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# Questions tagged [hamiltonian]

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### Efficient method to find square root of a Hamiltonian

I'm working with a Hamiltonian $H$ represented as a linear combination of Pauli strings: $$H = \sum_j \alpha_j P_j,$$ where $P_j \in \{I, X, Y, Z\}^{\otimes n}$ are tensor products of Pauli matrices ...
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### Is a molecular Hamiltonian defined uniquely? or Where do differences in pennylane Hamiltonians come from?

For a fixed fermion-qubit mapping, basis, active space, and geometry, is the electronic structure Hamiltonian uniquely defined? I would think so, since for a given basis the one- and two-body ...
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### Is there a general method for calculating expectation values for time-dependent wavefunctions?

Is there a general method for calculating expectation value? I have a workshop question, and I'm sure what a good process to follow is. It is given that $$|\psi(t = 0)\rangle = |0\rangle\,,\tag{1}$$ ...
84 views

### How to combine measurement of each term in Hamiltonian $H = aH_1 + bH_2$ to get final results?

I have a Hamiltonian $$H = aH_1 + bH_2\,,\tag{1}$$ with $a$ and $b$ being coefficients, and I want to apply each term/evolution separately, then recombine the measurement results to get the result for ...
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### Understanding circuit to Hamiltonian embedding where we do not have a separate clock register

I am trying to understand the clock construction given in this paper, to embed a circuit to a Hamiltonian, which doesn't need to access a separate clock register. The construction, at a high level, ...
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1 vote
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### How are edge weights "loaded" in the problem hamiltonian when solving TSP with QAOA?

I've come across several of the QAOA tutorials, and yet I'm afraid I haven't found any explanation on this. According to the Qiskit tutorial on QAOA, the cost function for the target problem has a ...
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1 vote
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### Problems with Exact Diagonalization Implementation in Quantum System Evolution

I've been trying to implement exact diagonalization to study the time evolution of quantum states and subsequently compute local magnetizations. I have written functions for evolving the state and ...
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### Intuitive explanation on dependence of Hamiltonian simulation on norm?

Suppose I have two Hamiltonians, $H_1$ and $H_2$, that I want to simulate for time $T$. If $\|\|H_1\|\|>\|\|H_2\|\|$, why is it more costly to simulate $H_1$ compared to $H_2$? Is there an ...
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### How can I implement a Hamiltonian which is sum of tensored pauli operators on qiskit?

I am working with a Tight Binding Hamiltonian with N sites and one orbital at each site in a closed chain. I have converted the fermionic expression to a spin expression using Jordan Wigner ...
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### Backwards evolution arising from changing evolution picture

This may not be a question strictly belonging to the realm of quantum computing, but it does arise from problems in QI and optics, so I choose to ask it here. Suppose $A$ is a Hermitian operator ...
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1 vote
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### Hamiltonian of Bose-Hubbard model

In https://medium.com/qiskit/introducing-bosonic-qiskit-a-package-for-simulating-bosonic-and-hybrid-qubit-bosonic-circuits-1e1e528287bb , could anyone explain the rationale behind the use of ...
1 vote
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### Excplicit Description of Hamiltonians?

The wikipedia article for Hamiltonian simulation lists two complexities: gate and query complexity. These two types of complexity refer to two different things; gate complexity is the asymptotic ...
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### Why does the quantum walk operator only have two eigenvectors?

In Child's paper on the relationship between discrete and continuous quantum walks, he makes the following claim. Although he provides a proof after this: I don't understand how the walk operator ...
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