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 condition on the local particle dimension. The resulting code is well-defined when the local Hilbert space dimension is prime. These codes can be divided into two different classes: the local stabilizer generators are either symmetric or antisymmetric with respect to the inversion operation. These is a nontrivial correspondence between these two classes. For any symmetric code without string logical operator, there exists a complementary antisymmetric code with the same property and vice versa. We derive a sufficient condition for the absence of string logical operator in terms of the algebraic constraints on the defining parameters of the code. Minimal number of local particle dimension which satisfies the condition is 5. These codes have logarithmic energy barrier for any logical error.
A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order the code distance, and thus braided, by a constant depth local unitary quantum circuit followed by a permutation of qubits. Our gates are protected in the sense that the length of error strings do not grow by more than a constant factor. When applied to the Fibonacci code, ou…
One of the key compilation steps in Quantum Computing (QC) is to determine an initial logical to physical mapping of the qubits used in a quantum circuit. The impact of the starting qubit layout can vastly affect later scheduling and placement decisions of QASM operations, yielding higher values on critical performance metrics (gate count and circuit depth) as a result of quantum compilers introducing SWAP operations to meet the underlying physical neighboring and connectivity constraints of the quantum device. In this paper we introduce a novel qubit mapping approach, string-based qubit mappi…
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 $-$ such as the cubic code $-$ to be robust to highly correlated, one-dimensional errors that span their lattice. The challenge remains to design decoding algorithms that utilise the high distance of these codes. Here, we begin the development of such algorithms by proposing an efficient decoder for the `Fibonacci code'; a two-dimensional classical code that mimi…
We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubi…
Self-correcting quantum memories demonstrate robust properties that can be exploited to improve active quantum error-correction protocols. Here we propose a cellular automaton decoder for a variation of the color code where the bases of the physical qubits are locally rotated, which we call the XYZ color code. The local transformation means our decoder demonstrates key properties of a two-dimensional fractal code if the noise acting on the system is infinitely biased towards dephasing, namely, no string-like logical operators. As such, in the high-bias limit, our local decoder reproduces the b…
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 code distance, and give a number of equivalent formulations thereof, generalizing various exact error-correction criteria. Our tradeoff bounds relate the number of physical qubits $n$, the number of encoded qubits $k$, the code distance $d$, the accuracy parameter $δ$ that quantifies how well the erasure channel can be reversed, and the locality parameter $\e…
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；University of Cambridge（剑桥大学）；Universität Tübingen（蒂宾根大学）
Simplified circuit-level decoding using Knill error correction
Inria Paris（巴黎国家信息与自动化研究所）；Quandela（夸当德拉）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
Hierarchical QAOA for the Vehicle Routing Problem via Clustered Decomposition and Local Feasibility Repair
Center for Quantum Science and Technology, Siksha ’O’ Anusandhan (Deemed to be University)（Siksha 'O' Anusandhan（视为大学）量子科学与技术中心）；Department of Physics and Astronomy, University of Exeter（埃克塞特大学物理与天文系）；Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata（加尔各答印度科学教育研究所物理科学系）
