For questions regarding quantum computation by state injection.
Questions tagged [state-injection-model]
11 questions
23
votes
1 answer
How does magic state distillation overhead scale compare to quantum advantages?
I'm interested in the model of quantum computation by magic state injection, that is where we have access to the Clifford gates, a cheap supply of ancilla qubits in the computational basis, and a few expensive-to-distill magic states (usually those…
Emily Tyhurst
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2
votes
2 answers
How to inject a $\sqrt{X}$ gate, rather than Hadamard
It follows the protocol for Hadamard gate injection:
Considering that $H \simeq \sqrt{Z}\sqrt{X}\sqrt{Z}$, it should be equivalent to inject $\sqrt{X}$ wrapped between $\sqrt{Z}$ gates.
I am led to think that $\sqrt{X}$ injection is possible, with…
Daniele Cuomo
- 2,068
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1
vote
1 answer
Understanding errors in rotated surface code magic state injection
I am going over this paper by Lao, and I am trying to understand how they count the two-qubit errors that induce logical errors.
I am looking at the middle-type injection, which looks like this:
Now, they count which two-qubit errors change the…
Shoham Jacoby
- 302
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1
vote
1 answer
State injection in a surface code
I am reading this paper on lattice surgery by Dominic Horsman
et al, and am struggling to understand a simple method they put forward in their Figure 8(a)(b)(c) to inject an arbitrary state into a planar surface.
The protocol they put forward is…
quantumctrl
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1
vote
1 answer
Post selection during hook injection
I was reading the paper about "Cleaner magic states with hook injection"1, which is really cool, and I get technically, but it is unclear in which stages do you perform the post-selection.
Alternatively, which measurements along the way would cause…
Yaniv Kurman
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1
vote
0 answers
Catalytic Hadamard Injection
This is how one can inject a Hadamard gate.
Can this also by transformed to a catalytic version? I.e. where the magic state remains preserved into the $|+\rangle$ state.
Daniele Cuomo
- 2,068
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1
vote
1 answer
How to inject a $Y^{\frac{1}{4}}$ gate into a circuit
I need to perform a controlled-$H$ gate, which is non-Clifford.
Its standard decomposition is
$$Y^{-\frac{1}{4}}_b\cdot CX^{\phantom{\frac{1}{4}}}_{a,b}\cdot Y^{\frac{1}{4}}_b.$$
By means of some auxiliary qubits, one should be able to inject a…
Daniele Cuomo
- 2,068
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- 25
0
votes
1 answer
Li injection in the surface code
I am trying to reproduce Li-injection method in the surface code (from here).
Specifically, I start with d1=7 surface code, perform the injection + two rounds of stabilizer measurements, and check the "acceptance rate". If there were no errors, I…
David Dentelski
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2 answers
Help finding mistake when modifying $T$ injection protocols
I am a little confused about where I am going wrong when computing the action of the following circuit:
My understanding is that the CNOT gate acts on the second qubit as a control and the first qubit as a target. However, we can flip the CNOT so…
am567
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0
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Postponing post-processing through state injection protocols
I am trying to build a $T$ injecton protocol and study how an $X^b$ post-process, supposed to happen before the protocol, behaves if delayed after the protocol.
The first example comes from the combination of the two protocols of figure 2. from this…
Daniele Cuomo
- 2,068
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0
votes
2 answers
Is this kind of $T$ injection correct?
I found the protocol in figure on internet, without proof.
Here, $|\omega\rangle = TH|0\rangle$.
It is refered as catalytic injection. I doubt its correctness on the second qubit as it outputs $|\omega\rangle$, no matter what $|\varphi\rangle$…
Daniele Cuomo
- 2,068
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