Related papers: Logical operator tradeoff for local quantum codes
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
We show that the U(2) group structure of thin barriers can be adopted for quantum information processing when used in combination with environmental potential whose bouncing modes are profile preserving. Qubits are realized as wave…
Local decoders provide a promising approach to real-time quantum error-correction by replacing centralized classical decoding, with significant hardware constraints, by a fully distributed architecture based on a simple, local update rule.…
High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…
We present a quantum LDPC code family that has distance $\Omega(N^{3/5}/\operatorname{polylog}(N))$ and $\tilde\Theta(N^{3/5})$ logical qubits. This is the first quantum LDPC code construction which achieves distance greater than $N^{1/2}…
Qudits with local dimension $d>2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group…
Two-dimensional quantum colour codes hold significant promise for quantum error correction, offering advantages such as planar connectivity and low overhead logical gates. Despite their theoretical appeal, the practical deployment of these…
Is the notion of a quantum computer resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting quantum computers. To this end, we…
We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on…
An algorithm which encodes the $L\times L$ 2D toric code logical state with a circuit of depth $2L+1$, using only local controlled-NOT($CX$) and Hadamard($H$) gates, is presented.
The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising…
Atomic, molecular and optical (AMO) approaches to quantum computing are promising due to their increased connectivity, long coherence times and apparent scalability. However, they have a significantly reduced cadence of syndrome extraction…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between…
Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an ``always-on'' decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit…
A leading twist expansion in terms of bi-local operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other processes. Operators of…
We exhibit d-dimensional limit-periodic Schrodinger operators that are uniformly localized in the strongest sense possible. That is, for each of these operators, there is a uniform exponential decay rate such that every element of the hull…
We investigate layer codes, a family of three-dimensional stabilizer codes that can achieve optimal scaling of code parameters and a polynomial energy barrier, as candidates for self-correcting quantum memories. First, we introduce two…