Related papers: Approximate low-weight check codes and circuit low…
Understanding entanglement cost in non-local quantum computation (NLQC) is relevant to complexity, cryptography, gravity, and other areas. This entanglement cost is largely uncharacterized; previous lower bound techniques apply to narrowly…
Quantum error mitigation (QEM) has emerged as a powerful tool for the extraction of useful quantum information from quantum devices. Here, we introduce the Subspace Noise Tailoring (SNT) algorithm, which efficiently combines the cheap cost…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a…
There is a growing body of work on proving hardness results for average-case estimation problems by bounding the low-degree advantage (LDA) - a quantitative estimate of the closeness of low-degree moments - between a null distribution and a…
We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…
Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…
We develop a new technique, based on a low-energy theorem (LET) of NSVZ type derived in arXiv:1701.07833, for the nonperturbative investigation of SU(N) QCD with N${}_f$ massless quarks - or, more generally, of massless QCD-like theories -…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds…
We present the theoretical analysis of steady state regimes and low-frequency noises in quasi-ballistic FETs. The noise analysis is based on the Langevin approach, which accounts for the microscopic sources of fluctuations originated from…
The complexity of the commuting local Hamiltonians (CLH) problem still remains a mystery after two decades of research of quantum Hamiltonian complexity; it is only known to be contained in NP for few low parameters. Of particular interest…
As in classical coding theory, quantum analogues of low-density parity-check (LDPC) codes have offered good error correction performance and low decoding complexity by employing the Calderbank-Shor-Steane (CSS) construction. However,…
Considerable research efforts have recently been made to show that a random neural network $N$ contains subnetworks capable of accurately approximating any given neural network that is sufficiently smaller than $N$, without any training.…
We consider the cubic Schr\"odinger equation on the euclidean space perturbed by a short-range potential $V$. The presence of a negative simple eigenvalue for $-\Delta+V$ gives rise to a curve of small and localized nonlinear ground states…
An experimental cryptographic proof of quantumness will be a vital milestone in the progress of quantum information science. Error tolerance is a persistent challenge for implementing such tests: we need a test that not only can be passed…
This work provides the first explicit and non-random family of $[[N,K,D]]$ LDPC quantum codes which encode $K \in \Theta(N^\frac{4}{5})$ logical qubits with distance $D \in \Omega(N^\frac{3}{5})$. The family is constructed by amalgamating…
Recent lattice QCD results for the low-lying odd-parity excitations of the nucleon near the $N^{*}(1535)$ and $N^{*}(1650)$ resonance positions have revealed that the lattice QCD states have magnetic moments consistent with predictions from…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…