Quantum Computing – An Update
As of 2024, seven approaches to building physical qubits exist, with no consensus on the best. Quantum computers excel in specific algorithms, but significant challenges remain in achieving practical applications.
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quantum computing is crucial for progress. As of 2024, there are seven main approaches to building physical qubits, including superconducting circuits and trapped ions, but no consensus on the best method has emerged. Each approach has shown incremental improvements in the number of physical qubits, yet the focus should shift to logical qubits, which are essential for practical applications. Quantum computers are not universally faster than classical computers; they excel in specific algorithms, such as Grover's and Shor's, which can optimize complex problems and break current cryptographic systems, respectively. The challenge lies in the number of physical qubits required to create a single logical qubit, which can range from hundreds to millions depending on error rates. Current error rates for physical qubits are around 1% to 0.1%, necessitating extensive error correction measures. Advances in materials science are expected to help reduce these error rates, making quantum computing more viable. Despite the progress, the field still has significant hurdles to overcome before achieving a fully functional quantum computer.
- Seven approaches to building physical qubits are being explored, with no clear leader.
- Quantum computers excel in specific algorithms but are not universally faster than classical computers.
- Thousands of physical qubits are needed to create a single logical qubit due to error rates.
- Advances in materials science are crucial for reducing error rates in quantum computing.
- Current best efforts have only achieved around 1,000 physical qubits, indicating more work is needed.
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3 comments> With an error rate of 1% the surface error correction code requires ~ 500 physical qubits required to encode one logical qubit.
This was the correction near the end:
> With an error rate of 0.3% the surface error correction code requires ~ 10 thousand physical qubits to encode one logical qubit to achieve 10^-10 logical qubit error rate.
The qubit count at an error rate of 1% was clearly off because the threshold of the surface code under circuit noise is a bit below 1%. Meaning at 1% it would have infinite cost; way more than 500. To get good numbers you need be well below the threshold. At a 0.1% error rate, assuming a square grid of qubits with local connections, the best physical-per-logical estimate that I'm aware of is 600, from surface codes plus a few extra parity checks layered on top [1][2]. Another code that achieves a teraquop footprint of ~600 on a planar grid is the honeycomb code [3][4] but that number requires a dissipative two qubit gate which seems to be harder to build than the usual unitary ones.
[1]: https://www.youtube.com/watch?v=Ge7fEaXjvq4
[2]: https://arxiv.org/pdf/2312.04522
I had a brief run-in with error-correcting gates. My research topic was about a simple bit-flip operation (quantum dot qubits) under random "telegraph" noise -- different laser pulse shapes result in different error rates which are actually a function of time (on the scale of the pulse itself). Point being that even given a particular physical qubit framework, individual gates are actually a family of (physical) operations with different error rates (and other features, of course) to be optimized for the same logical operation. Not too unlike the idea of NAND vs NOR flash.
Personally, I feel that's slightly "good" in the sense that there are many paths we can take to get quantum computation "good enough".
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Shor's algorithm necessitates extensive qubit resources and advanced error correction. The OPX1000 controller enhances qubit management, while collaboration with NVIDIA aims to improve data processing latency for effective quantum computing.
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Microsoft and Quantinuum created 12 logical qubits with a low error rate, demonstrating their reliability in a hybrid chemistry simulation, and plan to expand their qubit-virtualization system for future advancements.
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Google uncovers how quantum computers can beat today's best supercomputers
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