332 citations · 1.1k across the 33 of their papers we have counts for
35 papers
Classical Adversarial Fault-Tolerance and PCPs
Anurag Anshu, Nikolas P. Breuckmann, Louis Golowich +2
We show how to compile an arbitrary classical circuit into a fault-tolerant circuit, which performs the desired computation even when an almost-linear number of bits are adversaria…
Fault-Tolerant Quantum Computation with Adversarial Errors
Nikolas P. Breuckmann, Louis Golowich, Umesh Vazirani
We prove a fault-tolerance theorem for quantum computation against adversarial noise. For every quantum circuit on logical qudits of depth , we construct a fault…
Optimal Decoding with the Worm
Zac Tobias, Nikolas P. Breuckmann, Benedikt Placke
We propose a new decoder for "matchable'' qLDPC codes that uses a Markov Chain Monte Carlo algorithm - called the worm algorithm - to approximately compute the probabilities of log…
Copy-cup Gates in Tensor Products of Group Algebra Codes
Ryan Tiew, Nikolas P. Breuckmann
We determine conditions on classical group algebra codes so that they have pre-orientation for cup products and copy-cup gates. This defines quantum codes that have constant-depth…
Logical Operators and Derived Automorphisms of Tile Codes
Nikolas P. Breuckmann, Shin Ho Choe, Jens Niklas Eberhardt +2
The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well un…
Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes
Benedikt Placke, Grace M. Sommers, Nikolas P. Breuckmann +2
Complex free-energy landscapes with many local minima separated by large barriers are believed to underlie glassy behavior across diverse physical systems. This is the heuristic pi…
Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary
Vincent Steffan, Shin Ho Choe, Nikolas P. Breuckmann +2
We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for…
Topological Quantum Spin Glass Order and its realization in qLDPC codes
Benedikt Placke, Tibor Rakovszky, Nikolas P. Breuckmann +1
Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, an…
Bottlenecks in quantum channels and finite temperature phases of matter
Tibor Rakovszky, Benedikt Placke, Nikolas P. Breuckmann +1
We prove an analog of the "bottleneck theorem," well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hi…
Low-Overhead Entangling Gates from Generalised Dehn Twists
Ryan Tiew, Nikolas P. Breuckmann
We generalise the implementation of logical quantum gates via Dehn twists from topological codes to the hypergraph and balanced products of cyclic codes. These generalised Dehn twi…
Cups and Gates I: Cohomology invariants and logical quantum operations
Nikolas P. Breuckmann, Margarita Davydova, Jens N. Eberhardt +1
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology in…
Circuit-to-Hamiltonian from tensor networks and fault tolerance
Anurag Anshu, Nikolas P. Breuckmann, Quynh T. Nguyen
We define a map from an arbitrary quantum circuit to a local Hamiltonian whose ground state encodes the quantum computation. All previous maps relied on the Feynman-Kitaev construc…
Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
Oscar Higgott, Nikolas P. Breuckmann
We construct families of Floquet codes derived from colour code tilings of closed hyperbolic surfaces. These codes have weight-two check operators, a finite encoding rate and can b…
Fault-Tolerant Connection of Error-Corrected Qubits with Noisy Links
Joshua Ramette, Josiah Sinclair, Nikolas P. Breuckmann +1
One of the most promising routes towards scalable quantum computing is a modular approach. We show that distinct surface code patches can be connected in a fault-tolerant manner ev…
The Random-Bond Ising Model and its dual in Hyperbolic Spaces
Benedikt Placke, Nikolas P. Breuckmann
We analyze the thermodynamic properties of the random-bond Ising model (RBIM) on closed hyperbolic surfaces using Monte Carlo and high-temperature series expansion techniques. We a…
A construction of Combinatorial NLTS
Anurag Anshu, Nikolas P. Breuckmann
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity (wi…
NLTS Hamiltonians from good quantum codes
Anurag Anshu, Nikolas P. Breuckmann, Chinmay Nirkhe
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complex…
Improved single-shot decoding of higher dimensional hypergraph product codes
Oscar Higgott, Nikolas P. Breuckmann
In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kal…
Fold-Transversal Clifford Gates for Quantum Codes
Nikolas P. Breuckmann, Simon Burton
We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical o…
Quantum phase transitions of interacting bosons on hyperbolic lattices
Xingchuan Zhu, Jiaojiao Guo, Nikolas P. Breuckmann +2
The effect of many-body interaction in curved space is studied based on the extended Bose--Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Mont…
Quantum Low-Density Parity-Check Codes
Nikolas P. Breuckmann, Jens Niklas Eberhardt
Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity…
Balanced Product Quantum Codes
Nikolas P. Breuckmann, Jens N. Eberhardt
This work provides the first explicit and non-random family of LDPC quantum codes which encode logical qubits with distance $D \in Ω(N^\frac{3}…
Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
Oscar Higgott, Nikolas P. Breuckmann
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators…
Single-Shot Decoding of Linear Rate LDPC Quantum Codes with High Performance
Nikolas P. Breuckmann, Vivien Londe
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code…