Questions 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].

160 questions
Filter by
Sorted by
Tagged with
141 views

281 views

Cirq.simulate expectation value of a Hamiltonian

I want to simulate the final state of an ansatz in cirq using simulate. Now I want to calculate the expectation value of a Hamiltonian. How do I do this? I can only find simulator.run examples in cirq....
65 views

322 views

Proof that any unitary can be written as $U=e^{-iH}$ with $H$ Hamiltonian with bounded norm

I am looking for a proof that any unitary matrix can be written as: $$U = e^{-iH}$$ where $H$ is some Hamiltonian with bounded norm. That is $$||H||_{2} = O(1).$$
108 views

Simulate a random quantum state time evolution in Qiskit Aqua

I am trying to evolve a quantum state through a PauliTrotterEvolution in aqua and I'm trying to do so by initializing a random state, by using ...
262 views

XX and YY and ZZ Hamiltonians in vqe

I'm trying to implement a vqe in cirq and I have sort of a brain knot. I have a 4 qubit chain with periodic boundary condition. So in fact a 2x2 qubit grid. Now 2 of them each are coupled. How do I ...
162 views

Impact of ordering Hamiltonian terms for Trotterization

In Trotterization, the typical Hamiltonian considered is: $$H = \sum_{p, q} h_{pq} a^{\dagger}_p a_q + \sum_{p, q, r, s} a^{\dagger}_p a^{\dagger}_q a_r a_s$$ Which is then converted into a sequence ...
96 views

Changing the Basis

I am attempting to use a VQE algorithm to find the ground state of a deuterium nucleus by applying a constructed hamiltonian to an ansatz state with one parameter created by a circuit. While I am ...
79 views

Is there a tool to get the quantum circuit corresponding to a sparse matrix?

If I know a sparse matrix, is there any tool that allows me to get the corresponding quantum circuit directly? If not what should I do? For example，I want to try hamilton simulation and I have the ...
275 views

Representation of rotation operators $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ about arbitrary axis for $3$ qubits

I was wondering in how to interpret and represent the operator $e^{-i\theta(I-Z_1\otimes Z_2 \otimes Z_3)}$ for a 3 qubit system in a circuit using qiskit. I was thinking I could just perform an ...
191 views

Why does one need a non-commuting Hamiltonian for an algorithm to exhibit "quantumness"

In two places so far, I've heard statements of the sort "... and we need the Hamiltonian to be non-commuting. If not, the algorithm is classical, and we get no benefit from using a quantum computer." ...
85 views

What do coupling coefficients mean in terms of Pauli gates, and why are they time dependent?

I am reading this error mitigation paper by the IBM team and I am slightly confused about the meaning of "coupling coefficients" when describing multi-qubit Hamiltonian. I have only seen ...
255 views