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# Questions tagged [trotterization]

For questions regarding Trotterization, concerning product formulas related to quantum simulation, Trotter errors, Trotter-Suzuki limits and their applications and implementation in quantum computers.

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

The problems arises from a consideration written on the book "Quantum computation and quantum information" from Michael A. Nielsen and Isaac L. Chuang on page 259. In this chapter it's ...
52 views

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

I would like to know how to perform trotterization of a time-dependent operator (such as a Hamiltonian) on a gate-based quantum computer? I've seen examples for time-independent Hamiltonians, but I ...
1 vote
52 views

### Calculation of Trotter-Suzuki error bound

Suppose we are given Hamiltonian in the form: $$H = -\sum_{k=0}^{n-1} \alpha\sigma^x_k\sigma^x_{k+1} + \beta\sigma^y_k\sigma^y_{k+1} + \gamma\sigma^z_k\sigma^z_{k+1},$$ where $n$ is the number of ...
21 views

### Cirq/OpenFermion Trotterization of parametrised FermionOperator?

I am using OpenFermion and Cirq. I would like to define a Hamiltonian with a symbolic parameter and then generate a quantum circuit via Trotterization of its time evolution, which then also contains ...
18 views

### How do I use 'aux_operators' in 'TrotterQRTE' time evolution problem?

I'm trying to evolve a 3 qubit system under a Pauli Sum Hamiltonian in QISKIT using the TrotterQRTE method, and observe the projection of on the singlet state at every time step. How do I program the ...
1 vote
39 views

### How to Trotterize a CNOT gate?

I came across a paper that said that they Trotterized a CNOT gate into 4 blocks of CU gates where the CU gate parameters are specified. This was all done on Qiskit. How does this Trotterization ...
1 vote
61 views

### 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 ...
113 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 ...
182 views

### What is the difference between Trotter, Lie-Trotter and Trotter-Suzuki approximations?

What is the difference between (1) Trotter (2) Lie-Trotter and (3) Trotter-Suzuki approximation? Are they all different? what are the formulas and errors associated in each of these approximations in ...
58 views

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

I am trying to exponentiate a multi-controlled NOT gate (MCX) via .exp_i() function for trotterization in Qiskit , but I cannot find such a gate represented in opflow. Is there a convenient way around ...
1 vote
203 views

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

I've been reading this paper about the procedure to simulate a many-body quantum system on a quantum device. I got confused by Figure 1. on page 3, and the 3 steps explained below the figure. It seems ...
1 vote
122 views

### Using QDRIFT on qiskit

I was recently trying to use Qiskit's inbuilt QDRIFT to construct a circuit for a simple Hamiltonian $H = XX + YY$. but I'm having an issue converting the result of ...
74 views

### Confirming locality of a Hamiltonian through decomposition

I was trying to understand Trotterization. The given Hamiltonian is decomposed into a sum of $k$-local Hamiltonians which can be exponentiated in $O(1)$ gate complexity. After which the Trotter ...
165 views

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

I am doing an assignment and I am being asked to investigate the scaling of the error with the number of repetions $n$ of a approximation of the Hadamard with $R_x$ and $R_y$. This is the ...
202 views

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

I was trying to implement Trotterization for a $k$-local Hamiltonian simulation using qiskit. For this, say I want to apply $e^{\lambda \sigma^1_z \otimes \sigma^2_z \otimes \sigma^3_z}$ (this being ...
107 views

### Trotter error for bosons in various encodings

Mapping second-quantized bosonic modes onto qubits can be done using various encodings. Each of those have their pro et contra. Fewer qubits — more gates, and vice versa. Encoding an $N$-level bosonic ...