Skip to main content

# Tag Info

## Hot answers tagged hamiltonian

7 votes
Accepted

TL;DR: You can always achieve simultaneous diagonalization of $H_A\otimes\mathbb{1}$ and $\mathbb{1}\otimes H_B$ even if $[H_A, H_B]\ne 0$. And yes, this does follow from the fact that $[H_A\otimes\... • 23k 6 votes ### How does a quantum system identify hermitian and unitary matrices? This is a bit like asking how your car identifies whether the vector you're giving it is its new position or its new velocity. There are various things you can do to quantum systems. All can be ... • 38.8k 5 votes Accepted ### Is it possible to implement any random Hamiltonian using quantum circuit I think you are asking whether a quantum computer can efficiently simulate the evolution of any Hamiltonian, as long as the Hamiltonian is represented by a hermitian matrix. There are some details ... • 12.8k 4 votes ### Can we always simultaneously diagonalize$H_A \otimes \mathbb{1}$and$\mathbb{1} \otimes H_B$? I'm assuming these Hamiltonians act on separate subsystems, since that's the only way to guarantee that$[H_A \otimes \mathbb{1}, \mathbb{1} \otimes H_B] = 0$. Since the two Hamiltonians act on ... • 1,233 3 votes ### Is there an efficient algorithm for decomposing an arbitrary Hamiltonian into Pauli strings? Your output size is$4^n$numbers, so you're certainly not going to do better than$\Omega(4^n)$complexity. At least, not without some sort of sparsity guarantee and some way to compute those big ... • 38.8k 3 votes ### Is there an efficient algorithm for decomposing an arbitrary Hamiltonian into Pauli strings? For example see the one proposed recently in https://arxiv.org/abs/2401.16378. In my tests, I could decompose random$N=11$-qubit Hamiltonian in about$ \sim 150$minutes. • 261 3 votes Accepted ### Hamiltonian in CNOT gate implementation The total Hamiltonian$\hat{H}$is written as the sum of the following three terms: $$\hat{H}_1 = \frac{\hbar \omega_1}{2} \hat{\sigma}_{z1} \otimes \hat{I}$$ $$\hat{H}_2 = \hat{I} \otimes \frac{\... • 1,552 3 votes Accepted ### 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? TL;DR: In general, this cannot be done exactly, because of the relationship between the eigenvectors of A and e^A. That said, the Feynman's clock construction gets pretty close to realizing the ... • 23k 3 votes Accepted ### How does a quantum system identify hermitian and unitary matrices? Aha, think I might have an idea about your confusion. So most quantum systems you'll learn about in an introduction to quantum computing evolve according to some unitary process, usually denoted U(t)... • 1,438 2 votes Accepted ### Can a Hamiltonian of a tripartite system map an product state into a product state? Let's just do the special case of 3 qubits. Without loss of generality (up to unitary transformations, rescalings,...), H_A and H_B might as well be Pauli Z matrices. There are two possibilities ... • 59.4k 2 votes ### Adiabatic computing basics Just as with the case of algorithms like QAOA and VQE, the Hamiltonians are actually already known (for example, a Hamiltonian encoding a graph problem); in fact, the use case for any of these ... • 1,233 2 votes Accepted ### How to implement Hamiltonian 0.01Z? I found the answer. The R_x and R_z gates do exactly that. Decomposing the Pauli Trotter Evolution funktion helped answer that. 2 votes ### How to implement Hamiltonian 0.01Z? If I got it well, to implement what you want in Qiskit you can do the following: ... • 1,552 2 votes ### About the formulation of an Ising Hamiltonian The square comes from the definition of the Hamilton H_A given in equation (8) of the referenced paper. This term is described by "... is an energy which provides a penalty if the number of ... • 133 2 votes Accepted ### How to write the hamiltonian for w state? I understand from the comments that the question is really to find a Hamiltonian H and a corresponding time t such that$$ e^{-iHt}|000\rangle=|w\rangle $$where$$ |w\rangle=\frac{1}{\sqrt{3}}(|... • 59.4k 1 vote ### help understanding gate to hamiltonian and representation There are many ways that you could go about doing this. (You might also want to take a look at what you"know" about exponentiating a matrix, because you've exponentiated$A$not$iA$.) One ... • 59.4k 1 vote ### Underlying Hamiltonians and pulse level controls of different commercially available quantum computers This hamiltonian is a very basic approximation of the underlying device and in general does not accurately reflect the complexity of the device. It is up to each provider to decide whether to return ... 1 vote ### Phase accumulation for multiple Rabi driving pulses Good question! Your first equation mixes a couple of abstractions that we typically sweep under the rug, so let's start by taking a step back. When we apply a control pulse to a qubit, it's usually ... • 1,438 1 vote ### Is there a general method for calculating expectation values for time-dependent wavefunctions? I won't give the final answer (close to it), but instead try and point you in the general direction. Initial State: The given initial state is$ | \psi(t=0) \rangle = | 0 \rangle $. Pauli X Matrix: ... • 763 1 vote Accepted ### How to combine measurement of each term in Hamiltonian$H = aH_1 + bH_2$to get final results? Community Wiki It seems like you wish to perform a "Local Hamiltonian Simulation" where your Hamiltonian$H$is the sum of two separate terms: $$H=aH_1+bH_2.$$ That is, you wish to ... 1 vote ### Knapsack problem formulation It seems I mixed 2 formulations. It solves the problem with algorithm. Regarding randomness it is connected to backend set up on IBM Q. • 29 1 vote ### How can I implement a Hamiltonian which is sum of tensored pauli operators on qiskit? The simplest way to do that is to use HamiltonianGate ... • 10.9k 1 vote ### Excplicit Description of Hamiltonians? Your circuit appears a little confusing to me. The Hamiltonian$H$is a hermitian matrix, and is not a ket (a vector) itself. The output of the evolution is not$|e^{-iHt}\pm\varepsilon\rangle$, but ... • 12.8k 1 vote ### Meaning of 'O_i' and 'Δ_i' terms in PulseBackend Hamiltonians After some research and feedback from the IBM slack channel, I figured out the meaning:$\Delta_i$represents the anharmonicity of the transmon qubit and has units of frequency$O_i$is the number ... 1 vote ### How to choose values of phi for Hamiltonian simulation with Quantum Singular Value Transform? Appendix C in "Grand Unification of Quantum Algorithms" mentioned the pyqsp open source package. QSPPACK package contains an implementation of the Remez exchange algorithm. This package is ... • 10.9k 1 vote Accepted ### Understanding Hamiltonian's of the Single Qubit Gates and Toffoli gate It is true that every unitary can be written as$U=e^{i H t}$where$H$is a Hermitian matrix. Also, if$H$is a 2-local Hamiltonian acting on$n$qubits, then$U=e^{i H t}$is a$2^n \times 2^n\$ ...
• 2,684

Only top scored, non community-wiki answers of a minimum length are eligible