10 papers
Random unitary circuits with constant spectral gap
Tim Baer, Jeongwan Haah
We prove constant lower bounds for the spectral gap of the following random walks on unitary groups on qubits. (i) Random Pauli Rotation: choose an -qubit…
Growth and collapse of subsystem complexity under random unitary circuits
Jeongwan Haah, Douglas Stanford
For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial…
Short remarks on shallow unitary circuits
Jeongwan Haah
(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved qua…
The code distance of Floquet codes
Keller Blackwell, Jeongwan Haah
For fault-tolerant quantum memory defined by periodic Pauli measurements, called Floquet codes, we prove that every correctable, undetectable spacetime error occurring during the s…
Roadmap to fault tolerant quantum computation using topological qubit arrays
David Aasen, Morteza Aghaee, Zulfi Alam +179
We describe a concrete device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap e…
Geometrically Enhanced Topological Quantum Codes
David Aasen, Jeongwan Haah, Matthew B. Hastings +1
We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric…