Related papers: Logical operator tradeoff for local quantum codes
We study the fundamental limits on the reliable storage of quantum information in lattices of qubits by deriving tradeoff bounds for approximate quantum error correcting codes. We introduce a notion of local approximate correctability and…
We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have string-like logical operators,…
We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli…
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 understood in terms of their logical operators and boundary…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the…
Locality-preserving logical operators in topological codes are naturally fault-tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure…
Recently, Bravyi and K\"onig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a…
The Bacon-Shor code is a quantum error correcting subsystem code composed of weight 2 check operators that admits a single logical qubit, and has distance $d$ on a $d \times d$ square lattice. We show that when viewed as a Floquet code, by…
We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both…
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a…
We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints…
We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
We evaluate the usefulness of holographic stabilizer codes for practical purposes by studying their allowed sets of fault-tolerantly implementable gates. We treat them as subsystem codes and show that the set of transversally implementable…
We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
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…
We construct rotated logical states by applying rotation operators to stabilizer states, extending the logical basis and modifying stabilizer generators. Rotation operators affect the effective code distance $d_R$, which decays…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…