text, January 1997

Error rates and resource overheads of encoded three-qubit gates
journal, October 2017

The surface code with a twist
journal, April 2017

The boundaries and twist defects of the color code and their applications to topological quantum computation
journal, October 2018

Error rates and resource overheads of encoded three-qubit gates
text, January 2017

The boundaries and twist defects of the color code and their applications to topological quantum computation
text, January 2018