2 citations · 3 across the 9 of their papers we have counts for
5 papers · 2 filters
Non-Clifford Gates are Required for Long-Term Memory
Jon Nelson, Joel Rajakumar, Michael J. Gullans
We show that all Clifford circuits under interspersed depolarizing noise lose memory of their input exponentially quickly, even when given access to a constant supply of fresh qubi…
Error correction phase transition in noisy random quantum circuits
Jon Nelson, Joel Rajakumar, Michael J. Gullans
In this work, we study the task of encoding logical information via a noisy quantum circuit. It is known that at superlogarithmic depth, the output of any noisy circuit without res…
Limitations of Noisy Geometrically Local Quantum Circuits
Jon Nelson, Joel Rajakumar, Michael J. Gullans
Quantum circuits with a constant rate of depolarizing noise per qubit per time step are known to converge to the uniform distribution at depth , and hence become t…
Measurement-induced entanglement in noisy 2D random circuits
Zhi-Yuan Wei, Jon Nelson, Joel Rajakumar +4
We study measurement-induced entanglement (MIE) generated by column-by-column sampling of noisy 2D random circuits of size and depth . Focusing primarily on Clifford circuit…
The rotation-invariant Hamiltonian problem is QMA-complete
Jon Nelson, Daniel Gottesman
In this work, we study a variant of the local Hamiltonian problem where we restrict to Hamiltonians that live on a lattice and are invariant under translations and rotations of the…