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Quantum Computing Stack Exchange

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 doing some preliminary research on the state of…
Anurag Bhandari
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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 lets us use directly the Schrodinger equation…
Bidon
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Error scaling of the 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 $R_y$. Abbreviating $\theta = \frac {\pi} {\sqrt2}$, this is the…
tommasopeduzzi
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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 evolution is implemented in the quantum circuit…
FearlessVirgo
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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 mode with unary mapping requires $(N+1)$ qubits,…
mavzolej
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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 approximation is applied. The Hamiltonian can be…
Zee
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Lower bound for the product formula complexity in terms of spectral norm

The $\tilde{\alpha} t^{1+1/p} \epsilon^{-1/p}$ bound on gate complexity for simulating time evolution with product formulas is very problem-specific and requires computing nested commutators. On general grounds, can we say that in terms of the…
mavzolej
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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 should Implement the time evolution of this…
Ruebli
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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 simulating a Hamiltonian evolution, let's say…
FearlessVirgo
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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 efficient local Hamiltonian simulation such as…
Mark Spinelli
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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 independently. So here it is. In quantum adiabatic…
deb2014
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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 studied the Grover search algorithm as a quantum simulation and…
Francesco Greco
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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 would like to know which is the theory for…
bjail66
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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 qubits, and $\alpha$, $\beta$, $\gamma$ $\in…
Albert65
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Qiskit trotter simulation choice of initial state under transverse field Ising hamiltonian

The code is from https://github.com/qiskit-community/qiskit-algorithms/blob/stable/0.3/docs/tutorials/13_trotterQRTE.ipynb. While simulating many-body system evolving under a transverse field Ising hamiltonian, when I change the initial state from 6…
Deren Liu
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