# Stuck on Codercise I.5.4 **URL:** \ **Category:** Codebook\ **Created:** [February 24, 2024, 6:35am UTC](https://discuss.pennylane.ai/t/stuck-on-codercise-i-5-4/4151 "2024-02-24T06:35:22Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![Sfdq](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/sfdq/32/2042_2.png) [@Sfdq](https://discuss.pennylane.ai/u/Sfdq)\ **Post date:** [February 24, 2024, 6:35am UTC](https://discuss.pennylane.ai/t/stuck-on-codercise-i-5-4/4151/1 "2024-02-24T06:35:22Z")
Hello, I was able to simplify the circuit as follows: ![image](https://canada1.discourse-cdn.com/flex012/uploads/pennylane/original/2X/c/cc01e4ad63bce14bd651376f12ddcc9727940fc4.png) However, I received the following error: Incorrect: Your resulting output doesn’t look quite right. Incorrect: more than 1 T gates are needed. Incorrect: the optimal depth of the circuit is not 4. Incorrect: the optimal T-count of the circuit is not 1. Incorrect: the optimal T-depth of the circuit is not 1. In wire 0: the pairs of H-gates, T-gates, and adjoint T-gates cancel each other, and one H-gate remains In wire 1: the pair of H-gates cancel each other and the 2 pairs of T-gates become S-gates, one T-gate, and H-gate remain In wire 2: the pair of H-gates cancel each other, the 2 pairs of adjoint T-gates become adjoint S-gates, and one H-gate remains I am not sure where the simplification went wrong. ---
**Author:** ![AvanishM](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/avanishm/32/2326_2.png) [@AvanishM](https://discuss.pennylane.ai/u/AvanishM)\ **Post date:** [February 25, 2024, 8:44pm UTC](https://discuss.pennylane.ai/t/stuck-on-codercise-i-5-4/4151/2 "2024-02-25T20:44:22Z")
The simplification went wrong because you can only cancel out the pairs of gates when they are right next to each other. For example H T H cannot be simplified to T, but H H T can be. This is because the operators do not commute: you cannot generally swap the ordering of matrix transformations around. Now with this I’m sure your simplification will be very different. ---
**Author:** ![Sfdq](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/sfdq/32/2042_2.png) [@Sfdq](https://discuss.pennylane.ai/u/Sfdq)\ **Post date:** [February 26, 2024, 11:09am UTC](https://discuss.pennylane.ai/t/stuck-on-codercise-i-5-4/4151/3 "2024-02-26T11:09:19Z")
Yes, my updated simplification is now different. I forgot about the non-commutativity, looks like I need to revise the basics. Thank you for your explanation. ---
**Author:** ![isaacdevlugt](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/isaacdevlugt/32/1159_2.png) [@isaacdevlugt](https://discuss.pennylane.ai/u/isaacdevlugt)\ **Post date:** [February 26, 2024, 9:50pm UTC](https://discuss.pennylane.ai/t/stuck-on-codercise-i-5-4/4151/4 "2024-02-26T21:50:08Z")
Hey @Sfdq! Welcome to the forum 🙂 If you have any further questions or concerns, write back! ---
**Author:** ![GianAsara](https://avatars.discourse-cdn.com/v4/letter/g/c68b51/32.png) [@GianAsara](https://discuss.pennylane.ai/u/GianAsara)\ **Post date:** [May 10, 2024, 10:42pm UTC](https://discuss.pennylane.ai/t/stuck-on-codercise-i-5-4/4151/5 "2024-05-10T22:42:35Z")
Hi, I am also stuck with the error: “Error: Hadamard: wrong number of wires. 3 wires given, 1 expected.” I guess it is something related to the optimisation and the reduction of the number of Hadamard gates, but I really don’t see it. Any advice? Thanks, Gian Here is my circuit: ```auto dev = qml.device('default.qubit', wires=3) @qml.qnode(dev) def too_many_ts(): """You can implement the original circuit here as well, it may help you with testing to ensure that the circuits have the same effect. Returns: array[float]: The measurement outcome probabilities. """ qml.Hadamard(wires=[0,1,2]) qml.T(wires=[0,1]) qml.adjoint(qml.T(wires=2)) qml.T(wires=0) qml.Hadamard(wires=[0,1,2]) qml.adjoint(qml.T(wires=[0,2])) qml.T(wires=1) qml.adjoint(qml.T(wires=[0,2])) qml.T(wires=1) qml.T(wires=1) qml.adjoint(qml.T(wires=2)) qml.T(wires=1) qml.Hadamard(wires=[0,1,2]) return qml.probs(wires=[0, 1, 2]) @qml.qnode(dev) def just_enough_ts(): """Implement an equivalent circuit as the above with the minimum number of T and T^\dagger gates required. Returns: array[float]: The measurement outcome probabilities. """ ################## # YOUR CODE HERE # ################## # IMPLEMENT THE CIRCUIT, BUT COMBINE AND OPTIMIZE THE GATES # TO MINIMIZE THE NUMBER OF TS qml.Hadamard(wires=[0,1,2]) qml.S(wires=0) qml.T(wires=1) qml.adjoint(qml.T(wires=2)) qml.Hadamard(wires=[0,1,2]) qml.adjoint(qml.S(wires=[0, 2])) qml.S(wires=1) qml.S(wires=1) qml.adjoint(qml.T(wires=2)) qml.Hadamard(wires = [0, 1, 2]) return qml.probs(wires=[0, 1, 2]) ################## # YOUR CODE HERE # ################## # FILL IN THE CORRECT VALUES FOR THE ORIGINAL CIRCUIT original_depth = 8 original_t_count = 13 original_t_depth = 6 # FILL IN THE CORRECT VALUES FOR THE NEW, OPTIMIZED CIRCUIT optimal_depth = 6 optimal_t_count = 3 optimal_t_depth = 2 ``` ---
**Author:** ![CatalinaAlbornoz](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/catalinaalbornoz/32/1196_2.png) [@CatalinaAlbornoz](https://discuss.pennylane.ai/u/CatalinaAlbornoz)\ **Post date:** [May 14, 2024, 12:04am UTC](https://discuss.pennylane.ai/t/stuck-on-codercise-i-5-4/4151/6 "2024-05-14T00:04:40Z")
Hi @GianAsara, What the error is saying is that you’re trying to apply the Hadamard to 3 qubits at the same time but it can only be applied to one at a time. So `qml.Hadamard(wires=[0,1,2])` should actually be split into three lines if you want to apply it to the three wires. I hope this helps!