corrected (#2637)

docs/source/guide/pec-1-intro.md

@@ -102,7 +102,7 @@ We now show how to use PEC to reduce this error.
 
 +++
 
-## Appling probabilistic error cancellation (PEC)
+## Applying probabilistic error cancellation (PEC)
 
 +++
 

docs/source/guide/pec-3-options.md

@@ -196,7 +196,7 @@ assert depolarizing_h_rep == h_rep
 
 It is possible to define a qubit-independent {class}`.OperationRepresentation` by setting the option `is_qubit_dependent` to `False`.
 
-In this case, a signle {class}`.OperationRepresentation` representing a gate acting on some arbitrary qubits can be used to mitigate
+In this case, a single {class}`.OperationRepresentation` representing a gate acting on some arbitrary qubits can be used to mitigate
 the same gate even if acting on different qubits.
 
 ```{code-cell} ipython3

docs/source/guide/pec-4-low-level.md

@@ -174,7 +174,7 @@ executor = mitiq.Executor(batched_execute, max_batch_size=100)
 We execute all the auxiliary circuits generated in the previous section to obtain a list of noisy expectation values.
 
 ```{code-cell} ipython3
-noisy_expecation_values = executor.evaluate(
+noisy_expectation_values = executor.evaluate(
     sampled_circuits, 
     force_run_all=False,  # Set True if shot noise is present in quantum results.
 )
@@ -190,15 +190,15 @@ only once by setting `force_run_all=False`.
 independence of the quantum results.*
 
 ```{code-cell} ipython3
-print(f"{len(noisy_expecation_values)} noisy expectation values efficiently evaluated by executing only {len(executor.quantum_results)} unique circuits.")
+print(f"{len(noisy_expectation_values)} noisy expectation values efficiently evaluated by executing only {len(executor.quantum_results)} unique circuits.")
 ```
 
 Equivalently, but less efficiently, we could have done as follows:
 
 ```{code-cell} ipython3
-noisy_expecation_values_direct = batched_execute(sampled_circuits)
+noisy_expectation_values_direct = batched_execute(sampled_circuits)
 
-assert noisy_expecation_values_direct == noisy_expecation_values
+assert noisy_expectation_values_direct == noisy_expectation_values
 ```
 
 ### Estimate the ideal expectation value from the noisy results
@@ -212,7 +212,7 @@ the noisy auxiliary expectation values, after scaling them by the corresponding
 ```{code-cell} ipython3
 # Scale noisy results by one-norm coefficient and by sampled signs
 unbiased_samples = [
-  one_norm * value * sign for value, sign in zip(noisy_expecation_values, sampled_signs)
+  one_norm * value * sign for value, sign in zip(noisy_expectation_values, sampled_signs)
 ]
 
 # Estimate ideal expectation value