5 papers
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
It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at depth, where is the number…
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…
Polynomial-Time Classical Simulation of Noisy Quantum Circuits with Naturally Fault-Tolerant Gates
Jon Nelson, Joel Rajakumar, Dominik Hangleiter +1
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-…