Gate-based quantum computers are similar to classical computers in that you can decompose any operation into a combination of a small set of universal gates (li

Gate-based quantum computers are similar to classical computers in that you can decompose any operation into a combination of a small set of universal gates (like single-bit NOT and two-bit NAND for classical computers). Typically you combine arbitrary single-qubit rotations along the X, Y, Z axes with a two-qubit gate like CNOT or iSWAP to obtain a full set of universal gates. You can then decompose your algorithm into these gates for running it, which is often doable efficiently (e.g. the Grover algorithm can be implemented easily using the gate set described above). You can also efficiently implement any classical gate operations on a quantum computer using a set of universal, reversible gates (e.g. single qubit NOT and classical CNOT). Finally, you need to read qubit states so you have to provide a readout of individual qubits, typically you implement the projection operator along the Z axis. Now, for each of these operations you can characterize your error rate. For the processor I built during my PhD those error rates were around 9 % for qubit readout, 10 % for the universal two-qubit gate and around 1 % for single qubit gates. These errors stemmed from qubit decoherence (dephasing and relaxation), limitations of the readout and limitations of the signal precision for the manipulation. Errors are often different for each qubit and depend on the operation and the state the qubits are in (there’s crosstalk and different decoherence depending on the qubit frequencies as well), but you can usually give an upper bound for the error. Systems today are much better already btw. Given the different error rates you can very easily see how much error you will accumulate during a given gate sequence and what algorithms you will be able to run. We were for example able to perform the 2-qubit Grover algorithm with more than 50 % fidelity, which demonstrated quantum speed up for that very simple case. For a small subset of your qubits you can also perform quantum state tomography and quantum process tomography to statistically characterize their state and the quantum evolution they went through (including errors and decoherence), which allows you to characterize the errors in your system experimentally in a more precise way. Again this technique is limited by the fidelity of single qubit operations and readout, but it can nevertheless provide very good data for error analysis. For larger qubit systems tomography becomes intractable but there are other techniques that can allow you to characterize errors for these systems as well (e.g. randomized benchmarking). So please stop telling people that it’s not possible to quantify errors, it is simply not true. Quantum computers are like classical computers in the sense that they obey the laws of physics and have various error sources that can be measured and characterized. The precision that’s required is higher than for classical computers but there’s no fundamental reason why quantum computers can’t work, it’s just a though engineering problem.