Research Statement
Quantum communication and computation offer the possibility of secure and high rate information transmission, fast computational solution of certain important problems, and efficient physical simulation of quantum phenomena at the heart of modern information technology. However, faithful transmission of quantum information and successful realization of quantum computers rely upon the identification of suitable error-correcting codes to make such processes and machines robust against faults due to decoherence,
ubiquitous in quantum systems. This quest involves a combination of knowledge from physics, mathematics, information theory, and computer science, because new kinds of non-classical errors arise.
My research strives to bring us closer to the goal of reliable transmission and processing of quantum information. From the theoretical point of view, I am seeking to construct a broad theory for building a large class of quantum error-correcting codes, particularly aiming at overcoming the barrier of non-classical errors to link quantum
coding theory to topics that have been studied or are now actively being studied in classical coding theory, so that some mature methods and tools used in the classical coding theory can be applied for helping with the understanding of quantum communication and computation. From the practical point of view, my focus is on the design of quantum error-correcting codes with nice properties which in different cases make them suitable
for high rate quantum information transmission through practical physical channels, and reliable quantum computation with high noise tolerance and low resource requirement. I will also apply these novel quantum error-correcting codes to the study of different models of quantum computation, particularly the one-way quantum computation model, the teleportation-based quantum computation model and the topological quantum computation model. These models other than the circuit model provide alternative approaches for building large-scale quantum computers in practice.
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Publications
Quantum state reduction for universal measurement based computation
X. Chen, R. Duan, Z. Ji, B. Zeng
Physical Review Letters 105, No. 2, 020502 (2010)
Optical one-way quantum computing with a simulated valence-bond solid
R. Kaltenbaek, J. Lavoie, B. Zeng, S.D. Bartlett
Nature Physics 6, 850-854 (2010)
Tensor product representation of a topological ordered phase: Necessary symmetry conditions
X. Chen, B. Zeng, Z.-C. Gu, I.L. Chuang, X.-G. Wen
Physical Review B 82, 165119 (2010)
Multi-Error-Correcting Amplitude Damping Codes
R. Duan, M. Grassl, Z. Ji, B. Zeng
Proceedings of 2010 IEEE International Symposium on Information Theory, (2010)
Gapped two-body Hamiltonian whose unique ground state is universal for one-way quantum computation
X. Chen, B. Zeng, Z.-C. Gu, B. Yoshida, I.L. Chuang
Physical Review Letters 102, No. 22, 220501 (2009)
Generalized concatenated quantum codes
M. Grassl, P. Shor, G. Smith, J. Smolin, B. Zeng
Physical Review A 79, No. 5, 050306(R) (2009)
Codeword stabilized quantum codes: Algorithm & Structure
I.L. Chuang, A.W. Cross, G. Smith, J. Smolin, B. Zeng
Journal of Mathematical Physics 50, No. 4, 042109 (2009)
Generalized concatenation for quantum codes
M. Grassl, P. Shor, B. Zeng
Proceedings of 2009 IEEE International Symposium on Information Theory, (2009)
Nonbinary codeword stabilized quantum codes
X. Chen, B. Zeng, I.L. Chuang
Physical Review A 78, No. 6, 062315 (2008)
Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit
X. Chen, H. Chung, A.W. Cross, B. Zeng, I.L. Chuang
Physical Review A 78, No. 1, 012353 (2008)
Semi-Clifford operations, structure of Ck hierarchy and gate complexity for fault-tolerant quantum computation
B. Zeng, X. Chen, I.L. Chuang
Physical Review A 77, No. 4, 042313 (2008)
Local unitary versus local Clifford equivalence of stabilizer and graph states
B. Zeng, H. Chung, A.W. Cross, I.L. Chuang
Physical Review A 75, No. 3, 032325 (2007)
Multiparty correlation measure based on the cumulant
D.L. Zhou, B. Zeng, Z. Xu, L. You
Physical Review A 74, No. 5, 052110 (2006)
Quantum information cannot be split into complementary parts
D.L. Zhou, B. Zeng, L. You
Physics Letters A 352, 41-44 (2006)
N-qubit entanglement via the Jy2-type collective interaction
D.L. Zhou, B. Zeng, J.S. Tang, Z. Xu, L. You
Physics Letters A 345, 38-44 (2005)
Measuring the parity of an n-qubit state
B. Zeng, D.L. Zhou, L. You
Physical Review Letters 95, No. 11, 110502 (2005)
Entanglement and spin-squeezing properties for three bosons in two modes
B. Zeng, D.L. Zhou, Z. Xu, L. You
Physical Review A 71, No. 4, 042317 (2005)
Encoding a logical qubit into physical qubits
B. Zeng, D.L. Zhou, Z. Xu, C.P. Sun, L. You
Physical Review A 71, No. 2, 022309 (2005)
Quantum computation based on d-level cluster states
D.L. Zhou, B. Zeng, Z. Xu, C.P. Sun
Physical Review A 68, No. 6, 062303 (2003)
Criterion for testing multiparticle negative-partial-transpose entanglement
B. Zeng, D.L. Zhou, P. Zhang, Z. Xu, L. You
Physical Review A 68, No. 4, 042316 (2003)
High-dimensional multi-particle cat-like state teleportation
B. Zeng, X.S. Liu, Y.S. Li, G.L. Long
Communications in Theoretical Physics 38, No. 5, 537 (2002)
Entanglement properties of some fractional quantum Hall liquids
Physical Review A 66, No. 4, 042324 (2002)
Closure of orbits and dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator
Journal of Mathematical Physics 43, 897-903 (2002)
Remote-state preparation in higher dimension and the parallelizable manifold Sn-1
Physical Review A 65, No. 2, 022316 (2002)
Entanglement in a two-identical-particle system
Y.S. Li, B. Zeng, X.S. Liu, G.L. Long
Physical Review A 64, No. 5, 054302 (2001)
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