Carview!

3 votes

1 answer

63 views

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

3,414

asked Jun 20 at 3:31

2 votes

0 answers

90 views

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

2,324

asked Jun 17 at 14:34

2 votes

1 answer

145 views

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

asked Jun 9 at 0:01

1 vote

1 answer

150 views

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

asked Jun 1 at 20:41

4 votes

1 answer

79 views

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

asked May 23 at 15:47

1 vote

2 answers

120 views

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

15.8k

asked Apr 28 at 13:12

0 votes

0 answers

64 views

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

855

asked Apr 19 at 7:33

1 vote

1 answer

142 views

Other Hamiltonian Simulation Use Cases than Quantum Chemistry

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

deb2014

537

asked Apr 7 at 9:42

1 vote

0 answers

66 views

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

15.8k

asked Apr 6 at 14:33

1 vote

1 answer

77 views

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

asked Mar 19 at 16:52

1 vote

1 answer

45 views

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

asked Mar 11 at 4:55

3 votes

1 answer

111 views

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

111

asked Mar 6 at 17:29

1 vote

2 answers

230 views

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

111

asked Feb 26 at 23:32

2 votes

1 answer

64 views

Qiskit Circuit Construction

I have the following code block implementing $e^{-itP}$ where $P$ is a Pauli string: ...

user82261

305

asked Feb 11 at 1:32

2 votes

0 answers

64 views

Can we edge-color $d$-regular Cayley graphs with only $d$ colors, rather than $(d+1)^2 n^6$ as in Aharanov and Ta-Shma?

Inspired by a recent comment from John Watrous, consider a Cayley graph $\Gamma$ of a group $G$ of order $O(\exp n),$ with generating set $R\subseteq G$ having $d=\vert R\vert$ such generators. Rather ...

Mark Spinelli

15.8k

asked Feb 10 at 17:29

Stack Exchange Network

Questions tagged [hamiltonian-simulation]

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

Qiskit Circuit Construction

Can we edge-color $d$-regular Cayley graphs with only $d$ colors, rather than $(d+1)^2 n^6$ as in Aharanov and Ta-Shma?

Hot Network Questions

Questions tagged [hamiltonian-simulation]

Related Tags