734 citations · 6k across the 61 of their papers we have counts for
46 papers · 1 filter
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…
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…
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…
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…
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…
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…
Incompressibility and spectral gaps of random circuits
Chi-Fang Chen, Jeongwan Haah, Jonas Haferkamp +3
Random reversible and quantum circuits form random walks on the alternating group and unitary group , respectively. Known bounds on the spectr…
Efficient approximate unitary designs from random Pauli rotations
Jeongwan Haah, Yunchao Liu, Xinyu Tan
We construct random walks on simple Lie groups that quickly converge to the Haar measure for all moments up to order . Specifically, a step of the walk on the unitary or orthogn…
Splitting decoders for correcting hypergraph faults
Nicolas Delfosse, Adam Paetznick, Jeongwan Haah +1
The surface code is one of the most popular quantum error correction codes. It comes with efficient decoders, such as the Minimum Weight Perfect Matching (MWPM) decoder and the Uni…
Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits
David Aasen, Jeongwan Haah, Parsa Bonderson +2
We develop protocols for Hastings-Haah Floquet codes in the presence of dead qubits.
Measurement Quantum Cellular Automata and Anomalies in Floquet Codes
David Aasen, Jeongwan Haah, Zhi Li +1
We investigate the evolution of quantum information under Pauli measurement circuits. We focus on the case of one- and two-dimensional systems, which are relevant to the recently i…
Query-optimal estimation of unitary channels in diamond distance
Jeongwan Haah, Robin Kothari, Ryan O'Donnell +1
We consider process tomography for unitary quantum channels. Given access to an unknown unitary channel acting on a -dimensional qudit, we aim to output a classical des…
Performance of planar Floquet codes with Majorana-based qubits
Adam Paetznick, Christina Knapp, Nicolas Delfosse +4
Quantum error correction is crucial for any quantum computing platform to achieve truly scalable quantum computation. The surface code and its variants have been considered the mos…
Boundaries for the Honeycomb Code
Jeongwan Haah, Matthew B. Hastings
We introduce a simple construction of boundary conditions for the honeycomb code that uses only pairwise checks and allows parallelogram geometries at the cost of modifying the bul…
Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
Jeongwan Haah, Robin Kothari, Ewin Tang
We study the problem of learning a Hamiltonian to precision , supposing we are given copies of its Gibbs state at a know…
Classification of Small Triorthogonal Codes
Sepehr Nezami, Jeongwan Haah
Triorthogonal codes are a class of quantum error correcting codes used in magic state distillation protocols. We classify all triorthogonal codes with , where is th…
Dynamically Generated Logical Qubits
Matthew B. Hastings, Jeongwan Haah
We present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement…
Fiber Bundle Codes: Breaking the Barrier for Quantum LDPC Codes
Matthew B. Hastings, Jeongwan Haah, Ryan O'Donnell
We present a quantum LDPC code family that has distance and logical qubits. This is the first quantum LDPC code constructi…
A degeneracy bound for homogeneous topological order
Jeongwan Haah
We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits).…
How Dynamical Quantum Memories Forget
Lukasz Fidkowski, Jeongwan Haah, Matthew B. Hastings
Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such sys…
Measurement sequences for magic state distillation
Jeongwan Haah, Matthew B. Hastings
Magic state distillation uses special codes to suppress errors in input states, which are often tailored to a Clifford-twirled error model. We present detailed measurement sequence…
Optimization of the surface code design for Majorana-based qubits
Rui Chao, Michael E. Beverland, Nicolas Delfosse +1
The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface co…
The Group Structure of Quantum Cellular Automata
Michael Freedman, Jeongwan Haah, Matthew B. Hastings
We consider the group structure of quantum cellular automata (QCA) modulo circuits and show that it is abelian even without assuming the presence of ancillas, at least for most rea…
Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D
Jeongwan Haah
We study locality preserving automorphisms of operator algebras on -dimensional uniform lattices of prime -dimensional qudits (QCA), specializing in those that are translatio…