Bei Zeng

Remote-state preparation in higher dimension and the parallelizable manifold Sn-1

This paper proves that the remote-state preparation (RSP) scheme in real Hilbert space can only be implemented when the dimension of the space is 2, 4, or 8. This fact is shown to be related to the parallelizability of the (n-1)-dimensional sphere Sn-1. When the dimension is 4 and 8 the generalized scheme is explicitly presented. It is also shown that for a given state with components having the same norm, RSP can be generalized to arbitrary dimension case.

Codeword Stabilized Quantum Codes

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.

Entanglement in a two-identical-particle system

The definition of entanglement in identical-particle system is introduced. The separability criterion in two-identical-particle system is given. The physical meaning of the definition is analyzed. Applications to two-boson and two-fermion systems are made. It is found that some different entanglement and correlation phenomena in identical-boson systems exist, and they may have applications in the field of quantum information.

Transversality Versus Universality for Additive Quantum Codes

Logic gates can be performed on data encoded in quantum code blocks such that errors introduced by faulty gates can be corrected. The important class of transversal gates acts bitwise between corresponding qubits of code blocks and thus limits error propagation. If any quantum gate could be implemented using transversal gates, the set would be universal. We study the structure of GF(4)-additive quantum codes and prove that no universal set of transversal logic gates exists for these codes. This result is in stark contrast with the classical case, where universal transversal gate sets exist, and strongly supports the idea that additional quantum techniques, based, for example, on quantum teleportation or magic state distillation, are necessary to achieve universal fault-tolerant quantum computation on additive codes.

Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator

The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems. It not only plays a key role in investigating the holographic duality between a strongly interacting quantum system and a gravitational system, but also diagnoses the chaotic behavior of many-body quantum systems and characterizes the information scrambling. Based on the OTOCs, three different concepts -- quantum chaos, holographic duality, and information scrambling -- are found to be intimately related to each other. Despite of its theoretical importance, the experimental measurement of the OTOC is quite challenging and so far there is no experimental measurement of the OTOC for local operators. Here we report the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator. We observe that the OTOC behaves differently in the integrable and non-integrable cases. Based on the recent discovered relationship between OTOCs and the growth of entanglement entropy in the many-body system, we extract the entanglement entropy from the measured OTOCs, which clearly shows that the information entropy oscillates in time for integrable models and scrambles for non-intgrable models. With the measured OTOCs, we also obtain the experimental result of the butterfly velocity, which measures the speed of correlation propagation. Our experiment paves a way for experimentally studying quantum chaos, holographic duality, and information scrambling in many-body quantum systems with quantum simulators.

Gapped Two-Body Hamiltonian Whose Unique Ground State Is Universal for One-Way Quantum Computation

Many-body entangled quantum states studied in condensed matter physics can be primary resources for quantum information, allowing any quantum computation to be realized using measurements alone, on the state. Such a universal state would be remarkably valuable, if only it were thermodynamically stable and experimentally accessible, by virtue of being the unique ground state of a physically reasonable Hamiltonian made of two-body, nearest-neighbor interactions. We introduce such a state, composed of six-state particles on a hexagonal lattice, and describe a general method for analyzing its properties based on its projected entangled pair state representation.

Uniqueness of quantum states compatible with given measurement results

We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a

Graph Concatenation for Quantum Codes

d

Optical one-way quantum computing with a simulated valence-bond solid

-dimensional Hilbert space, there exists a set of

Codeword stabilized quantum codes

4d\ensuremath{-}5