Computationally Universal Phase of Quantum Matter.

We provide the first example of a symmetry protected quantum phase that has universal computational power. This two-dimensional phase is protected by one-dimensional linelike symmetries that can be understood in terms of the local symmetries of a tensor network. These local symmetries imply that every ground state in the phase is a universal resource for measurement-based quantum computation.

[1]  Yao Sun,et al.  Recent advances in near-infrared II fluorophores for multifunctional biomedical imaging , 2018, Chemical science.

[2]  Tzu-Chieh Wei,et al.  Universal quantum computing using (Z d ) 3 symmetry-protected topologically ordered states , 2017, 1711.00094.

[3]  Ching-Yu Huang,et al.  Universal measurement-based quantum computation in two-dimensional symmetry-protected topological phases , 2017, 1705.06833.

[4]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[5]  Xie Chen,et al.  Quantum circuit complexity of one-dimensional topological phases , 2014, 1401.3820.

[6]  Stephen D. Bartlett,et al.  Symmetry protection of measurement-based quantum computation in ground states , 2012, 1207.4805.

[7]  J. Zittartz,et al.  Quantum phase transition in spin-3/2 systems on the hexagonal lattice — optimum ground state approach , 1997 .

[8]  Y. Tschinkel,et al.  Algebra, Geometry, and Physics in the 21st Century , 2017 .

[9]  Xiao-Gang Wen,et al.  Symmetry protected topological orders and the group cohomology of their symmetry group , 2011, 1106.4772.

[10]  Tzu-Chieh Wei,et al.  Computational Power of Symmetry-Protected Topological Phases. , 2016, Physical review letters.

[11]  D. Gross,et al.  Novel schemes for measurement-based quantum computation. , 2006, Physical review letters.

[12]  F. Verstraete,et al.  Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , 2008, 0907.2796.

[13]  Frank Verstraete,et al.  Matrix product state representations , 2006, Quantum Inf. Comput..

[14]  Akimasa Miyake,et al.  Quantum computation on the edge of a symmetry-protected topological order. , 2010, Physical review letters.

[15]  Akimasa Miyake,et al.  Resource quality of a symmetry-protected topologically ordered phase for quantum computation. , 2014, Physical review letters.

[16]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[17]  Akimasa Miyake,et al.  Hierarchy of universal entanglement in 2D measurement-based quantum computation , 2015, npj Quantum Information.

[18]  Tzu-Chieh Wei,et al.  Symmetry-protected topological phases with uniform computational power in one dimension , 2016, 1609.07549.

[19]  Andrew S. Darmawan,et al.  Measurement-based quantum computation in a two-dimensional phase of matter , 2011, 1108.4741.

[20]  T. Wei,et al.  Emergence of XY-like phase in deformed spin- 3 2 AKLT systems , 2016, 1605.08417.

[21]  Stephen D Bartlett,et al.  Identifying phases of quantum many-body systems that are universal for quantum computation. , 2008, Physical review letters.

[22]  Robert Raussendorf.  Quantum computation via translation-invariant operations on a chain of qubits , 2005 .

[23]  Stephen D Bartlett,et al.  Symmetry-protected phases for measurement-based quantum computation. , 2012, Physical review letters.

[24]  Akimasa Miyake,et al.  Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry. , 2018, Physical review letters.

[25]  David Perez-Garcia,et al.  Matrix product unitaries: structure, symmetries, and topological invariants , 2017, 1703.09188.

[26]  Xiao-Gang Wen,et al.  Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order , 2010, 1004.3835.

[27]  Tommaso F. Demarie,et al.  Universality of quantum computation with cluster states and (X, Y)-plane measurements , 2016, Scientific Reports.

[28]  D. Gross,et al.  Index Theory of One Dimensional Quantum Walks and Cellular Automata , 2009, 0910.3675.

[29]  Xiao-Gang Wen,et al.  Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order , 2009, 0903.1069.

[30]  Stephen D. Bartlett,et al.  Symmetry-protected topological order at nonzero temperature , 2016, 1611.05450.

[31]  A. H. Werner,et al.  The Topological Classification of One-Dimensional Symmetric Quantum Walks , 2016, Annales Henri Poincaré.

[32]  Beni Yoshida,et al.  Topological phases with generalized global symmetries , 2015, 1508.03468.

[33]  Tzu-Chieh Wei,et al.  Symmetry-protected topologically ordered states for universal quantum computation , 2015, 1509.02947.