4
votes
Accepted
40th Question IBM Sample test
Qubits are initially in the ∣0⟩ state. The Rz gate, which is a rotation around the z-axis, only changes the phase of the qubit states and not the probabilities of measuring 0 or 1 in the computational ...
- 618
3
votes
Complexity of translation between Measurement Based and Circuit Based with Error Correction
Accourding to Browne et al. it seems the translation from GBQC to MBQC is of size O(N^3) and from MBQC to GBQC the translation is of size ...
3
votes
pennylane: How to carry out MB rotation without CB rotation?
Good question - let me give it a shot. First of all, note that the application of a single-qubit gate before a measurement in the computational basis is mathematically the same as doing a projective ...
- 33
3
votes
pennylane: How to carry out MB rotation without CB rotation?
What an interesting observation 😄
I work on the PennyLane team so hopefully I can help you.
While indeed, the demo does use RZ in the MBQC part, it is not a gate that mandatorily needs to be added in ...
3
votes
Accepted
Equivalence of circuits in measurement-based QC
In step 2, you are doing two measurements, $X$ on qubit 1 and $X$ on qubit 2. To move to step 3, you need to bring these measurements earlier in the circuit, which means updating what they look like ...
- 60.5k
2
votes
Equivalence of circuits in measurement-based QC
If $AU \equiv UB$ then $M_{A} \cdot U \equiv U \cdot M_B$.
Measuring $B$ before $U$ is equivalent to measuring $A$ after $U$ if $U$ conjugates $B$ into $A$.
The transition from step 2 to step 3 is ...
- 40.6k
2
votes
Complexity of translation between Measurement Based and Circuit Based with Error Correction
Stabilizer simulation can be done in $O(gq + rq^2)$ time, where $g$ is the total number of operations, $q$ is the number of qubits, and $r$ is the number of measurements that needed random results. ...
- 40.6k
2
votes
Accepted
Fault tolerance of MBQC
In "Fault-tolerant quantum computation with cluster states"[1], Nielsen and Dawson (2005) studied fault-tolerance in MBQC with cluster states. They proved threshold theorems similar to the ...
- 11.5k
2
votes
How does measurement based quantum computing (MBQC) behave under error propagation?
Because of the deferred measurement principle, any circuit where measurement amplified errors could be translated into a circuit where unitary operations amplified errors. Therefore measurements can't ...
- 40.6k
2
votes
Accepted
Are close states still close after measurement (regarding trace distance)?
You can't say anything. Consider for example
$$\begin{align}
|\psi_1\rangle = \sqrt{\epsilon}|00\rangle + \sqrt{1-\epsilon}|11\rangle \\
|\psi_2\rangle = \sqrt{\epsilon}|01\rangle + \sqrt{1-\epsilon}|...
- 2,853
1
vote
Removing ancilla qubit from circuit with Hadamard test controlled-Z gate
For special unitaries $U$ you can use the standard decomposition of a controlled-$U$.
You can then try to move backward in the circuit the conditioned gate $Z$. According to the deferred measurement ...
- 2,030
1
vote
How to get the surviving stabilisers of a fusion network
Equation 4 of of the paper defines $S=Z_R(F)$.
The generators of $R$ and $F$ are defined by the network and are given in Figure 5c.
The rest is some linear algebra to get $S$.
I was able to verify ...
- 2,242
1
vote
Accepted
Fault-tolerant correlated measurement on logical qubits
This approach will get you the correct measurement result, but will also collapse the encoded state.
Consider first the case with no underlying stabilizer code.
You start with your Bell pair $\left|00\...
- 665
1
vote
Can you apply a CNOT gate on qubits in MBQC that aren´t next to each other?
Maybe you should clarify exactly what you mean by MBQC, because to me this seems like a trivial "of course you can".
For example, a CNOT can be implemented up to Pauli tracking by this ...
- 40.6k
1
vote
Accepted
Hadamard Gate on Cluster States
Your calculation shows that you are doing the right thing for a single step. You just don't seem to be carrying it through for a set of 4 steps. Overall, you should be getting
$$
(X^{m_4}HS)(X^{m_3}HS)...
- 60.5k
1
vote
Is the topological cluster state a single-shot stabilizer code?
I believe this is just a matter of definition, in some sense the topological state is a single-shot code.
One difference between the topological cluster state and single-shot 3D codes is that the size ...
- 1,714
1
vote
Accepted
Using Pymatching to decode lattice surgery process
There's nothing fundamentally different about getting pymatching to decode lattice surgery instead of memory. Make a stim circuit describing the exact operations that implement the surface codes being ...
- 40.6k
1
vote
Accepted
Which feedback is *necessary* for surface-code based and measurement based quantum computing?
That's right, a surface code computation that only performs Clifford gates can be performed without any feedback. Tracking the errors is sufficient to correct them. The corrections can be done ...
- 40.6k
1
vote
Accepted
perform a SWAP measurement using local operations and classical feedback
Measure SWAP from 7 CNOTs, linear connectivity, ancilla outside:
(Note: improved this to not need any feedback anymore, and to just generally be cleaner.)
- 40.6k
1
vote
Accepted
Is this generalized 2D cluster state still a universal resource?
TLDR: Yes, it's universal. If you only measure on one of the two registers, No.
Longer answer...
Let's deal with the measuring just one register first. So we're doing nothing with the other register. ...
- 60.5k
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