Related papers: Computing Efficiently in QLDPC Codes
Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no single error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all…
A major goal in quantum computing is to build a fault-tolerant quantum computer. One approach involves quantum low-density parity-check (qLDPC) codes that support transversal non-Clifford gates. In this work, we provide a large family of…
While Clifford operations are relatively easy to implement in fault-tolerant quantum computers,continuous rotation gates remain a significant bottleneck in typical quantum algorithms. In this work, we ask the question: "What is the most…
Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…
Error correction allows a quantum computer to preserve states long beyond the decoherence time of its physical qubits. Key to any scheme of error correction is the decoding algorithm, which estimates the error state of qubits from the…
Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and…
Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…
Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant…
A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate. We prove…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The groups of Pauli and Clifford gates constitute the…
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…
Recent experimental progress in realizing surface code on hardware, including demonstrations of break-even logical memory on devices with up to hundreds of physical qubits, has materially advanced the prospects for fault-tolerant quantum…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…
Scalable quantum computation requires not only quantum codes with low memory overhead but also encoded operations with low space-time overhead. High rate quantum low-density parity-check (qLDPC) codes address the former by achieving a high…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome…
We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a…
Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still…
Fault-tolerant quantum computing hinges on efficient logical compilation, in particular, translating high-level circuits into code-compatible implementations. Gate-by-gate compilation often yields deep circuits, requiring significant…