We’re rewarding the question askers & reputations are being recalculated! Read more.

# 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].

34 questions
Filter by
Sorted by
Tagged with
75 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 ...
134 views

### Number of Qubits Required for Simulation of Caffeine and Penicillin Molecules

I recently read this report from BCG, which stated: For scientists trying to design a compound that will attach itself to, and modify, a target disease pathway, the critical first step is to ...
29 views

258 views

### Implement a Hamiltonian in O(n) - exercise question

I have the following exercise to solve: Consider the Boolean function $f(x_1 . . . x_n) = x_1 \oplus \dots \oplus x_n$ where $x_1 \dots x_n$ is an nbit string and $\oplus$ denotes addition mod $2$...
31 views

### How to pick number of simulation qubits for finding eigenvalue of fermionic Hamiltonian?

I am having some trouble understanding how the number of simulation qubits are chosen when finding the eigenvalue of a fermionic Hamiltonian. For the phase-estimation algorithm, is the number of ...
141 views

### Circuit construction for Hamiltonian simulation

I would like to know how to design a quantum circuit that given a Hermitian matrix $\hat{H}$ and time $t$, maps $|\psi\rangle$ to $e^{i\hat{H}t} |\psi\rangle$. Thank you for your answer.
323 views

### Simulate hamiltonian evolution

I'm trying to figure out how to simulate the evolution of qubits under the interaction of Hamiltonians with terms written as a tensor product of Pauli matrices in a quantum computer. I have found the ...
38 views

### Numerical approximation to eigenstates and their differentials

I am working in Adiabatic Quantum Computing and I have a $6\times6$ Hamiltonian. I have only the symbolic expression for its eigenstates which have complicated expressions in solutions of degree $6$ ...
256 views

187 views

### Is there a way to express the general 4X4 Hamiltonian in some block diagonal form of 2X2 matrices that I can solve, knowing the exact solution of 2X2?

Is there a way to express the general $4 \times 4$ Hamiltonian in some block diagonal form of $2 \times 2$ matrices that I can solve, knowing the exact solution of $2\times 2$? This is necessary for ...
150 views

### Introductory resources for learning about quantum Hamiltonians

I am seeking introductory resources which will enable me to answer these questions (textbooks, lecture series, etc.): Given a simple quantum system, how do I derive its Hamiltonian? Given a ...
887 views

### How do I construct a Density Matrix corresponding to a Hamiltonian?

I have a Hamiltonian and I want to know the corresponding density matrix. The matrix I'm interested in is the one in this question.
271 views

### Why is this Hamiltonian matrix diagonal?

I've only recently started using density matrices in my work but I am confused with the following code that I have whether I am getting the right matrix: ...
323 views

### Example of Hamiltonian Simulation solving interesting problem?

Hamiltionian Simulation (= simulation of quantum mechanical systems) is claimed to be one of the most promising applications of a quantum computer in the future. One of the earliest – and most ...
234 views

### Is there a Hamiltonian simulation technique implemented somewhere?

I was wondering if there was some code available for Hamiltonian simulation for sparse matrix. And also if they exist, they correspond to a divide and conquer approach or a Quantum walk approach?
217 views

### Advantage of simulating sparse Hamiltonians

In @DaftWullie's answer to this question he showed how to represent in terms of quantum gates the matrix used as example in this article. However, I believe it to be unlikely to have such well ...
213 views

368 views

### Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is $|\Psi_0\rangle$?

This is a sequel to Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm and Quantum algorithm for linear systems of ...
402 views

### Hamiltonian simulation is BQP-complete

Many papers assert that Hamiltonian simulation is BQP-complete (e.g., Hamiltonian simulation with nearly optimal dependence on all parameters and Hamiltonian Simulation by Qubitization). It is easy ...