Questions tagged [state-injection-model]
For questions regarding quantum computation by state injection.
10 questions
1
vote
0
answers
75
views
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,...
- 55
1
vote
1
answer
218
views
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 ...
- 11
0
votes
2
answers
83
views
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 ...
- 739
2
votes
2
answers
107
views
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 ...
- 2,058
1
vote
1
answer
108
views
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.
...
- 57
1
vote
0
answers
41
views
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.
- 2,058
0
votes
1
answer
149
views
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 ...
- 2,058
0
votes
2
answers
303
views
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 $|\...
- 2,058
1
vote
1
answer
75
views
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 ...
- 2,058
21
votes
1
answer
555
views
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 ...
- 1,097