# Hamiltonian Simulation with QSP
**URL:** https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020
**Category:** PennyLane Help
**Created:** [February 18, 2025, 4:18pm UTC](https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020 "2025-02-18T16:18:10Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@Shehara](https://discuss.pennylane.ai/u/Shehara)
#### Post date: [February 18, 2025, 4:18pm UTC](https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020/1 "2025-02-18T16:18:10Z")
Hello Everyone,
I am trying to perform Hamiltonian simulation by building a circuit using linear combinations of `cos(Ht)` and `-isin(Ht)` similar to the attached pic.
I was able to find phase factors for `cos(Ht)` using **pyqsp** and **QSPPACK** packages. However, I can’t seem to approximate `-isin(Ht)` as a polynomial (because its complex) and calculate phase factors using above packages.
I would like to know if there is any other alternative way to build `-isin(Ht)` by first approximating `-sin(Ht)` and multiply using a quantum gate to obtain `-isin(Ht)`.
Or, is there any other way to approximate `-isin(Ht)` using these packages.
Thanks a lot for the assistance!
P.S: This is my code for calculating phase factors using **pyqsp** package.
```auto
# Import relevant modules and methods.
import matplotlib.pyplot as plt
import numpy as np
from pyqsp import angle_sequence, response
from pyqsp.poly import PolyTaylorSeries
# Specify definite-parity target function for QSP.
func = lambda x: np.sin(3 * x)
polydeg = 3 # Desired QSP protocol length.
max_scale = 0.5 # Maximum norm (<1) for rescaling.
true_func = lambda x: max_scale * func(x) # For error, include scale.
"""
With PolyTaylorSeries class, compute Chebyshev interpolant to degree
'polydeg' (using twice as many Chebyshev nodes to prevent aliasing).
"""
poly = PolyTaylorSeries().taylor_series(
func=func,
degree=polydeg,
max_scale=max_scale,
chebyshev_basis=True,
cheb_samples=2 * polydeg,
)
# Compute full phases (and reduced phases, parity) using symmetric QSP.
(phiset, red_phiset, parity) = angle_sequence.QuantumSignalProcessingPhases(
poly, method="sym_qsp", chebyshev_basis=True
)
"""
Plot response according to full phases.
Note that `pcoefs` are coefficients of the approximating polynomial,
while `target` is the true function (rescaled) being approximated.
"""
response.PlotQSPResponse(
phiset, pcoefs=poly, target=true_func, sym_qsp=True, simul_error_plot=True
)
```
---
### Author:  [@CatalinaAlbornoz](https://discuss.pennylane.ai/u/CatalinaAlbornoz)
#### Post date: [February 19, 2025, 2:21am UTC](https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020/2 "2025-02-19T02:21:55Z")
Hi @Shehara ,
Unfortunately we’re not experts on the pyqsp nor QSPPACK packages here. We’re experts on PennyLane though, which has functionality for Quantum Signal Processing and QSVT. You can take a look at our tutorials on these topics [here](https://pennylane.ai/search?q=QSP&contentType=DEMO).
I hope these PennyLane tutorials can help you out.
---
### Author:  [@Guillermo\_Alonso](https://discuss.pennylane.ai/u/Guillermo_Alonso)
#### Post date: [February 19, 2025, 3:42am UTC](https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020/3 "2025-02-19T03:42:20Z")
To give you a little hint, apply an S gate after the first Hadamard, add a phase “i” in the black control 😉
---
### Author:  [@Shehara](https://discuss.pennylane.ai/u/Shehara)
#### Post date: [February 20, 2025, 3:59pm UTC](https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020/4 "2025-02-20T15:59:09Z")
Hi Catalina, Thank you so much for sharing the tutorials. I will go through them.
---
### Author:  [@Shehara](https://discuss.pennylane.ai/u/Shehara)
#### Post date: [February 20, 2025, 4:01pm UTC](https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020/5 "2025-02-20T16:01:13Z")
Thank you Guillermo, thanks a lot for the hint, yes indeed it applies the phase ‘i’, which is what I need. I will implement in Pennylane and see the results.
---
### Author:  [@CatalinaAlbornoz](https://discuss.pennylane.ai/u/CatalinaAlbornoz)
#### Post date: [February 20, 2025, 9:22pm UTC](https://discuss.pennylane.ai/t/hamiltonian-simulation-with-qsp/8020/6 "2025-02-20T21:22:28Z")
Let us know if you have any PennyLane questions @Shehara !