2 citations · 3 across the 9 of their papers we have counts for
10 papers
A polynomial-time classical sampler for noisy quantum circuits from statistical mechanics
Jon Nelson, Joel Rajakumar, Chao Yin +2
Developing classical simulation algorithms for noisy quantum circuits is essential to delineating the limits of quantum advantage. Existing classical sampling approaches for genera…
Noise-induced contraction of MPO truncation errors in noisy random circuits and Lindbladian dynamics
Zhi-Yuan Wei, Joel Rajakumar, Jon Nelson +3
We study how matrix-product-operator (MPO) truncation errors evolve when simulating two setups: (1) 1D Haar-random circuits under either depolarizing noise or amplitude-damping noi…
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…
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-…
Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes
Jon Nelson, Gregory Bentsen, Steven T. Flammia +1
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed th…
Hamiltonians whose low-energy states require T gates
Nolan J. Coble, Matthew Coudron, Jon Nelson +1
The recent resolution of the NLTS Conjecture [ABN22] establishes a prerequisite to the Quantum PCP (QPCP) Conjecture through a novel use of newly-constructed QLDPC codes [LZ22]. Ev…