Questions tagged [hamiltonian-simulation]

Hamiltonian simulation is a class of algorithms that, given a Hermitian matrix A, output a quantum circuit implementing an approximation to the unitary exp[iAt].

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Can we use quantum phase estimation to learn anything about the dynamics of puzzles like the Rubik's cube?

Introduction Consider a state $\vert\psi\rangle$ as below, which is in a superposition of a difference between a Rubik's cube in a solved state and a Rubik's cube in the "superflip" state. ...
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VQE Cirq example

Is my understanding correct that in this example the Hamiltonian measurement is not performed through measuring individual Pauli operators because all its terms are mutually commuting? So, for each ...
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Paradox on the evolution direction in controlled Hamiltonian simulation for Quantum Phase Estimation

Suppose we want to perform Quantum Phase Estimation over a Linear Combination of Unitaries Hamiltonian. One of the most efficient ways to do so is to use qubitization: \begin{equation} Q=(2|0\rangle\...
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How can I decompose a matrix in terms of Pauli matrices?

I need to see an example of how Hamiltonian, i.e. any Hermitian matrix, can be decomposed into a linear combination of Pauli matrices. I would prefer an option to do this in larger than 2 dimensions, ...
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Simulating the Ising-like model as a quantum circuit

We are interested in simulating the 1d Ising model Hamiltonian using a Quantum Circuit (QC). A similar question was posted before with no answers. Here we will assume, for simplicity, 3 lattice sites ...
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Nyquist–Shannon sampling theorem for Quantum Evolution

In classical digital signal processing one can try to identify the dynamics of a system by sampling its evolution from an initial time $t_0$ to a final time $t_1$. Sampling $N$ times results in a ...
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Applying QPE on a large matrix on amazon-braket

I'm running a QPE algorithm on the amazon-braket but it can only apply on a 22 or 44 matrix, when I want to expand it into a 5*5 or more, it will come an error. As I know, there is no theoretical ...
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Why does quantum phase estimation complexity scale with maximum representable energy?

In Quantum simulation of chemistry with sublinear scaling in basis size Ryan Babbush and other authors from Google Quantum team argue, when talking about performing Quantum Phase Estimation in 1st ...
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How can I convert exponentials of pauli matrices to circuits of this form in Qiskit?

For example the following circuit is for $e^{-i(Z\otimes Z\otimes Z)\Delta t}$ I know this can even be done without the ancilla qubit, having the CNOTs control the last qubit and applying an RZ on ...
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Are these two circuits equivalent in performing controlled time-evolution?

I want to perform the controlled time-evolution of some 2 or 3-qubit Hamiltonian. Say we have this example: $$H= Z_0\otimes Z_1 + Z_1\otimes Z_2$$ The circuit performing the time-evolution ...
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How to implement NM Algorithm for Variational Quantum Eigensolver?

First of all: thanks for reading again. I appreciate the feedback I have gotten from this community the past weeks as I started to feel ready to ask questions about quantum computing topics. I am ...
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Calculating the ground states of an Ising Hamiltonian on a real quantum computer

I have followed this tutorial and based on it, I've written the following function in qiskit, which can explicitly calculate the ground states of a transverse-field Ising Hamiltonian. ...
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What is the usefulness of the Suzuki-Trotter formula?

I can't seem to wrap my head around the suzuki-trotter 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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Intuition behind the construction of an ansatz circuit

I'm learning about the VQE algorithm. When I looked at the declaration in Qiskit I saw you need to pass an ansatz which prepares the state. I looked at some commonly used ansatz functions, e.g. ...
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What do coupling coefficients mean in terms of Pauli gates, and why are they time dependent?

I am reading this error mitigation paper by the IBM team and I am slightly confused about the meaning of "coupling coefficients" when describing multi-qubit Hamiltonian. I have only seen ...
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How to construct a Hamiltonian for an ensemble of atoms interacting with each other?

How to construct a Hamiltonian for an ensemble of atoms interacting with each other? For example if the one atom hamiltonian can be written as: \hat{H}=\left(\begin{matrix}0&\Omega_p(t)&0\\\...