# What is more important, minimizing the number of gates, or the number of qubits?

I am new to the quantum world, and I have 2 circuits that measure cosine similarity between 2 binary vectors. One uses a swap test, the other uses something called a hyper-state generation procedure.

So the first circuit needs a lower number of basic gates (i.e. CX and U gates) but it requires double the size of qubits compared to the second circuit.

So my question is, which would introduce more noise while running on a real quantum computer, the circuit with a high number of qubits, or the circuit with a high number of gates?

For the NISQ-era, it probably depends on the quantum computing platform you're using.

Using more qubits makes you more susceptible to SPAM (state preparation and measurement) errors, while using more gates can introduce more errors if your gate fidelity is low. Hence, a platform with good initialization and readout but worse 1- and 2-qubits gates would probably have less noise using the qubit-intensive technique, while a platform with high fidelity 1- and 2-qubits but worse initialization and measurement would probably have less noise using the gate-intensive technique.

However as Ohad said, there's also practical concerns about how many qubits you need because current realizations of quantum computers are limited in the number of available qubits.

• So is there a problem with using state preparation and measurements? does this introduce more errors? Commented Aug 10, 2022 at 18:06
• In physical realizations of QC, yes, sometimes it's hard to get all of your qubits to start in $|0\rangle$ and sometimes when you try to readout a state like $|1\rangle$ and you'll measure $|0\rangle$. These are preparation and measurement errors, respectively. Commented Aug 10, 2022 at 21:31

Basically, more gates usually implies on larger circuit depth - the deeper the circuit is - it will take more time to run it - and we’ll get more noise (due to decoherence that evolves with time). I used the word “usually” because there can be gates acting in parallel and therefore not adding depth - that depends on the design of the circuit and on the properties of the quantum hardware.

As far as I know, the problem with using more qubits is the lack of qubits in today’s quantum computers. I assume that using more qubits (if available) for creating “shallower” circuits is preferable in terms of noise.