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Entanglement generation for commuting Hamiltonian

Consider an $n$ qubit Hamiltonian $H$ given by \begin{equation} H = \sum_{i=1}^{m} H_i, \end{equation} where each $H_i$ is a $k$-local term and it holds that \begin{equation} e^{H} = e^{H_m} \cdot e^{...
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About the formulation of an Ising Hamiltonian

I am reading the paper from Andrew Lucas, Ising formulations of many NP problems, and I am stuck with the formulation of the following Ising Hamiltonian: $$H = A \bigg( K - \sum_v x_v \bigg)^2 + B\...
Laura's user avatar
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How to write the hamiltonian for w state?

Suppose the $w$ stare $|w\rangle=(1/3)^{½}(|100\rangle+|010\rangle+|001\rangle) $ Let's say the eigenvalues of this state are $k_i$ then the hamiltonian corresponding to it is as follows: $H =k_1 |100\...
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help understanding gate to hamiltonian and representation

So I have this question: Given an operator, find some Hamiltonian implementing this operator/gate. I have realized that this is a swap gate and I know the matrix for it. I also know that $U = \text{...
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Understanding Interaction in Cross Resonance Gates with Transmon Qubits

I have a question regarding the operation of 2-qubit gates. Two transmon qubits are coupled via a capacitor, and a microwave is applied to one of the transmons. The Hamiltonian for this setup can be ...
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3 votes
1 answer
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Underlying Hamiltonians and pulse level controls of different commercially available quantum computers

My research area is in quantum state transfer, and I am trying to perform a 'proof of principle' that requires the underlying Hamiltonians of quantum systems and the control I can have on these ...
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I would like to know the textbook/paper on hamiltonian for rf-SQUID

I am a graduate student in the Department of Computer Engineering, and I am currently doing research on superconducting quantum computers. In particular, I am focusing on quantum annealing machines ...
Aki's user avatar
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Derivation of energy gap formula for adiabatic Grover algorithm

I am having a difficulty in finding the full derivation for local search energy gap, as described in In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?. I looked ...
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Relationship between the eigenvalues of a Laplacian matrix and the eigenvalues of the Hamiltonian of a graph for Max-Cut

Is there a relationship between the eigenvalues of a Laplacian matrix of a graph and the eigenvalues of the Hamiltonian for Max-Cut? It is shown here, that Max-Cut can be written as a maximization ...
QC_Pod's user avatar
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Phase accumulation for multiple Rabi driving pulses

When a single-qubit gate is operated by Rabi driving, the resulting operator is equivalent to $$ \hat{O} = R_z(\omega t) R_x(\Omega t)\tag{1}$$ where $\omega$ is the frequency of the driving field, $\...
jackphen's user avatar
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Is there a general method for calculating expectation values for time-dependent wavefunctions?

Is there a general method for calculating expectation value? I have a workshop question, and I'm sure what a good process to follow is. It is given that $$|\psi(t = 0)\rangle = |0\rangle\,,\tag{1}$$ ...
qiclueless's user avatar
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1 answer
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How to combine measurement of each term in Hamiltonian $H = aH_1 + bH_2$ to get final results?

I have a Hamiltonian $$H = aH_1 + bH_2\,,\tag{1}$$ with $a$ and $b$ being coefficients, and I want to apply each term/evolution separately, then recombine the measurement results to get the result for ...
Moustafa's user avatar
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When does a Hamiltonian result in the construction of an IC-POVM?

Consider a generic $d_A$-dimensional quantum system $A$, for example made of $n$ qubits. Now consider a second higher-dimensional system $B$, with $d_B=d_A^2$, and the quantum map $$ \rho_A \...
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How can one use QAOA to obtain parameters that approximate the first excited state of the target Hamiltonian?

One can use QAOA to find the ground state and its energy by minimizing the expectation value of a target Hamiltonian (say, $H_T$) with respect to the QAOA ansatz and obtaining optimal parameters ...
Pratham Hullamballi's user avatar
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1 answer
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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-\...
Angelo_M's user avatar
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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,...
Dr. T. Q. Bit's user avatar
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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 ...
Alternative7's user avatar
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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 ...
Hakan Akgün's user avatar
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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 ...
confusion's user avatar
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2 answers
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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 ...
Cheshta Joshi's user avatar
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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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1 vote
1 answer
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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 ...
Andrew Baker's user avatar
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1 answer
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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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1 answer
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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 ...
random person's user avatar
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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 ...
random person's user avatar
5 votes
1 answer
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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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1 vote
1 answer
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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?
INDRANIL MAITI's user avatar
1 vote
2 answers
66 views

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 ...
Fabrice Schöneberger's user avatar
4 votes
1 answer
234 views

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 ...
FearlessVirgo's user avatar
2 votes
2 answers
172 views

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 ...
MonteNero's user avatar
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3 votes
2 answers
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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 ...
Jayakumar's user avatar
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0 answers
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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 ...
Loic Stoic's user avatar
1 vote
1 answer
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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: <...
Sanson Jones's user avatar
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1 answer
149 views

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, $\...
Loic Stoic's user avatar
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1 answer
157 views

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 ...
Loic Stoic's user avatar
5 votes
2 answers
200 views

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 $$ ...
Physics Penguin's user avatar
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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 ...
Loic Stoic's user avatar
4 votes
0 answers
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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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1 vote
1 answer
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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 ...
quest's user avatar
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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 ...
quest's user avatar
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