# 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].

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### Hamiltonian Simulation: What's the meaning of t in $\exp(iAt)$?

My main goal is to find eigenvalues of some hamiltonian matrix $A$. When implementing Quantum Phase Estimation, I need to provide my circuit with informations about $A$. From what I have seen so far, ...
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### Turning Deutsch-Josza into a continuous problem

I am wondering whether anyone has investigated if there is a notion of a continuous oracle. My starting off point is to consider the Deutsch-Josza problem, in which the oracle acts on the state in a ...
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### non-stoquastic vs quantum annealer

Why non-stoquastic Hamiltonian is difficult to implement for a quantum annealer? In another way, why stoquastic vs non-stoquastic matters? Thanks.
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### What problems in chemistry or materials science could be solved with 100 fault-tolerant qubits?

Background IBM, Infleqtion, QuEra, and other quantum hardware companies have announced roadmaps where they expect to have 100 or more fault-tolerant qubits by the end of the decade. It seems ...
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### Qiskit TimeEvolutionProblem with complex operator

I have been using Qiskit to simulate some oscillators using Hamiltonian simulation. A next step I would like to make is adding dissipation of these oscillators in some way. I think it would be ...
1 vote
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### How to approximate the time-dependent Hamiltonian in quantum adiabatic theory by the non time-dependent Hamiltonian?

Recently, I am learning how to solve the linear equation $A\left | x \right \rangle =\left | b \right \rangle$ using quantum adiabatic theory. In the solving process, people usually need to set the ...
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### Calculating number of CNOT gates in Pauli evolution gate

How to calculate the number of CNOT gates for a Pauli exponentiation for given time? I am performing Trotterization which involves performing Pauli evolution ...
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### Particle number expectation value in QuTip

I am learning now to use QuTiP by going through their documentation site. I am trying to understand what does the argument - particle number expectation value in thermal density matrix do? How does it ...
1 vote
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### Qiskit: Evolve TrotterQRTE from Operator

I am trying to implement the method in the following paper: Exponential Quantum Speedup in Simulating Coupled Classical Oscillators using Qiskit. All is good until I call evolve on ...
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### Are commuting unitary operators related to commuting Hamiltonians?

TL/DR: Can unitary operators: $$U_a=e^{-it(H_{a1}+H_{a2}+\cdots)}$$ and $$U_b=e^{-it(H_{b1}+H_{b2}+\cdots)}$$ commute, even though $[H_{aj},H_{ak}]\ne 0$ and $[H_{bj},H_{bk}]\ne 0$ for all $j,k$? ...
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### Modeling a chemical reaction when there is a catalyst

I'd like to construct potential energy surfaces (PES) for chemical reactions with and without the presence of a catalyst. Something like this The closest paper that is https://arxiv.org/pdf/2007....
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### Complexity of controlled-$U^j$ operations in QPE applied to Hamiltonian simulation

One method to obtain the eigenvalues of a Hamiltonian $H$ is by applying quantum phase estimation to its time-evolution operator $U(t) = e^{-iHt}$. If I want to obtain an eigenvalue to $k$ bits in ...
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### How to simulate low-rank hamiltonian?

I want to implement a unitary $U\,,$ $$U=\text{exp}(-it|u\rangle\langle u|)\,,$$ where $|u\rangle$ is a known state. Are there any methods to do this efficiently?
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### Why is "reducing Hamiltonian energy" also optimizing a Quantum Machine Learning model?

From what I observed, most hybrid qml architectures surround the ideas of Hamiltonian states, and it seems like our goal to optimize a circuit is to keep energy states as low as possible. But why is ...
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### How to define an energy function, for predicting protein structure in quantum computing? [closed]

Let q denote a particular configuration of the protein in a grid, written in the form where $x_i$ and $y_i$ are the $x$ and $y$ coordinate of the $i$th amino acid. For this configuration, how to ...
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### How is geometric frustration different from (not) being frustration free?

In the context of Ising models, some Hamiltonians can be described as geometrically frustrated - such as, I think, the antiferromagnetic kagome lattice, as well as a one-dimensional anisotropic, next-...
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### What properties of a local Hamiltonian are basis-(in)dependent?

Some properties of a Hamiltonian are unique to its spectrum and are basis-independent. For example, I think whether the Hamiltonian's gap remains constant as $n$ goes to infinity, or whether the ...
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