Related papers: New techniques for bounding stabilizer rank
In this paper, we study quotients of groupoids and coarse moduli spaces of stacks in a general setting. Geometric quotients are not always categorical, but we present a natural topological condition under which a geometric quotient is…
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…
Magic-state resource theory is a powerful tool with applications in quantum error correction, many-body physics, and classical simulation of quantum dynamics. Despite its broad scope, finding tractable resource monotones has been…
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond…
In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…
This paper provides a stabilizing preparation method for quantum Gaussian states by utilizing continuous measurement. The stochastic evolution of the open quantum system is described in terms of the quantum stochastic master equation. We…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian--Einstein metrics. Our main constructive step is by investigating the arithmetic property of the upper half plane in Bridgeland's…
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state…
Stabilizer states constitute a set of pure states which plays a dominant role in quantum error correction, measurement--based quantum computation, and quantum communication. Central in these applications are the local symmetries of these…
We give another proof, using tools from Geometric Invariant Theory, of a result due to S. Sam and A. Snowden in 2014, concerning the stability of Kro-necker coefficients. This result states that some sequences of Kronecker coefficients…
We establish a bulk--boundary correspondence for translation-invariant stabilizer states in arbitrary spatial dimension, formulated in the framework of modules over Laurent polynomial rings. To each stabilizer state restricted to half-space…
We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords…
We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy…
We apply the stabilizer method to the study of some complicated molecules, such as water and benzene. In the minimal STO-3G basis, the former requires 14 qubits, and the latter 72 qubits, which is very challenging. Quite remarkably, We are…
Vast developments in quantum technology have enabled the preparation of quantum states with more than a dozen entangled qubits. The full characterization of such systems demands distinct constructions depending on their specific type and…
The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…