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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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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 ...
1 vote
0 answers
26 views

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 ...
0 votes
1 answer
42 views

Trotterized time-evolution with tensorcircuit

I would like to do a Trotterized time-evolution with Tensorcircuit of a spin-Hamiltonian and started with the example https://github.com/tencent-quantum-lab/tensorcircuit/blob/master/examples/...
0 votes
0 answers
22 views

Spin Hamiltonian to Quantum Circuits and are there any group theory associated with the quantum circuits?

Can we think of Quantum Circuits as another representation to describe the dynamics of a system other than its Hamiltonian? How can we go from the spin Hamiltonian version (for eg: SSH Model ...
3 votes
1 answer
112 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 ...
2 votes
0 answers
46 views

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 ...
6 votes
2 answers
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 ...
0 votes
2 answers
260 views

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: <...
1 vote
0 answers
357 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 \...
1 vote
0 answers
61 views

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 ...
2 votes
1 answer
98 views

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 ...
2 votes
1 answer
408 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
1 answer
314 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 ...
1 vote
0 answers
41 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
0 answers
67 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
2 answers
66 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 ...
5 votes
1 answer
256 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 ...
3 votes
1 answer
1k 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 ...
0 votes
1 answer
76 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
1 answer
337 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 ...
6 votes
2 answers
206 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 ...
1 vote
1 answer
248 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 ...
3 votes
1 answer
127 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 ...
5 votes
0 answers
137 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 ...
9 votes
1 answer
1k views

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 ...
0 votes
1 answer
424 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 ...