For an HHL algorithm implemented exactly as depicted in Figure 2 of this paper by Dutta et. al (https://arxiv.org/abs/1811.01726), how do I go about changing the eigenvalues that they use? Obviously, if the eigenvalues are changed, then the matrix A should be changed appropriately, but this is more of a question about how the controlled y rotations change.

In this paper, if the eigenvalues are set equal to $\lambda = [1\ 2\ 4\ 8]$, then the controlled y rotations are implemented from left to right with the y rotations being set equal to $R_y(\frac{8\pi}{\lambda_1 2^{r}})=R_y(\frac{8\pi}{2^{r}})$, $R_y(\frac{8\pi}{\lambda_2 2^{r}})=R_y(\frac{4\pi}{2^{r}})$, $R_y(\frac{8\pi}{\lambda_3 2^{r}})=R_y(\frac{2\pi}{2^{r}})$, and $R_y(\frac{8\pi}{\lambda_4 2^{r}})=R_y(\frac{\pi}{2^{r}})$, respectively. Here, $r$ is an arbitrary integer whose value effects the accuracy of the final outcome. But now let's say that I want to change the eigenvalues to $\lambda = [1\ 3\ 4\ 8]$, would the y rotation corresponding to the second eigenvalue as well as the state defined as $|j_2\rangle$, be given by $R_y(\frac{8\pi}{\lambda_2 2^{r}})=R_y(\frac{8\pi}{3\times 2^{r}})$?

If this is not the case, what is the appropriate way to change this setup to get this calculation to work? Are there any swap gates that I need to add? Do I need to implement some sort of method to run this algorithm while increasing the number of clock qubits and if so, how do I do this?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.