# Tag Info

Accepted

### Ground state energy estimation - VQE vs. Ising vs. Trotter–Suzuki

In each of the examples you mentioned, the task breaks very roughly down into two steps: finding a Hamiltonian that describes the problem in terms of qubits, and finding the ground state energy of ...
• 1,068
Accepted

### Jordan-Wigner Transform and Trotterization: which goes first?

Short answer: When you do the Jordan-Wigner transformation, you essentially insert a linear combination of tensor products of Pauli matrices for each fermionic creation and annihilation operator. As ...
• 433
Accepted

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

I think you are asking whether a quantum computer can efficiently simulate the evolution of any Hamiltonian, as long as the Hamiltonian is represented by a hermitian matrix. There are some details ...
• 12.8k
Accepted

### Calculation of Trotter-Suzuki error bound

There are two aspects of your question that I will address separately: the computational and analytical. I believe the underlying issue is the same, but I will nonetheless address them separately. ...
• 645

• 261
Accepted

### Confirming locality of a Hamiltonian through decomposition

As long as you tweak your condition to require strict inequalities, $$\exists \sigma_{\gamma_1\dots\gamma_n} \text{ s.t } c_{\gamma_1\dots\gamma_n} > 0 \tag{1} \\ |\{i|\gamma_i > 0\}| > k$$...
• 7,183

### How to perfrom a time-dependent Hamiltonian simultation using the Trotter-Suzuki formula?

There's really not any difference. Imagine I'm trying to simulate a Hamiltonian $$H(t)=f(t)H_1+g(t)H_2$$ from time $t=0$ to $T$. I'm going to break this down into $N$ little time steps $\delta=T/N$. ...
• 59.4k
Accepted

### How to implement Hamiltonian $0.01Z$?

I found the answer. The R_x and R_z gates do exactly that. Decomposing the Pauli Trotter Evolution funktion helped answer that.

### How to implement Hamiltonian $0.01Z$?

If I got it well, to implement what you want in Qiskit you can do the following: ...
• 1,552

### Time evolution of Hamiltonian

I found out, that one can do that using the $Z$-rotations instead of $X$-rotations because the $Z$-rotation is already diagonal. that makes it way easier to see what $e^{\sigma^{z}}$ should be. So one ...
• 85
1 vote

### Qiskit TimeEvolutionProblem with complex operator

You can use quantum imaginary time evolution (QITE) techniques to simulate $e^{Ht}$. Qiskit algorithms package contains ImaginaryTimeEvolver interface with two ...
1 vote

### Qiskit: Evolve TrotterQRTE from Operator

You can use SparsePauliOp.from_operator() method to construct a SparsePauliOp from an ...
1 vote
Accepted

### Applying Suzuki-Trotter approximation to a Quantum Circuit in Qiskit

The method SuzukiTrotter.synthesize() takes an instance of PauliEvolutionGate as a parameter. The issue in your code is that you ...
1 vote

### The approximation of the time evolution operator U, using Trotter formula, can't hold anymore taking a time step of $\Delta t = \pi$

As you allude to, Nielsen and Chuang say on pp. 259-260, Now initially we imagined that $\Delta t$ was small, since we were considering the case of quantum simulation, but Equation (6.28) shows that ...
1 vote

### Exponentiating a multi-controlled NOT gate for trotterization

MCXGate exists in Qiskit's circuit library. So, you can get the operator as follows: ...
1 vote
Accepted

### Using QDRIFT on qiskit

An easy way to use QDrift in Qiskit is to pass it as a synthesis method to PauliEvolutionGate ...
1 vote

### Investigating the scaling of the error of a Trotter-Suzuki-approximation

For this particular calculation, you can keep your results exact for quite a long time. To see this, start with the exact thing $$H_0=e^{i\pi/2(X+Z)/\sqrt{2}}=i\frac{X+Z}{\sqrt{2}}.$$ Now for the ...
• 59.4k
1 vote
Accepted

### How to do rotations along arbitrary multi-qubit basis

One way to do that is by using PauliEvolutionGate: ...
1 vote

### What is the usefulness of the Suzuki-Trotter formula?

Your question is not so much about the usefulness of the Trotter-Suzuki formula per se, but is rather about the usefulness of Hamiltonian simulation in general (and eigenvalue sampling in particular), ...
• 12.8k

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