Related papers: Self-correction phase transition in the dissipativ…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
We investigate the steady-state phases of the one-dimensional quantum contact process model. We present the Liouvillian gap in the thermodynamic limit and uncover the metastability of the system. Exploiting the mean-field approximations…
We study the four-dimensional Z_2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs)…
We use the effective potential method of quantum field theory to obtain the quantum corrections to the zero temperature phase diagram of systems with competing order parameters. We are particularly interested in two different scenarios:…
We discuss and review several thermodynamic criteria that have been introduced to characterize the thermal stability of a self-correcting quantum memory. We first examine the use of symmetry-breaking fields in analyzing the properties of…
Lindbladian formalism, as tuned to dissipative and open systems, has been all-pervasive to interpret non-equilibrium steady states of quantum many-body systems. We study the fate of free fermionic and superconducting phases in a dissipative…
To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We describe a simple quantum error correcting code built out of a time-dependent transverse field Ising model. The code is similar to a repetition code, but has two advantages: an $N$-qubit code can be implemented with a finite-depth…
We present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act…
We propose and analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator, simplifying a previous proposal to alleviate implementation constraints. It approximately stabilizes periodic grid states…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
We develop a method to search for the optimal code space, induced decay rates and control Hamiltonian to implement autonomous quantum error correction (AQEC) for a general open quantum system. The system is defined by a free-evolution…
Open system quantum dynamics can generate a variety of long-range entangled mixed states, yet it has been unclear in what sense they constitute phases of matter. To establish that two mixed states are in the same phase, as defined by their…
Floquet code is a dynamical quantum memory with a periodically evolving logical space. As a defining feature, the code exhibits an anyon automorphism after each period, giving rise to a non-trivial evolution of each logical state. In this…
In this paper, we study an open quantum system consisting of a qubit coupled to a harmonic oscillator subject to two-photon relaxation and demonstrate that such a system can be utilized to construct a cat qubit capable of passive error…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations,…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…