Related papers: Approximate low-weight check codes and circuit low…
Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale,…
We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…
Noise within solid-state systems at low temperatures, where many of the degrees of freedom of the host material are frozen out, can typically be traced back to material defects that support low-energy excitations. These defects can take a…
We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density…
For a weighted graph $G = (V, E, w)$ and a designated source vertex $s \in V$, a spanning tree that simultaneously approximates a shortest-path tree w.r.t. source $s$ and a minimum spanning tree is called a shallow-light tree (SLT).…
In this work we construct tests that allow a classical user to certify high dimensional entanglement in uncharacterized and possibly noisy quantum devices. We present a family of non-local games $\{G_n\}$ that for all $n$ certify states…
Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian…
$\mathsf{StoqMA}$ captures the computational hardness of approximating the ground energy of local Hamiltonians that do not suffer the so-called sign problem. We provide a novel connection between $\mathsf{StoqMA}$ and distribution testing…
Strong nonlocality, proposed by Halder {\it et al}. [\href{https://doi.org/10.1103/PhysRevLett.122.040403}{Phys. Rev. Lett. \textbf{122}, 040403 (2019)}], is a stronger manifestation than quantum nonlocality. Subsequently, Shi {\it et al}.…
A textbook chain of reasoning, originating with Girvin, MacDonald, and Platzman, predicts that Landau-level mixing (LLM) at nu=1/3 should soften the long-wavelength structure factor S(L): virtual excitations suppress V_1, the magnetoroton…
We continue a line of work on extracting random bits from weak sources that are generated by simple processes. We focus on the model of locally samplable sources, where each bit in the source depends on a small number of (hidden) uniformly…
Standard approaches to quantum statistical inference rely on measurements that induce a collapse of the wave function, effectively consuming the quantum state to extract information. In this work, we investigate the fundamental limits of…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
After a brief historical background on the $\Ls$, we revisit the 25 year old controversy on whether $\Ls$ is a $qqq$ (L=1) three quark state or a $\K$ quasi virtual bound state. This work is stimulated by the recent suggestion of Isgur that…
Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for…
We provide an $\Omega(log(n))$ lower bound for the depth of any quantum circuit generating the unique groundstate of Kitaev's spherical code. No circuit-depth lower bound was known before on this code in the general case where the gates can…
The Gilbert-Pollak Conjecture \citep{gilbert1968steiner}, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times…
The study of ground state energies of local Hamiltonians has played a fundamental role in quantum complexity theory. In this paper, we take a new direction by introducing the physically motivated notion of "ground state connectivity" of…
We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest…
Predictions for systems in entangled states cannot be described in local realistic terms. However, after admixing some noise such a description is possible. We show that for two quNits (quantum systems described by N dimensional Hilbert…