Questions tagged [hamiltonian]
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Knapsack problem formulation
I would like to use a knapsack problem formulation based on Lucas paper. Namely, I try to implement the following math formula for Hamiltonian $H =H_A + H_B$, where
$$H_{B} = -B\sum_{i=1}^{n}v_{i}x_{i}...
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Understanding circuit to Hamiltonian embedding where we do not have a separate clock register
I am trying to understand the clock construction given in this paper, to embed a circuit to a Hamiltonian, which doesn't need to access a separate clock register.
The construction, at a high level, ...
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How could I get this lemma about stoquastic hamiltonian in the paper "Complexity of stoquastic frustration-free Hamiltonians"
In the paper Complexity of stoquastic frustration-free Hamiltonians, I was confused about the derivation of Lemma 4.5: How could we get $\delta Tr(O(I-\Pi_a)) \leq Tr(OH_a)$ given that $\delta (I-\...
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Algorithm for finding the appropriate rotating frame Hamiltonian?
Context
Consider an $N$-level Hamiltonian with energies $\omega_1...\omega_N$ with coupling drives at frequencies $f_{i,j}$ which couple the $i$ and $j$-th levels (not necessarily resonantly, so $f_{i,...
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How are edge weights "loaded" in the problem hamiltonian when solving TSP with QAOA?
I've come across several of the QAOA tutorials, and yet I'm afraid I haven't found any explanation on this. According to the Qiskit tutorial on QAOA, the cost function for the target problem has a ...
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Problems with Exact Diagonalization Implementation in Quantum System Evolution
I've been trying to implement exact diagonalization to study the time evolution of quantum states and subsequently compute local magnetizations. I have written functions for evolving the state and ...
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Intuitive explanation on dependence of Hamiltonian simulation on norm?
Suppose I have two Hamiltonians, $H_1$ and $H_2$, that I want to simulate for time $T$. If $\|\|H_1\|\|>\|\|H_2\|\|$, why is it more costly to simulate $H_1$ compared to $H_2$? Is there an ...
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How can I implement a Hamiltonian which is sum of tensored pauli operators on qiskit?
I am working with a Tight Binding Hamiltonian with N sites and one orbital at each site in a closed chain. I have converted the fermionic expression to a spin expression using Jordan Wigner ...
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Backwards evolution arising from changing evolution picture
This may not be a question strictly belonging to the realm of quantum computing, but it does arise from problems in QI and optics, so I choose to ask it here. Suppose $A$ is a Hermitian operator ...
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Hamiltonian of Bose-Hubbard model
In https://medium.com/qiskit/introducing-bosonic-qiskit-a-package-for-simulating-bosonic-and-hybrid-qubit-bosonic-circuits-1e1e528287bb , could anyone explain the rationale behind the use of ...
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Excplicit Description of Hamiltonians?
The wikipedia article for Hamiltonian simulation lists two complexities: gate and query complexity.
These two types of complexity refer to two different things; gate complexity is the asymptotic ...
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Can a Hamiltonian of a tripartite system map an product state into a product state?
Suppose we have a finite dimensional Hilbert space $\mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_C$ and a Hamiltonian has the following form:
$$H = H_A \otimes I \otimes I + I \otimes H_B \...
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Adiabatic computing basics
I am reading about adiabatic quantum computing- specifically, about how it can find the lowest energy configuration of the Ising model. It is said that the initial state is a superposition of all the ...
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Hamiltonian in CNOT gate implementation
I am studying the physical implementation of the CNOT gate from "Introduction to Quantum Computing" (Ray LaPierre) and I am confused about the order of operators in the tensor product of the ...
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How to splice Hamiltonians corresponding to channels $\Phi_1$ and $\Phi_2$ so as to obtain a Hamiltonian corresponding to $\Phi_2\circ\Phi_1$?
Suppose I have two quantum channels $\Phi_1:B(\mathcal{H}_1)\rightarrow B(\mathcal{H}_2)$ and $\Phi_2:B(\mathcal{H}_2)\rightarrow B(\mathcal{H}_3)$, and let $\Phi=\Phi_2\circ \Phi_1$.
Stinespring ...
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Operating Hamiltonian on discrete variable state [closed]
I have a hamiltonian consisting of combinations of a and a(dragger). i need to act this on discrete variable state like |0,0,0,1> and so on. Is there any library to do these kinds of operations?
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How to implement Hamiltonian $0.01Z$?
I have a task in an assignment that wants me to apply a Hamiltonian to a state.
The Hamiltonial is 0.01*sigma_z. I know how to apply a Z gate to a state but I don't know to process the factor 0.01 in ...
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Is it possible to implement any random Hamiltonian using quantum circuit
Are there any restrictions on implementing the evolution of any random Hamiltonian? Suppose I want to implement Rabi oscillations using a quantum circuit, I initialize the state and the Hamiltonian ...
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Can we always simultaneously diagonalize $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$?
Suppose we have systems $A$ and $B$ with respective Hamiltonians $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$. These Hamiltonians commute, so they share the same eigenbasis and hence can be ...
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How does a quantum system identify hermitian and unitary matrices?
I am a beginner in quantum computing. I know that multiplying a state $|u\rangle$ with a hermitian matrix $M$ yields spectral decomposition and multiplying $|u\rangle$ with a unitary matrix yield an ...
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Proof of $cos(Ht) = \sum_\sigma cos(\sigma) \left | w_\sigma \right > \left < v_\sigma \right |$ in Quantum Singular Value Transform
I am reading the grand unification of quantum algorithms, and read over the hamiltonian simulation technique.
However, I am a bit confused. They pose that
$
e^{-iHt} = cos(Ht) - isin(Ht)
$
for all ...
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Meaning of 'O_i' and 'Δ_i' terms in PulseBackend Hamiltonians
For OpenPulse enabled backends, the Hamiltonian can be retrieved via its configuration. The configuration holds a dictionary containing for example the Hamiltonian as a LaTeX string.
Example code:
<...
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How is the P function applied in QSVT for the case of Hamiltonian simulation if it only modifies singular values?
I am watching Andras Gilyen's talk on QSVT here.
On one slide he mentions the core of QSVT:
Given $U$--- a block encoding of matrix $A$ that has singular values $\lambda$, left singular vectors, $\...
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How to choose values of phi for Hamiltonian simulation with Quantum Singular Value Transform?
I am reading the review, Grand Unification of Quantum Algorithms, which covers the area known as "Quantum Singular Value Transform (QSVT)."
I am really trying to understand it behind the ...
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Is there an efficient algorithm for decomposing an arbitrary Hamiltonian into Pauli strings?
Basically the title. If I have a $2^N\times 2^N$ Hamiltonian $H$ of random numbers (we can take the Hamiltonian as normalized if we want) and $N$ is an integer, is there an efficient way of writing
$$
...
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Why does the quantum walk operator only have two eigenvectors?
In Child's paper on the relationship between discrete and continuous quantum walks, he makes the following claim.
Although he provides a proof after this:
I don't understand how the walk operator ...
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Analysis of error propagation in time-independent Hamiltonian computations
With a Feynman-Kitaev Hamiltonian, quantum computation does not need to apply any gates; you construct the Hamiltonian, initialize the system, and let it propagate on its own.
However, the Hamiltonian ...
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Understanding Hamiltonian's of the Single Qubit Gates and Toffoli gate
As a most general shape, we can write our unitary(unitary here single qubit gates and toffoli gates) in that shape:
$U = \exp({iHt})$
H is the hamiltonian. However single qubit gates does not reqire ...
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General Shape of the Hamiltonian for a Desired Unitary
Suppose that, the unitary(the gate) that we want to have is 8*8 matrix. Now I want to write the most general shape of the Hamiltonian for my unitary and I want to prove that the unitary can be ...
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