Related papers: Unfolding the Toric Code Model with Emergent Qubit…
We construct SU($N$) toric code model describing the dynamics of SU($N$) electric and magnetic fluxes on a two dimensional torus. We show that the model has $N^2$ topologically distinct ground states $|\psi_0\rangle_{({\mathsf p},{\mathsf…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits $n_q$, it is shown that the…
This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform…
It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary…
Topological phases of matter are considered the bedrock of novel quantum materials as well as ideal candidates for quantum computers that possess robustness at the physical level. The robustness of the topological phase at finite…
We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of…
Kitaev's toric code is an exactly solvable model with $\mathbb{Z}_2$-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge.…
The power of quantum random number generation is more than just the ability to create truly random numbers$\unicode{x2013}$it can also enable self-testing, which allows the user to verify the implementation integrity of certain critical…
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…
The execution of quantum circuits on real systems has largely been limited to those which are simply time-ordered sequences of unitary operations followed by a projective measurement. As hardware platforms for quantum computing continue to…
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
The first generations of quantum computers will execute fault-tolerant quantum circuits, and it is very likely that such circuits will use surface quantum error correcting codes. To the best of our knowledge, no complete design automation…
Using the framework of Tutte embeddings, we begin an exploration of \emph{quantum graph drawing}, which uses quantum computers to visualize graphs. The main contributions of this paper include formulating a model for quantum graph drawing,…
We present a theory of quantum circuits based on logical qubits encoded in chirality of electron spin complexes in lateral gated semiconductor triple quantum dot molecules with one electron spin in each dot. Using microscopic Hamiltonian we…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli…
We study the electronic structure of magnetic and non-magnetic quantum corrals embedded in s-wave superconductors. We demonstrate that a quantum mirage of an impurity bound state peak can be projected from the occupied into the empty focus…