Related papers: Universality Classes of Stabilizer Code Hamiltonia…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum…
The investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some…
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Electric fields, applied to insulators, cause transitions between valence and conduction bands, giving rise to current. Adjustments of the Hamiltonian can perfect the quality of the insulator, shutting down transitions whilst fully…
Achieving noise resilience is an outstanding challenge in Hamiltonian-based quantum computation. To this end, energy-gap protection provides a promising approach, where the desired quantum dynamics are encoded into the ground space of a…
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this…
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 introduce a new class of generative quantum-neural-network-based models called Quantum Hamiltonian-Based Models (QHBMs). In doing so, we establish a paradigmatic approach for quantum-probabilistic hybrid variational learning, where we…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by…
Simulating non-equilibrium phenomena in strongly-interacting quantum many-body systems, including thermalization, is a promising application of near-term and future quantum computation. By performing experiments on a digital quantum…
We develop the strong coupling quantum thermodynamics based on the solution of the exact master equation. We find that both the Hamiltonian and the temperature must be renormalized due to the system-reservoir couplings. With the…
We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing…
For all of the interest in dynamical phase transitions (DPT), it is still not clear the meaning or prevalence of these features in higher dimensional models. In this paper, we consider DPTs for stabilizer code models and quantum quenches…