4 ms·

The core argument here, concerning the number of variables that need to be manipulated, isn't very clear to me - I can't tell if that's because it's an unclear

The core argument here, concerning the number of variables that need to be manipulated, isn't very clear to me - I can't tell if that's because it's an unclear argument in general, or if the author tried to simplify it for laypeople to the extent that it became unconvincingly vague for people who know a thing or two about the subject area. Given the status of the author, I'm willing to give him the benefit of the doubt (and also assume that some clarity was lost in translation). Here's an easier-to-follow argument I've heard before (also simplified for laypeople) that might be close enough to the one the author intends to make to be useful: Quantum algorithms are supposed to be much more efficient than conventional algorithms at certain kinds of tasks. That efficiency is calculated with the assumption that each system starts in a state where it's prepared to execute the algorithm. For conventional computers, that makes sense for a number of reasons (e.g. data/program input is linear). For quantum computers, this assumption doesn't necessarily make sense because it takes a significant amount of work (in terms of measurements, etc.) to get the system (the machinery and physical representation of the initial data) into the right quantum state. In fact, the amount of work required scales horribly with the size of the input (in terms of qubits). If you think of those state preparation steps as part of the cost of the algorithm, the quantum algorithms won't, in general, outperform the classical ones. I've been out of the quantum computation loop for nearly a decade, so I have no idea whether that's a fair way of presenting the problem, but hopefully it helps someone understand the claims being made in the article.

ThePhysicist 8y ago
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.
greeneggs 8y ago
The argument here is nonsensical. For example, "With what exactitude must, say, the square root of 2 (an irrational number that enters into many of the relevant quantum operations) be experimentally realized? Should it be approximated as 1.41 or as 1.41421356237? Or is even more precision needed? Amazingly, not only are there no clear answers to these crucial questions, but they were never even discussed!" This is completely wrong. Of course the field has studied this problem; people aren't idiots. But your concern is also wrong. Preparing the initial state is easy; quantum algorithms generally start in the all-0s state. Even quantum devices like the D-Wave machine, for which there is considerable skepticism about its workings and power, can easily be initialized in the all-0s state. (With error correction, one needs to prepare the encoded all-0s state, which is indeed difficult to prepare. But in principle it is doable.)
- resource0x 8y ago
  Doable in principle? My impression was that the author doesn't argue against this. He claims it's unlikely to be doable in practice. That's the whole point of the article.
  - danishcrows 8y ago
    His argument is pretty poor. He refers to the threshold theorem which does rely on certain assumptions, and then claims that these assumptions cannot be satisfied in practice. This is apparently because "continuous quantities can be neither measured nor manipulated exactly", however this ISN'T an assumption of the threshold theorem. In fact the whole premise of the threshold theorem is that they can't. It's a straw man argument, the same one he's been making since the 1990s.
gitgud 8y ago
> unconvincingly vague for people who know a thing or two about the subject area. I feel like this phrase could be applied to many things I come across... unconvincingly vague

ThePhysicist 8y ago

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.

greeneggs 8y ago

The argument here is nonsensical. For example, "With what exactitude must, say, the square root of 2 (an irrational number that enters into many of the relevant quantum operations) be experimentally realized? Should it be approximated as 1.41 or as 1.41421356237? Or is even more precision needed? Amazingly, not only are there no clear answers to these crucial questions, but they were never even discussed!" This is completely wrong. Of course the field has studied this problem; people aren't idiots. But your concern is also wrong. Preparing the initial state is easy; quantum algorithms generally start in the all-0s state. Even quantum devices like the D-Wave machine, for which there is considerable skepticism about its workings and power, can easily be initialized in the all-0s state. (With error correction, one needs to prepare the encoded all-0s state, which is indeed difficult to prepare. But in principle it is doable.)

resource0x 8y ago
Doable in principle? My impression was that the author doesn't argue against this. He claims it's unlikely to be doable in practice. That's the whole point of the article.
- danishcrows 8y ago
  His argument is pretty poor. He refers to the threshold theorem which does rely on certain assumptions, and then claims that these assumptions cannot be satisfied in practice. This is apparently because "continuous quantities can be neither measured nor manipulated exactly", however this ISN'T an assumption of the threshold theorem. In fact the whole premise of the threshold theorem is that they can't. It's a straw man argument, the same one he's been making since the 1990s.

gitgud 8y ago

> unconvincingly vague for people who know a thing or two about the subject area. I feel like this phrase could be applied to many things I come across... unconvincingly vague