Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected medium-sized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond the application of DQC since entanglement distribution and purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder with a sequential schedule for distilling-qubit GHZ states using a ratefamily of lifted product QLDPC codes and obtain an input fidelity threshold ofunder i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield offor any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of-qubit GHZ states to construct a scalable GHZ purification protocol.
This content will become publicly available on June 27, 2024
Visualizations have played a crucial role in helping quantum computing users explore quantum states in various quantum computing applications. Among them, Bloch Sphere is the widely‐used visualization for showing quantum states, which leverages angles to represent quantum amplitudes. However, it cannot support the visualization of quantum entanglement and superposition, the two essential properties of quantum computing. To address this issue, we propose VENUS, a novel visualization for quantum state representation. By explicitly correlating 2D geometric shapes based on the math foundation of quantum computing characteristics, VENUS effectively represents quantum amplitudes of both the single qubit and two qubits for quantum entanglement. Also, we use multiple coordinated semicircles to naturally encode probability distribution, making the quantum superposition intuitive to analyze. We conducted two well‐designed case studies and an in‐depth expert interview to evaluate the usefulness and effectiveness of VENUS. The result shows that VENUS can effectively facilitate the exploration of quantum states for the single qubit and two qubits.
more » « less- NSF-PAR ID:
- 10426704
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Computer Graphics Forum
- Volume:
- 42
- Issue:
- 3
- ISSN:
- 0167-7055
- Page Range / eLocation ID:
- p. 247-258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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