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4 papers
Approximating the Determinant of Well-Conditioned Matrices by Shallow Circuits
Enric Boix-Adserà, Lior Eldar, Saeed Mehraban
The determinant can be computed by classical circuits of depth , and therefore it can also be computed in classical space . Recent progress by Ta-Shma [Ta…
Robust Quantum Entanglement at (nearly) Room Temperature
Lior Eldar
We formulate a mixed-state analog of the NLTS conjecture [FH14] by asking whether there exist topologically-ordered systems for which the thermal Gibbs state for constant temperatu…
The Systematic Normal Form of Lattices
Lior Eldar, Peter W. Shor
We introduce a new canonical form of lattices called the systematic normal form (SNF). We show that for every lattice there is an efficiently computable "nearby" SNF lattice, such…
Commuting Local Hamiltonians on Expanders, Locally Testable Quantum codes, and the qPCP conjecture
Dorit Aharonov, Lior Eldar
Understanding commuting local Hamiltonians (CLHs) is at the heart of many questions in quantum computational complexity and quantum physics: quantum error correcting codes, quantum…