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 ...
Dr. Eyal Cornfeld's user avatar
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 ...
Buskruid's user avatar
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 ...
Guillermo Alonso's user avatar
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 ...
DaftWullie's user avatar
  • 58.1k
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 ...
Craig Gidney's user avatar
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. ...
Craig Gidney's user avatar
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 ...
Egretta.Thula's user avatar
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\...
AG47's user avatar
  • 476
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 ...
Craig Gidney's user avatar
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)...
DaftWullie's user avatar
  • 58.1k
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 ...
Peter-Jan's user avatar
  • 1,529
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 ...
Craig Gidney's user avatar
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 ...
Craig Gidney's user avatar
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.)
Craig Gidney's user avatar
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. ...
DaftWullie's user avatar
  • 58.1k

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