Movatterモバイル変換

Question 1

1vote

1answer

52views

Limits of Hamiltonian Simulation on current IBM devices

I'm trying to simulate the 1D Ising Model with open periodic boundary conditions using the 2nd order Trotter product for 5 spins sites with J = -1.2 and h =-0.7.$$ H_{Ising} = -J\sum_{i=0}^{spinsites ...

Eddie

82

askedOct 7 at 19:36

Question 2

0votes

1answer

83views

How to implement an exp{-iat}?

I'd like to implement $e^{-iat}$ as part of an algorithm for hamiltonian simulation. This makes the operation:$$|a\rangle|0\rangle \rightarrow |a\rangle e^{-iat}|0\rangle$$According to Nathan ...

Lucas Amaral Dos Santos Barros

63

askedSep 27 at 0:15

Question 3

3votes

1answer

104views

Time complexity of applying $U(T)$ and possibility of instantaneous application via teleportation

Let $H(t)$ be a time-dependent Hamiltonian. Then, for $t \in [0,T]$, the evolution of $|\psi(t)\rangle$ is given by the Schrodinger equation$$\frac{d}{dt}|\psi(t)\rangle = -iH(t) |\psi(t)\rangle, \...

MonteNero

3,412

askedJun 20 at 3:31

Question 4

2votes

0answers

152views

Is it well-known that the Feynman-Kitaev Hamiltonian cannot be constructed from terms of bounded locality?

Suppose I have a depth-$D$ circuit of unitaries $U_1,\dots, U_D$. It's well-known that the Feynman-Kitaev Hamiltonian can implement this:$$H_U = \sum_{i=1}^D -U_i \otimes \vert x\rangle\langle x-1\...

Sam Jaques

2,334

askedJun 17 at 14:34

Question 5

2votes

1answer

188views

Complexity of quantum simulation of sparse Hamiltonians algorithm

I'm reading "Efficient quantum algorithms for simulating sparse Hamiltonians" by Berry, Ahokas et al. and I'm having some doubts about its complexity. First, the sparse Hamiltonian is ...

Lucas Amaral Dos Santos Barros

63

askedJun 9 at 0:01

Question 6

1vote

1answer

200views

Is there an efficient way to implement quantum read-only memory (QROM)?

I'm looking to understand how quantum read-only memory (QROM) is implemented, specifically how classical data can be loaded into ancilla qubits using controlled operations.From what I've read so far, ...

torrent5

11

askedJun 1 at 20:41

Question 7

4votes

1answer

96views

Hamiltonian for Combustion problem

I studied Hamiltonian Simulation for estimating the ground state of molecules, which is one of the main use case for quantum computers.I would like to extend this approach to more complex Chemistry ...

deb2014

537

askedMay 23 at 15:47

Question 8

1vote

2answers

168views

Is there a sign-problem when the wavefunction itself has positive and negative values, or is it only when the Hamiltonian has such entries?

Consider the following two problems:Let $A$ be an $s$-sparse $2^n\times 2^n$ Hermitian matrix with entries $A_{jk}$ in $\{0,1,-1\}$ both along the main diagonal and off the diagonal. Let $|\psi\...

Mark Spinelli

16.3k

askedApr 28 at 13:12

Question 9

0votes

0answers

81views

How to get quantum advantage in chemistry simulations in first quantization

In this post about 100 qubit fault tolerant devices it is stated that a system with 100 spin orbitals (or 50 spatial orbitals) is small enough that classical-computer algorithms can currently do the ...

Bram

1,371

askedApr 19 at 7:33

Question 10

1vote

1answer

166views

Other Hamiltonian Simulation Use Cases than Quantum Chemistry

Quoting Montanaro's quantum algorithm review :Quantum (Hamiltonian Simulation) is the simulation of physical systems by mappingtheir Hamiltonian to that of a set of qubits in order to extract some ...

deb2014

537

askedApr 7 at 9:42

Question 11

1vote

0answers

95views

Can problems about Perfect State Transfer ever be BQP-Complete?

I was watching a recent video by Krystal Guo on algebraic graph theory with a focus on Perfect State Transfer (PST) - which occurs on a graph $X$ having adjacency matrix $A(X)$ between vertices $u$ ...

Mark Spinelli

16.3k

askedApr 6 at 14:33

Question 12

1vote

1answer

111views

Resources for study Quantum simulation algorithm for beginners

My major is math,so I am new in physics.I am currently studying Chapter 4 of Nielsen & Chuang's book on quantum simulation algorithms, but I find some of the concepts difficult to understand. For ...

Kevin Anderson

11

askedMar 19 at 16:52

Question 13

1vote

1answer

62views

Improve efficiency in simulating $H = \frac{a}{4}\left[(1-Z_0)\otimes(1-Z_1)+(1-Z_1)\otimes(1-Z_2)\right] $

I want to construct quantum circuit to simulate time-evolution of the Hamiltonian$$H = \frac{a}{4}\left[(1-Z_0)\otimes(1-Z_1)+(1-Z_1)\otimes(1-Z_2)\right]$$Where $Z$ is the pauli $Z$ gate, $a$ is ...

IGY

371

askedMar 11 at 4:55

Question 14

3votes

1answer

147views

Isn't the Solovay-Kitaev Algorithm already great for Hamiltonian Simulation?

Reading Andrew Child's lecture notes I've come across the following remark:"There are a few cases where a Hamiltonian can obviously simulated efficiently. For example, this is the case if H only ...

Omeglac

141

askedMar 6 at 17:29

Question 15

1vote

2answers

369views

Resources on Hamiltonian Simulation

Can anyone recommend rigorous lecture notes or books on Hamiltonian simulation? I'm looking for sources that start from the basics and include formal proofs. I have some background in quantum ...

Omeglac

141

askedFeb 26 at 23:32

Movatterモバイル変換

Stack Exchange Network

Questions tagged [hamiltonian-simulation]

Limits of Hamiltonian Simulation on current IBM devices

How to implement an exp{-iat}?

Time complexity of applying $U(T)$ and possibility of instantaneous application via teleportation

Is it well-known that the Feynman-Kitaev Hamiltonian cannot be constructed from terms of bounded locality?

Complexity of quantum simulation of sparse Hamiltonians algorithm

Is there an efficient way to implement quantum read-only memory (QROM)?

Hamiltonian for Combustion problem

Is there a sign-problem when the wavefunction itself has positive and negative values, or is it only when the Hamiltonian has such entries?

How to get quantum advantage in chemistry simulations in first quantization

Other Hamiltonian Simulation Use Cases than Quantum Chemistry

Can problems about Perfect State Transfer ever be BQP-Complete?

Resources for study Quantum simulation algorithm for beginners

Improve efficiency in simulating $H = \frac{a}{4}\left[(1-Z_0)\otimes(1-Z_1)+(1-Z_1)\otimes(1-Z_2)\right] $

Isn't the Solovay-Kitaev Algorithm already great for Hamiltonian Simulation?

Resources on Hamiltonian Simulation

Hot Network Questions

Subscribe to RSS