Iris Cong

• Bachelor of Science
• PhD Student at Harvard University

This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform topologically protected operations on this encoding. In particular, we introduce a new and general computational prim...

This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We a...

We introduce and analyze a novel quantum machine learning model motivated by convolutional neural networks (CNN). Our quantum convolutional neural network (QCNN) makes use of only $O(\log(N))$ variational parameters for input sizes of $N$ qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices. We show...

Defects between gapped boundaries provide a possible physical realization of projective non-abelian braid statistics. A notable example is the projective Majorana/parafermion braid statistics of boundary defects in fractional quantum Hall/topological insulator and superconductor heterostructures. In this paper, we develop general theories to analyz...

We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev’s quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped bound...

Dynamical decoupling and Hamiltonian engineering are well-established techniques that have been used to control qubit systems. However, designing the corresponding methods for qudit systems has been challenging due to the lack of a Bloch sphere representation, more complex interactions, and additional control constraints. By identifying several gen...

The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computat...

Suppressing errors is the central challenge for useful quantum computing¹, requiring quantum error correction (QEC)2–6 for large-scale processing. However, the overhead in the realization of error-corrected ‘logical’ qubits, in which information is encoded across many physical qubits for redundancy2–4, poses substantial challenges to large-scale lo...

We develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Specifically, we present a geometric formalism that significantly simplifies qudit pulse sequence design, while incorporating the necessary robustness conditions. We experimentally demonstrate these techniques in a strongly-...

The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computat...

By leveraging shared entanglement between a pair of qubits, one can teleport a quantum state from one particle to another. Recent advances have uncovered an intrinsically many-body generalization of quantum teleportation, with an elegant and surprising connection to gravity. In particular, the teleportation of quantum information relies on many-bod...

Neutral-atom arrays have recently emerged as a promising platform for quantum information processing. One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations. To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could dec...

Neutral atom arrays have recently emerged as a promising platform for quantum information processing. One important remaining roadblock for large-scale quantum information processing in such systems is associated with the finite lifetime of atomic Rydberg states during entangling operations. Because such Rydberg state decay errors can result in man...

By leveraging shared entanglement between a pair of qubits, one can teleport a quantum state from one particle to another. Recent advances have uncovered an intrinsically many-body generalization of quantum teleportation, with an elegant and surprising connection to gravity. In particular, the teleportation of quantum information relies on many-bod...

Neural network-based machine learning has recently proven successful for many complex applications ranging from image recognition to precision medicine. However, its direct application to problems in quantum physics is challenging due to the exponential complexity of many-body systems. Motivated by recent advances in realizing quantum information p...

There were two errors in the original publication. First, the term BK in Eq. (2.20) was not well-defined in the case of non-normal subgroups K.

We survey some recent work on topological quantum computation with gapped boundaries and boundary defects and list some open problems.

This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform topologically protected operations on this encoding. In particular, we introduce a new and general computational prim...

We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped bound...

Defects between gapped boundaries provide a possible physical realization of projective non-abelian braid statistics. A notable example is the projective Majorana/parafermion braid statistics of boundary defects in fractional quantum Hall/topological insulator and superconductor heterostructures. In this paper, we develop general theories to analyz...

We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms show an exponential speedup in both the number of training vectors $M$ and the feature space dimension $N$. W...

We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms show an exponential speedup in both the number of training vectors $M$ and the feature space dimension $N$. W...