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We present rigorous bounds on the thermalization time of the family of quantum mechanical spin systems known as stabilizer Hamiltonians. The thermalizing dynamics are modeled by a Davies master equation that arises from a weak local…
In this paper, we explicitly construct (Abelian) anyonic excitations of arbitrary stabilizer Hamiltonians which are local on a 2D lattice of qubits. This leads directly to the conclusion that, in the presence of local thermal noise, such…
We explore feasibility of a quantum self-correcting memory based on 3D spin Hamiltonians with topological quantum order in which thermal diffusion of topological defects is suppressed by macroscopic energy barriers. To this end we…
We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group $\mathbb{Z}_d$. We have made the concept of the energy barrier therein mathematically well-defined, it is related to the minimum…
We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of $N$-qubits, serve as one of the…
We introduce a new primitive, called welding, for combining two stabilizer codes to produce a new stabilizer code. We apply welding to construct surface codes and then use the surface codes to construct solid codes, a variant of a 3-d toric…
We return to the question of how the choice of stabilizer generators affects the preservation of information on structures whose degenerate ground state encodes a classical redundancy code. Controlled-not gates are used to transform the…
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…
We investigate layer codes, a family of three-dimensional stabilizer codes that can achieve optimal scaling of code parameters and a polynomial energy barrier, as candidates for self-correcting quantum memories. First, we introduce two…
The storage of large-scale quantum information at finite temperature requires an autonomous and reliable quantum hard drive, also known as a self-correcting quantum memory. It is a long-standing open problem to find a self-correcting…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
The long-time dynamics of quantum systems, typically, but not always, results in a thermal steady state. The microscopic processes that lead to or circumvent this fate are of interest, since everyday experience tells us that not all spatial…
Understanding how microscopic few-body interactions give rise to thermal behavior in isolated quantum many-body systems remains a central challenge in nonequilibrium statistical mechanics. While individual energy eigenstates are expected to…
We present an error correcting protocol that enhances the lifetime of stabilizer code based qubits which are susceptible to the creation of pairs of localized defects (due to string-like error operators) at finite temperature, such as the…
Efficiency of a Brownian particle moving along the axis of a three-dimensional asymmetric periodic channel is investigated in the presence of a symmetric unbiased force and a load. Reduction of the spatial dimensionality from two or three…
Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent…
We discuss energy barriers and their relationship to self-correcting quantum memories. We introduce the solid code, a 3-d version of Kitaev's surface code, and then combine several solid codes using a technique called welding. The resulting…
In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent…
Landauer's principle laid the main foundation for the development of modern thermodynamics of information. However, in its original inception the principle relies on semiformal arguments and dissipative dynamics. Hence, if and how…
Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as…