相关论文: Low-overhead surface code logical Hadamard
We provide a recursively defined sequence of flag circuits which will detect logical errors induced by non-fault-tolerant $R_{\overline{Z}}(\frac{\pi}{2^l})$ gates on CSS codes with a fault distance of two. As applications, we give a family…
The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT…
Connecting multiple processors via quantum interconnect technologies could help overcome scalability issues in single-processor quantum computers. Transmission via these interconnects can be performed more efficiently using quantum…
Dual-rail erasure qubits can substantially improve the efficiency of quantum error correction, allowing lower error rates to be achieved with fewer qubits, but each erasure qubit requires $3\times$ more transmons to implement compared to…
Quantum error correction is a cornerstone of reliable quantum computing, with surface codes emerging as a prominent method for protecting quantum information. Surface codes are efficient for Clifford gates but require magic state…
Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some…
Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates.…
Current, near-term quantum devices have shown great progress in recent years culminating with a demonstration of quantum supremacy. In the medium-term, however, quantum machines will need to transition to greater reliability through error…
To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is a conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfil for superconducting qubits,…
We introduce several dynamical schemes that take advantage of mid-circuit measurement and nearest-neighbor gates on a lattice with maximum vertex degree three to implement topological codes and perform logic gates between them. We first…
We consider hierarchically implemented quantum error correction (HI-QEC), in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications. By employing qubit…
We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
Demonstrating subthreshold scaling of a surface-code quantum memory on hardware whose native connectivity does not match the code remains a central challenge. We address this on IBM heavy-hex superconducting processors by co-designing the…
We show that Gottesman's (1998) semantics for Clifford circuits based on the Heisenberg representation gives rise to a lightweight Hoare-like logic for efficiently characterizing a common subset of quantum programs. Our applications include…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
We propose the implementation of a deterministic Hadamard gate for logical photonic qubits encoded in superpositions of coherent states of a harmonic oscillator. The proposed scheme builds on a recently introduced set of conditional…