updates MPO class to allow construction of arbitrary Pauli Hamiltonians

CHANGELOG.md

@@ -11,6 +11,7 @@ This project adheres to [Semantic Versioning], with the exception that minor rel
 
 ### Added
 
+- updates MPO class to allow construction of arbitrary Pauli Hamiltonians ([#216]) ([**@aaronleesander**, **@thilomueller**])
 - added faster paths for TDVP dense effective Hamiltonian ([#280]) ([**@aaronleesander**])
 - added more stable and faster SVD and QR implementation ([#278]) ([**@aaronleesander**])
 - TDVP now utilizes a dense Hamiltonian for small tensor sizes (adjusted by global variable DENSE_THRESHOLD) ([#261]) ([**@aaronleesander**])
@@ -51,6 +52,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 
 <!-- PR links -->
 
+[#216]: https://github.com/munich-quantum-toolkit/yaqs/pull/216
 [#290]: https://github.com/munich-quantum-toolkit/yaqs/pull/290
 [#280]: https://github.com/munich-quantum-toolkit/yaqs/pull/280
 [#278]: https://github.com/munich-quantum-toolkit/yaqs/pull/278
@@ -65,6 +67,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 
 [**@denialhaag**]: https://github.com/denialhaag
 [**@aaronleesander**]: https://github.com/aaronleesander
+[**@thilomueller**]: https://github.com/thilomueller
 
 <!-- General links -->
 

docs/examples/analog_simulation.md

@@ -19,16 +19,39 @@ In this example, an Ising Hamiltonian is initialized as an MPO, and an MPS state
 A noise model is applied, and simulation parameters are defined for an analog simulation using the Tensor Jump Method (TJM).
 After running the simulation, the expectation values of the $X$ observable are extracted and displayed as a heatmap.
 
-Define the system Hamiltonian
+Define the system Hamiltonian. We show 3 possible ways to define the Ising Hamiltonian as an example.
 
 ```{code-cell} ipython3
 from mqt.yaqs.core.data_structures.networks import MPO
 
 L = 3
 J = 1
 g = 0.5
+
+# Method 1: Pre-implemented Hamiltonians
+H_0 = MPO.ising(L, J, g)
+
+# Method 2: Same Ising Hamiltonian built via the generic Pauli interaction interface
+H_0 = MPO.hamiltonian(
+    length=L,
+    two_body=[(-J, "Z", "Z")],
+    one_body=[(-g, "X")],
+    bc="open",
+)
+
+# Method 3: Explicit Pauli-string expansion
+terms = []
+
+# -J Σ Z_i Z_{i+1}
+for i in range(L - 1):
+    terms.append((-J, f"Z{i} Z{i+1}"))
+
+# -g Σ X_i
+for i in range(L):
+    terms.append((-g, f"X{i}"))
+
 H_0 = MPO()
-H_0.init_ising(L, J, g)
+H_0.from_pauli_sum(terms=terms, length=L)
 ```
 
 Define the initial state

docs/examples/transmon_emulation.md

@@ -32,16 +32,13 @@ w_r = 4/(2*np.pi)
 alpha = 0
 g = 2/(2*np.pi)
 
-H_0 = MPO()
-H_0.init_coupled_transmon(
-    length=length,
+H_0 = MPO.coupled_transmon(length=length,
     qubit_dim=qubit_dim,
     resonator_dim=resonator_dim,
     qubit_freq=w_q,
     resonator_freq=w_r,
     anharmonicity=alpha,
-    coupling=g  # T_swap = pi/2g
-)
+    coupling=g  # T_swap = pi/2g)
 ```
 
 ## Define the initial state