Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [lattice-surgery]

27 questions
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Getting intuition on the state-injection relations for the generalized $\exp(-iP \pi/8)$ $T$-gates (ideally using ZX calculus)

In Litinsky's paper, there are many circuits relations, like the one below. The left handside represents the "rotation" $\exp(-i P \phi)$ with $\phi=\pi/8$ with similar definitions for the orange ($\phi=\pi/4$) and gray box ($\phi=\pi/2$) on the…
Marco Fellous-Asiani
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How to reason about absorbing Pauli Product rotations into measurements?

In this image, the orange box refers to the operator $\exp(-i P \frac{\pi}{4})$ and the blue box refers to the Pauli Measurement $P'$. The idea behind these rules is to show how all the Pauli Product $\frac{\pi}{4}$ rotations at the end of the…
shashvat
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What are the differences between code deformation, code conversion, code switching and gauge fixing?

From my understanding so far: Code switching is essentially just a fault-tolerant mapping between two codes. It's called code conversion if it's gradational, i.e. changes to stabilizer generators are measured in each round of error correction. A…
tomek
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When do we need to decode live the syndromes? Various examples to understand

I would like to precisely understand why we need to decode syndrome "live" when we want to perform $T$ gates. For this reason I consider different scenario (some are fictive but helpful to understand the physics) in order to understand which exact…
Marco Fellous-Asiani
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Can you produce Non-Clifford gates via Lattice Surgery?

Is there any theorem stating that lattice merge/split operations (or perhaps more generally, so-called gauge-fixing) cannot produce a non-Clifford gate that can complete the universal gateset for the surface code?
usermm
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How does the expansion step for state injection in surface code lattice surgery work?

Looking at the oringal paper on lattice surgery on the surface code, the expansion step of the state injection process is meant to take $$\alpha|0\rangle_{L}+\beta|1\rangle_{L}$$ to a larger surface code patch. However, both this question and this…
GaussStrife
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Kraus decomposition of merging in lattice surgery

I am reading about lattice surgery from this paper. I am interested in the merge operation which takes 2 qubits to 1 qubit. I want to understand the logical-level Kraus operation that the merge does. For instance, the action of the rough merge…
qubit
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High logical error rates when implementing Lattice Surgery with Stim

I'm facing a strange issue with the logical error rate after implementing Lattice Surgery in Stim. For $d=3$ (I have some custom error annotations in the circuit), Logical error rate of X-basis Lattice Surgery, XX-Observable: 0.06361 Logical error…
control freak
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Number of logical cycles to implement $R_Z(\theta)$ gates in lattice surgery: why isn't it the number of layers $\times$ the $T$-count in $R_Z$?

Let's assume I want to implement a rotation $R_Z(\theta)$ for a lattice-surgery based computation, for $\theta$ being an arbitrary angle (i.e. the gate is not necessarily Clifford nor a $T$-gate). It can typically be done by Decomposing…
Marco Fellous-Asiani
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lattice surgery in state picture

I was following Surface code quantum computing by lattice surgery. A few questions about this paper have been asked in this forum, but I believe my question is new. The main text took a 'state picture' of what happens and in the appendix, the…
quTANum
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15-to-1 distillation protocol in lattice surgery: doesn't the potential rejection of the level-1 magic states makes it last longer than $15$ timestep?

Overview of my question I am following Litinsky's paper, and I would like to better understand how the duration of the level-2 15-to-1 distillation protocol is being estimated. Litinsky's says that it will last for $15$ clock cycles, but for me this…
Marco Fellous-Asiani
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Lattice Surgery: how does lattice merging act on the physical qubits?

I am reading 2013, Horsman D. et al. - Surface code quantum computing by lattice surgery. I have been trying to understand how the outcome of rough lattice merging, which is discussed using both stabilizer formalism and logical qubit formalism, can…
Giovanni Canossa
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level-2 15-to-1 distillation protocol from Litinsky: Why does it take 15 time steps and not 22?

I am reading Litinsky's paper (arXiv), and I am confused by the duration of the level-2 15-to-1 distillation protocol. Litinsky's writes that it will take 15 clock cycles, but to me it seems like it should be 22. There are (a) 4 distilled magic…
quantumsleep
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For lattice-surgery. How to move a logical qubit back to its original position after applying a logical H gate

I'm learning surface code and lattice surgery based on "Surface code quantum computing by lattice surgery" and "Surface codes: Towards practical large-scale quantum computation", and trying to implement a logical S gate using stim According to Fig.…
Yilun Zhao
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Why does measuring the $X$ stabilisers at the boundary for rough merging give $X_{L}X_{L}$

In the paper Surface code quantum computing by lattice surgery, for rough merging, they state that measuring the $X$ stabilisers at the boundary is equivalent to $X_{L}X_{L}$. What I don't understand is what the new $X$ stabiliser measurements…
GaussStrife
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