Suppose we are trying to solve Simon's problem with n=4. We ran 4 iterations of Simon's algorithm and obtained 0000, 1101, 1010, and 0110. What is the secret string s? (Assume that s is not the all-zero string 0000.)

1110

To solve Simon's problem, we need to find the secret string s. In Simon's algorithm, we run the algorithm multiple times, obtaining different bitstrings as results. Each bitstring provides a linear equation that forms a system of equations when combined.

In this case, we have run Simon's algorithm for n=4 and obtained the following bitstrings:
- 0000
- 1101
- 1010
- 0110

To find the secret string s, we need to look for a pattern in these bitstrings. Specifically, we are interested in finding a hidden string s such that for any x and y (not equal to each other) that satisfy the equation (x ⊕ s) = y, the bitstrings obtained by Simon's algorithm will produce the same y.

Let's examine these bitstrings and look for a common pattern. We can group the bitstrings by their corresponding outputs:
- 0000
- 1101
- 1010
- 0110

By comparing the bit positions, we can observe that the first and last bits are always the same (0 and 1 respectively). This means that the first and last bits of the secret string s are also 0 and 1 respectively.

Now, let's focus on the second and third bits. We can see that they differ across the bitstrings. This implies that the secret string s has a 1 in the second or third bit position.

Considering the bitstrings, we can't find a consistent pattern across all of them. This suggests that there might be multiple possible secret strings for this problem.

To find the specific secret string s, we need to use the information obtained from the bitstrings and continue the analysis of any additional bit positions. However, since it is not explicitly provided in the given information, it is not possible to determine the exact secret string s.