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Newest 'hamiltonian-simulation' Questions - Quantum Computing Stack Exchange
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Learn more about TeamsQuestions 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].
313 questions
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3
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1
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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
$$
\frac{d}{dt}|\psi(t)\rangle = -iH(t) |\psi(t)\rangle, \...
2
votes
0
answers
90
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Is it well-known that the Feynman-Kitaev Hamiltonian cannot be constructed from terms of bounded locality?
Suppose I have a depth-$D$ circuit of unitaries $U_1,\dots, U_D$. It's well-known that the Feynman-Kitaev Hamiltonian can implement this:
$$H_U = \sum_{i=1}^D -U_i \otimes \vert x\rangle\langle x-1\...
2
votes
1
answer
145
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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 ...
1
vote
1
answer
150
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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, ...
4
votes
1
answer
80
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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 ...
1
vote
2
answers
120
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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\...
0
votes
0
answers
64
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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 ...
1
vote
1
answer
143
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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 ...
1
vote
0
answers
66
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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 $u$ ...
1
vote
1
answer
78
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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 ...
1
vote
1
answer
46
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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 ...
3
votes
1
answer
112
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 ...
1
vote
2
answers
232
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 ...
2
votes
1
answer
64
views
Qiskit Circuit Construction
I have the following code block implementing $e^{-itP}$ where $P$ is a Pauli string:
...
2
votes
0
answers
64
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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 ...
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