23 papers
Stabilizer Learning under Global Depolarizing Noise with Polynomial Copies and Time
Aryeh Lev Zabokritskiy
We study learning the stabilizer structure of an unknown pure -qubit state observed through global depolarizing noise of unknown strength, with a fixed promised upper bound belo…
Concatenation Locality under Successive Adjacent Transpositions
Adelin Ataba, Aryeh Lev Zabokritskiy
We study codes correcting up to successive adjacent transpositions, using block concatenation to support blockwise encoding and decoding. A fixed set of words of lengt…
Optimal GHZ extraction from MABK violations
Avraham Kreindel, Aryeh Lev Zabokritskiy
We determine the least Greenberger-Horne-Zeilinger (GHZ) extractability compatible with a Mermin-Ardehali-Belinskii-Klyshko (MABK) Bell score for every . Extractability is…
Quantum Leakage from Shamir Sharing with Correlated Resources
Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
We bound local quantum leakage from Shamir sharing uniformly over prime fields and permitted share-dependent channels. The adversary receives all outputs and a reference to a resou…
Asymptotically unit-rate storage codes from binary BCH codes
Aryeh Lev Zabokritskiy
A storage code on a graph assigns a symbol to each vertex so that the symbol can be recovered from its neighbors. We prove that the binary full-parity storage codes on triangle-fre…
Systematic Codes Correcting Two Deletions with Three Redundant Symbols over Large Alphabets
Valery, Grishin, Aryeh Lev Zabokritskiy
We construct systematic -ary codes correcting two deletions with three redundant symbols over polynomial-size alphabets. For every information length , our first construc…
Efficient Non-Uniform Quantum Hermite Transform through Adaptive Sampling
Nitay Mayo, Aryeh Lev Zabokritskiy
On the span of the first oscillator modes, Gauss--Hermite quadrature gives an exact change of basis between mode coefficients and weighted position space samples. We implem…
Binary Multiple-Node-Erasure-Correcting Codes over Complete Graphs: Constructions, q-Ary Metric Balls, and Duality
Aryeh Lev Zabokritskiy
We study linear codes whose coordinates are the ordinary edges and self-loops of complete undirected graphs; a node erasure removes all coordinates incident with a failed vertex. T…
Coding for Multiple Reverse-Complement and Palindromic Duplications
Aryeh Lev Zabokritskiy
Reverse-complement (RC) and palindromic (PAL) duplications copy a length- block, reverse the copy, and insert it immediately after the original block; an RC duplication also com…
Prescribed-Difference Matchings with Four and Eight Holes: Fourier Filters for Compatible Boundaries
Avraham Kreindel, Aryeh Lev Zabokritskiy
Let and let have sum zero. The prescribed-difference matching problem asks whether can be partitioned into pairs w…
Correcting Connectivity in Arc-Based QUBO Models for Fixed-Fleet Vehicle Routing
Omer Gurevich, Maor Matityahu, Tal Mor +1
We revisit a degree-only arc Hamiltonian for fixed-fleet, homogeneous, uncapacitated vehicle routing. Its local penalties define only a cycle cover, so ground states may contain cu…
From Round-Trip State Echo to Error Recovery: Snapshot-Resolved Quantum-Hardware Diagnostics
Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
We examine which conclusions from quantum-hardware benchmarks persist when the same programs are run again. On eight fixed routes of IQM Emerald, round-trip state echo (RTSE), a di…
Quantitative Tiling Stability From Quadratic Discrepancy In Hamming Spaces
Valery, Grishin, Aryeh Lev Zabokritskiy
Quadratic ball discrepancy measures how uniformly a code meets Hamming balls over all centers and radii. Perfect codes minimize this quantity among codes of the same cardinality. W…
Asymptotically Tight Bounds for Generalized Covering Radii of Binary Primitive BCH Codes at All Higher Orders
Zeev Vladimir Belinsky, Aryeh Lev Zabokritskiy
We study the generalized covering radii of binary primitive BCH codes, which measure how many parity-check columns suffice to span several prescribed syndromes. For the four-error-…
How Far Can You Do Nothing On a Quantum Computer?
Nitay Mayo, Tal Mor, Aryeh Lev Zabokritskiy
We present a route-resolved comparative assessment of Rigetti's Cepheus-1-108Q and IBM Heron-r2 processors using the established do-nothing state-transfer protocol. Rather than pro…
The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes
Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
Let be the binary primitive triple-error-correcting BCH code of length . We determine its second generalized covering radius exactly: f…
Independent Sets in Multiset Profile Graphs via Weighted Local Covers
Aryeh Lev Zabokritskiy
Let be the unit-transfer graph on the nonnegative integer vectors whose coordinates sum to , equivalently on the multiplicity profiles of size- multisets over $q…
Perfect Codes As Exact Minimizers Of Quadratic Discrepancy In q-ary Hamming Spaces
Aryeh Lev Zabokritskiy
Total quadratic ball discrepancy measures the deviation of codeword counts from uniformity over all Hamming balls. We prove that, whenever a Hamming space and cardinality admit a p…
Extinction Depth and q-ary Error-Correcting Codes for the Limited Permutation Channel
Noam Ben Shimon, Aryeh Lev Zabokritskiy
In the radius-one limited permutation channel, errors consist of disjoint adjacent transpositions. A correcting code must separate distinct codewords: their error balls may not con…
Perfect Matchings with Prescribed Differences Beyond Hall: The Two-Hole Problem
Aryeh Lev Zabokritskiy
The Balister--Győri--Schelp (BGS) conjecture asks whether every zero-sum list of nonzero vectors in is the prescribed-difference profile of a perfect mat…
A -ary Local Criterion for the Radius-One Limited Permutation Channel and Almost-Optimal Binary Block-Concatenation Codes
Noam Ben Shimon, Aryeh Lev Zabokritskiy
The radius-one limited permutation channel maps a transmitted word to any word obtained by an arbitrary set of pairwise disjoint adjacent transposi…
Polynomial Constructions and Deletion-Ball Geometry for Multiset Deletion Codes
Avraham Kreindel, Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
We study error-correcting codes in the space of length- multisets over a -ary alphabet under the deletion metric, motivated by permutation channels in whi…
Multiset Deletion Codes: Cyclic Constructions, Bounds, and Exact Results
Avraham Kreindel, Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
We study deletion-correcting codes in the space of length- multisets over a -ary alphabet. We present an explicit cyclic Sidon-type construction for arbitrary alphabet size $…