[WIP] A game of surface codes demo #1355
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dime10
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Apr 30, 2025
| r"""A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery | ||
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| abstract |
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Is there an abstract to be added?
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| The game of surface codes [#Litinski]_ is a high-level framework for designing surface code quantum computing architectures. | ||
| The game helps us understand space-time trade-offs, where e.g. designs with a higher qubit overhead allow for faster computations and vice versa. | ||
| E.g., a space-efficient design might allow a computation with :math:`10^8` T gates to run in :math:`4` hours using :math:`55k` physical qubits, |
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some diversity
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| E.g., a space-efficient design might allow a computation with :math:`10^8` T gates to run in :math:`4` hours using :math:`55k` physical qubits, | |
| For example, a space-efficient design might allow a computation with :math:`10^8` T gates to run in :math:`4` hours using :math:`55k` physical qubits, |
| The game helps us understand space-time trade-offs, where e.g. designs with a higher qubit overhead allow for faster computations and vice versa. | ||
| E.g., a space-efficient design might allow a computation with :math:`10^8` T gates to run in :math:`4` hours using :math:`55k` physical qubits, | ||
| whereas an intermediate design may run the same computation in :math:`22` minutes using :math:`120k` physical qubits, | ||
| or a time-optimized design in :math:`1` second using :math:`1500` interconnected quantum computers with :math:`220k` physical qubits, each. |
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Just curious, are these real estimates or arbitrary numbers? :D
| However, it still helps to understand the correspondences in physical fault tolerant quantum computing (FTQC) architectures. | ||
| First of all it is important to note that we consider surface codes that implement `(Clifford + T) <https://pennylane.ai/compilation/clifford-t-gate-set>`__ circuits. | ||
| In particular, these circuits can be compiled to circuits that just perform `Pauli product measurements <https://pennylane.ai/compilation/pauli-product-measurement>`__. | ||
| This is because all Clifford operations can be moved to the end of the circuit and merged with measurements. |
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Not sure if it is too much detail at this point, but Clifford operations can also be implemented via measurements.
| We also note that the patches that represent qubits correspond to surface code qubits. | ||
| There is a detailed explanation in Appendix A in [#Litinski]_ that describes the surface code realizations of all operations that we are going to see. | ||
| These are useful to know in order to grasp the full depth of the game, but are not essential to understanding its rules and concluding design principles that we cover in this demo. | ||
| For further reading on these subjects, we recommend the `blog posts on the surface code and quantum error correction <https://arthurpesah.me/blog/>`__ by Arthur Pesah, our :doc:`demo on the toric code <tutorial_toric_code>`, as well as the three-part series on the `toric code <https://decodoku.blogspot.com/2016/03/6-toric-code.html>`__ by James Wooton |
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| For further reading on these subjects, we recommend the `blog posts on the surface code and quantum error correction <https://arthurpesah.me/blog/>`__ by Arthur Pesah, our :doc:`demo on the toric code <tutorial_toric_code>`, as well as the three-part series on the `toric code <https://decodoku.blogspot.com/2016/03/6-toric-code.html>`__ by James Wooton | |
| For further reading on these subjects, we recommend the `blog posts on the surface code and quantum error correction <https://arthurpesah.me/blog/>`__ by Arthur Pesah, our :doc:`demo on the toric code <tutorial_toric_code>`, as well as the three-part series on the `toric code <https://decodoku.blogspot.com/2016/03/6-toric-code.html>`__ by James Wooton. |
| Quantum computer designs | ||
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| The 15-to-1 distillation protocol is the simplest of a variety of protocols with each their different characteristics. |
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| The 15-to-1 distillation protocol is the simplest of a variety of protocols with each their different characteristics. | |
| The 15-to-1 distillation protocol is the simplest of a variety of protocols each with different characteristics. |
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| The 15-to-1 distillation protocol is the simplest of a variety of protocols with each their different characteristics. | ||
| The best choice for distillation protocol heavily depends on the error probabilities of the quantum computer in use, |
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| The best choice for distillation protocol heavily depends on the error probabilities of the quantum computer in use, | |
| The best choice of distillation protocol heavily depends on the error probabilities of the quantum computer in use, |
| The 15-to-1 distillation protocol is the simplest of a variety of protocols with each their different characteristics. | ||
| The best choice for distillation protocol heavily depends on the error probabilities of the quantum computer in use, | ||
| as well as the overall tolerance for errors we allow to still occur. | ||
| For example, assume we tolerate T infidelity of :math:`10^{-10}` and have :math:`p=10^{-4}`, then |
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| For example, assume we tolerate T infidelity of :math:`10^{-10}` and have :math:`p=10^{-4}`, then | |
| For example, assume we tolerate a T infidelity of :math:`10^{-10}` and have :math:`p=10^{-4}`, then |
| Intermediate setup consisting of the intermediate data block and two 15-to-1 distillation blocks on each end. | ||
| ** | ||
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| In this case we require 222 tiles, so :math:`222 \cdot 2 \cdot d^2 \approx 75k` physical qubits, and the same computation mentioned before would finish in half the time after about :math:`2h`. |
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Nice! I like this section with the different time constraints :)
| Conclusion | ||
| ---------- | ||
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| We've been introduced to a high-level description that allows us to reason about space-time trade-offs in FTQC architecture designs. |
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... high-level description of what?
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| We've been introduced to a high-level description that allows us to reason about space-time trade-offs in FTQC architecture designs. | |
| We've been introduced to a high-level description that allows us to reason about space-time trade-offs in FTQC architecture designs. |
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P0 Game of Surface Codes Demo 2025 Q2 [sc-87600]
open question:
do I understand it correct that single X and Z measurements are free, but joint measurements cost 1 🕒?>> yesWhat does it mean that the error probability of the distillation of 15 faulty magic states with$p$ leads to a faulty magic state with probability $35p^3$ , yet, the probability of failure is $(1-p)^n$ ? 🤔>> p is the infidelity of the state, and