Add QRAM demonstration v1

[ShifanXu]

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Deployed at: 2026-07-22 20:11:14 UTC

[drdren]

Thanks so much @ShifanXu ! I'm excited to see this demo on the website!

[drdren]

I notice that you use "work wires" here but "qubits" in the Select-Only QROM section. I think it would be better to pick one convention because this demo compares resource cost using this term. This applies to print-outs too!

[ShifanXu]

sounds good. let's change to work wires!

[drdren]

OK!

[drdren]

To clarify, these gate counts look very low compared to the BBQRAM and Hybrid QRAM numbers. This is because we can't decompose fairly to the same gate set or is this correct? We should choose Select-Only QROM in this case?

[ShifanXu]

i think it is due to It such Multi-controlled gates have many ways of decomposition, where we cannot decompose fairly to the same gate set. Here in the code it may only report the gate count of these large mcx gates. We might only report the one/rwo qubti gate counts for bb/hybrid insteaf of select only.

[ShifanXu]

i also notice the current comparison mixes resource-counting conventions. The SelectOnlyQRAM circuit is synthesized using the concrete classical bitstrings, so controlled writes corresponding to zero-valued data bits are removed. For this dataset, only six two-address-controlled X operations remain; since the address has two qubits, these are six Toffoli gates, which decompose to 36 CNOTs and 42 T/T† gates before further optimization. BBQRAM, however, is effectively counted closer to a worst-case routing implementation. For a data-independent comparison, Select-only should instead be counted as (Nm=12) Toffoli operations in this example and all constructions should be decomposed under the same ancilla and Clifford+T assumptions. Since the demonstrated operation uses fixed read-only classical data, “Select-only QROM” is also the more precise terminology. Also, in terms of depth, this is a small case when n=2. BB qram performs better in terms of depth asymptotically, where its constant factor could be larger.

[drdren]

Wow! This is excellent! We should have this in the demo itself! I left a comment below, in the "Comparing the three constructions" section, where I believe this discussion ought to be.

[drdren]

Also, I asked Marcus offline. His opinion (did not dive into it) is that if you called for a decomposition down to CNOTs, then it probably did so (Toffolis become T + CNOTs, as you noted). qp.decompose also performs some simplification e.g., cancel inverses. We could maybe count those gates together to see if the PennyLane output matches expectations?

[ShifanXu]

Then I would say this is mostly due to the fact that the example we give here is too small (n=2), so that the asymptotic scaling of BB QRAM hasn't shown up, where almost no parallelism here for BB QRAM, while select only QRAM can use zero-valued data to simply.

[drdren]

Hi! We discussed the language of "work wires" vs "qubits". Which should we use here?

[drdren]

Suggested change

	# `https://arxiv.org/abs/1906.11340 <https://arxiv.org/abs/1906.11340>`__, 2019.
	# `arXiv:1906.11340 <https://arxiv.org/abs/1906.11340>`__, 2019.

[drdren]

This comment acts as a reminder for us to update closer to the publication date.

[drdren]

Hi @ShifanXu, I love this paragraph and it is necessary to explain the counter-intuitive result that SelectOnlyQRAM appears to be more efficient. But I think we can write a couple of extra sentences that comment on this more explicitly to avoid any confusion in the reader.

You elucidated in a comment above, but I'd love to see that elucidation in this paragraph! Something like: the numbers look worse because (i) SelectOnlyQROM is tailored for a specific problem while the other QRAM forms are for data-independent worst-case scenarios and (ii) this is a small problem; we expect BBQRAM and hybrid QRAM to exhibit more favourable constant-factor resource requires at larger problem sizes.

As an aside, do you believe it is possible to run those larger problems offline and just copy-paste the result here?

[drdren]

Suggested change

	# | :class:`~.pennylane.BBQRAM` | :math:`O(2^n+n+m)` | Active routing path | Large width; local |
	# | ``BBQRAM`` | :math:`O(2^n+n+m)` | Active routing path | Large width; local |

[drdren]

Suggested change

	# | :class:`~.pennylane.HybridQRAM` | :math:`O(2^{n-k}+n+m)` | Select over | Tunable interpolation |
	# | ``HybridQRAM`` | :math:`O(2^{n-k}+n+m)` | Select over | Tunable interpolation |

The formatting did not work out.

[drdren]

Suggested change

	# | :class:`~.pennylane.SelectOnlyQRAM` | :math:`O(n+m)` | :math:`O(2^n m)` | Minimal width; |
	# | ``SelectOnlyQRAM`` | :math:`O(n+m)` | :math:`O(2^n m)` | Minimal width; |

[drdren]

OK, do you want to change the terminology to be Select Only QROM here and in all the other places? I just highlighted this place.

[drdren]

Should we change this to select-only QROM too?

[drdren]

Thank you so much @ShifanXu , I enjoyed reading your commentary! I left a few minor comments. The biggest item (which I elaborated on in a comment below) is that we should explicitly comment on why SelectOnlyQROM incorrectly appears to be the cheapest option. As an aside, I am happy to change the language to SelectOnlyQROM; just let me know where.