相关论文: Towards surgery with good quantum LDPC codes
Constructing quantum codes with good parameters and useful transversal gates is a central problem in quantum error correction. In this paper, we continue our work in arXiv:2502.01864 and construct the first family of asymptotically good…
Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear…
In this perspective, we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best…
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of…
Simulating fermionic systems on qubit-based quantum computers often demands significant computational resources due to the requirement to map fermions to qubits. Thus, designing a fault-tolerant quantum computer that operates directly with…
In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…
Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional…
Quantum low-density parity-check codes are promising candidates for quantum error correcting codes as they might offer more resource-efficient alternatives to surface code architectures. In particular, bivariate bicycle codes have recently…
Quantum computers have the potential to change the way we solve computational problems. Due to the noisy nature of qubits, the need arises to correct physical errors occurring during computation. The surface code is a promising candidate…
Fault-tolerant quantum computers, with error correction implemented using topological codes, will most likely require lattice surgery protocols in order to implement a universal gate set. Timelike failures during lattice surgery protocols…
Quantum low-density parity-check (qLDPC) codes can encode many logical qubits within a single code block at low physical qubit overhead, yet magic state injection into such codes remains largely underexplored. Existing state injection…
We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasi-cyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized…
How many T gates are needed to approximate an arbitrary $n$-qubit quantum state to within error $\varepsilon$? Improving prior work of Low, Kliuchnikov, and Schaeffer, we show that the optimal asymptotic scaling is…
Quantum computers will need effective error-correcting codes. Current quantum processors require precise control of each particle, so having fewer particles to control might be beneficial. Although traditionally quantum computers are…
Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error-correcting code. The recent discovery…
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 study finite-length qudit quantum low-density parity-check (LDPC) codes from translation-invariant CSS constructions on two-dimensional tori with twisted boundary conditions. Recent qubit work [PRX Quantum 6, 020357 (2025)] showed that,…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…