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

Disclaimer: I am a software engineer who is curious about quantum computing. Although I understand some basic concepts, theory and math behind it, I am by no means experienced in this domain. I am ...
207 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 ...
1k views

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

I can't seem to wrap my head around the Trotter-Suzuki formula. I have seen this answer but I am still confused of the applicability of the formula. Let me explain: As I understand it Trotterization ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
122 views

### Time evolution of Hamiltonian

I have given the following Hamiltonian $$\tilde H = - J_x (X_0 X_1 + X_2 X_3) - J_z (Z_0 Z_2 + Z_1 Z_3) - h\sum_j X_j + Z_j$$ Where, for example, $X_0 = \sigma^x \otimes I \otimes I \otimes I$ and I ...
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### 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 ...
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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 ...
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### Do Aharanov and Ta-Shma treat the entries of a sparse Hamiltonian as edges of a graph?

Background and history The mid-90's to early 2000's work on Hamiltonian simulation saw some pretty rapid advances. Within two years of Shor's algorithm, Lloyd outlined how Trotterization can lead to ...
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1 vote
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### 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 ...
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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 ...
1 vote
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### 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 ...
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1 vote
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### Qiskit TimeEvolutionProblem with complex operator

I have been using Qiskit to simulate some oscillators using Hamiltonian simulation. A next step I would like to make is adding dissipation of these oscillators in some way. I think it would be ...
1 vote
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### Qiskit: Evolve TrotterQRTE from Operator

I am trying to implement the method in the following paper: Exponential Quantum Speedup in Simulating Coupled Classical Oscillators using Qiskit. All is good until I call evolve on ...
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1 vote
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### 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 ...
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1 vote
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### Calculating Nested Commutator using a program

The $\tilde\alpha_{\text{comm}}$ mentioned in Theory of Trotter Error paper is calculated via the nested commutators. For a Hamiltonian $H = \sum_\gamma H_\gamma$, the formula for pth order is as ...
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1 vote
375 views

### Applying Trotterization to a Hamiltonian for Time Evolution in Qiskit

I'm currently working on a project where I need to simulate the time evolution of a quantum system using Qiskit. The Hamiltonian of my system is given by: H = -J \sum_{j=1}^{N-1} (\sigma_j^x \...
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1 vote
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### Link between AQC and QAOA

I try to understand precisely the link between AQC and QAOA, through the Trotter-Suzuki formula. A similar question is Derivation of QAOA from AQC, but I was asked by moderators to post my question ...
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1 vote
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### 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 ...
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1 vote
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### 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 ...
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### Applying Suzuki-Trotter approximation to a Quantum Circuit in Qiskit

I am trying to apply the Suzuki-Trotter approximation to a quantum circuit in Qiskit. However, when I attempt to use the st.synthesize() method on my quantum circuit, I encounter the following error: <...
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### 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 ...
461 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 ...
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