# Questions tagged [hamiltonian]

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I would like to use a knapsack problem formulation based on Lucas paper. Namely, I try to implement the following math formula for Hamiltonian $H =H_A + H_B$, where $$H_{B} = -B\sum_{i=1}^{n}v_{i}x_{i}... 2 votes 0 answers 36 views ### 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, ... 0 votes 0 answers 33 views ### How could I get this lemma about stoquastic hamiltonian in the paper "Complexity of stoquastic frustration-free Hamiltonians" In the paper Complexity of stoquastic frustration-free Hamiltonians, I was confused about the derivation of Lemma 4.5: How could we get \delta Tr(O(I-\Pi_a)) \leq Tr(OH_a) given that \delta (I-\... 1 vote 0 answers 75 views ### Algorithm for finding the appropriate rotating frame Hamiltonian? Context Consider an N-level Hamiltonian with energies \omega_1...\omega_N with coupling drives at frequencies f_{i,j} which couple the i and j-th levels (not necessarily resonantly, so f_{i,... 1 vote 1 answer 40 views ### 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 ... 1 vote 0 answers 35 views ### 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 ... 1 vote 0 answers 18 views ### 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 ... 2 votes 2 answers 100 views ### 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 ... 2 votes 0 answers 17 views ### 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 ... 1 vote 0 answers 71 views ### 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 1 answer 71 views ### 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 ... 2 votes 1 answer 39 views ### Can a Hamiltonian of a tripartite system map an product state into a product state? Suppose we have a finite dimensional Hilbert space \mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_C and a Hamiltonian has the following form:$$H = H_A \otimes I \otimes I + I \otimes H_B \...
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I am reading about adiabatic quantum computing- specifically, about how it can find the lowest energy configuration of the Ising model. It is said that the initial state is a superposition of all the ...
1 vote
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### Hamiltonian in CNOT gate implementation

I am studying the physical implementation of the CNOT gate from "Introduction to Quantum Computing" (Ray LaPierre) and I am confused about the order of operators in the tensor product of the ...
126 views

### How to splice Hamiltonians corresponding to channels $\Phi_1$ and $\Phi_2$ so as to obtain a Hamiltonian corresponding to $\Phi_2\circ\Phi_1$?

Suppose I have two quantum channels $\Phi_1:B(\mathcal{H}_1)\rightarrow B(\mathcal{H}_2)$ and $\Phi_2:B(\mathcal{H}_2)\rightarrow B(\mathcal{H}_3)$, and let $\Phi=\Phi_2\circ \Phi_1$. Stinespring ...
1 vote
27 views

### Operating Hamiltonian on discrete variable state [closed]

I have a hamiltonian consisting of combinations of a and a(dragger). i need to act this on discrete variable state like |0,0,0,1> and so on. Is there any library to do these kinds of operations?
1 vote
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### How to implement Hamiltonian $0.01Z$?

I have a task in an assignment that wants me to apply a Hamiltonian to a state. The Hamiltonial is 0.01*sigma_z. I know how to apply a Z gate to a state but I don't know to process the factor 0.01 in ...
149 views

### Is it possible to implement any random Hamiltonian using quantum circuit

Are there any restrictions on implementing the evolution of any random Hamiltonian? Suppose I want to implement Rabi oscillations using a quantum circuit, I initialize the state and the Hamiltonian ...
149 views

### Can we always simultaneously diagonalize $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$?

Suppose we have systems $A$ and $B$ with respective Hamiltonians $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$. These Hamiltonians commute, so they share the same eigenbasis and hence can be ...
266 views

### How does a quantum system identify hermitian and unitary matrices?

I am a beginner in quantum computing. I know that multiplying a state $|u\rangle$ with a hermitian matrix $M$ yields spectral decomposition and multiplying $|u\rangle$ with a unitary matrix yield an ...
1 vote
47 views

### Proof of $cos(Ht) = \sum_\sigma cos(\sigma) \left | w_\sigma \right > \left < v_\sigma \right |$ in Quantum Singular Value Transform

I am reading the grand unification of quantum algorithms, and read over the hamiltonian simulation technique. However, I am a bit confused. They pose that $e^{-iHt} = cos(Ht) - isin(Ht)$ for all ...
1 vote
39 views

### Meaning of 'O_i' and 'Δ_i' terms in PulseBackend Hamiltonians

For OpenPulse enabled backends, the Hamiltonian can be retrieved via its configuration. The configuration holds a dictionary containing for example the Hamiltonian as a LaTeX string. Example code: <...