114 citations · 342 across the 18 of their papers we have counts for
19 papers
On The Complexity of Redundancy-Free Quantum Hamiltonians
Matthew B. Hastings, Alexander Schmidhuber
We consider a class of redudancy-free Hamiltonians, which are those where the trace vanishes for any product of Hamiltonian terms in which at least one term appears an odd number o…
The Kikuchi Hierarchy is Sharp for XOR
Alexander Schmidhuber, Matthew B. Hastings
Planted noisy XOR and the strong refutation of random XOR are governed by a conjectured trade-off between signal strength and time: Level of the Kikuchi hierarchy shou…
A Spectral Proof of the Hypergraph Moore Bound
Alexander Schmidhuber, Matthew B. Hastings
A nonempty subfamily of a -uniform hypergraph is an \emph{even cover} if every vertex lies in an even number of its hyperedges; for these are edge-disjoint unions of cycle…
Accelerating Classical and Quantum Tensor PCA
Matthew B. Hastings
Spectral methods are a leading approach for tensor PCA with a ``spiked" Gaussian tensor. The methods use the spectrum of a linear operator in a vector space with exponentially high…
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…
A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes
David Aasen, Matthew B. Hastings, Vadym Kliuchnikov +8
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance o…
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…
Fault-tolerant quantum computation with a neutral atom processor
Ben W. Reichardt, Adam Paetznick, David Aasen +69
Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and ha…
A QCA for every SPT
Lukasz Fidkowski, Jeongwan Haah, Matthew B. Hastings
In three dimensions, there is a nontrivial quantum cellular automaton (QCA) which disentangles the three-fermion Walker--Wang model, a model whose action depends on Stiefel--Whitne…
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…
Pumping Chirality in Three Dimensions
Lukasz Fidkowski, Matthew B. Hastings
Using bosonization, which maps fermions coupled to a gauge field to a qubit system, we give a simple form for the non-trivial 3-fermion quantum cellular automaton…
Quantum Codes on Graphs
M. B. Hastings
We consider some questions related to codes constructed using various graphs, in particular focusing on graphs which are not lattices in two or three dimensions. We begin by consid…
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.
Classification of Quantum Cellular Automata
M. Freedman, M. B. Hastings
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this in…
Training A Quantum Optimizer
D. Wecker, M. B. Hastings, M. Troyer
We study a variant of the quantum approximate optimization algorithm [ E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with slightly different parametrization and differen…
Decoding in Hyperbolic Spaces: LDPC Codes With Linear Rate and Efficient Error Correction
M. B. Hastings
We analyze the four dimensional toric code in a hyperbolic space and show that it has a classical error correction procedure which runs in almost linear time and can be parallelize…
Matrix Product Operators and Central Elements: Classical Description of a Quantum State
M. B. Hastings
We study planar two-dimensional quantum systems on a lattice whose Hamiltonian is a sum of local commuting projectors of bounded range. We consider whether or not such a system has…
Topological Insulators and C^*-Algebras: Theory and Numerical Practice
M. B. Hastings, T. A. Loring
We apply ideas from -algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band p…
Locality in Quantum Systems
M. B. Hastings
These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider applications including correlation…