Related papers: High-Distance Error-Correcting Codes for Fermion-t…
A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into…
Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study…
We present a family of simple three-dimensional stabilizer codes, called the chiral color codes, that realize fermionic and chiral topological orders. In the qubit case, the code realizes the topological phase of a single copy of the…
I present a fault-tolerant quantum computing method for 2D architectures that is particularly appealing for photonic qubits. It relies on a crossover of techniques from topological stabilizer codes and measurement based quantum computation.…
We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. When the number $F$ of fermions is much smaller than the number $M$ of modes,…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where…
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical…
Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new…
The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic…
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…
There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…
In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…
We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…
We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and…
Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes.…
We introduce an exactly solvable model of interacting Majorana fermions realizing $Z_{2}$ topological order with a $Z_{2}$ fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete…
Floquet quantum error-correcting codes provide an operationally economical route to fault tolerance by dynamically generating stabilizer structures using only two-body Pauli measurements. But while it is well established that stabilizer…