# 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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### What does a solvable Hamiltonian model mean?

I have recently been reading about simulating the dynamics of many body Hamiltonians by means of quantum computers and I am a bit confused about some terminology. I understand that if you are able to ...
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### Expectation Value of Observable from evolved statevectors using qiskit on Hardware

I want to compute this <Zi Zj> - <Zi><Zj> for an entangled n-qubit initial state under the application of a general XY Hamiltonian for a range of ...
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### On the inverse of LCUs for Hamiltonian simulation

Let $H = \sum_j \alpha_j U_j$ be a linear combination of unitaries (LCU) representation for a Hamiltonian that we wish to simulate (i.e., construct a circuit approximating $e^{iHt}$). The standard ...
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### Are quantum states like the W, Bell, GHZ, and Dicke state actually used in quantum computing research?

I recently started studying quantum computing and learned about several well-known quantum states such as the W state, GHZ state, and Dicke state. I noticed that there are also some questions here on ...
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### Coding a hamiltonian in qiskit

I have a hamiltonian of the form: $H=\sum_{i=1}^N Z_i Z_{i+1}-Z_NZ_1$ And another one as: $H=-\sum_{i=1}^N X_i$ I need it to it for N terms. I am a bit lost can anybody help. I tried looking for ...
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### What are hamiltonians in the context of quantum computing

Sorry if this question is a bit too generic or basic, but my background lies only in mathematics and computer science. I am currently writing my thesis on the topic of simulating quantum computing ...
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### The support of the ground state of stoquastic Hamiltonian is connected

A Hamiltonian $H$ is stoquastic in the standard basis if all the off-diagonal terms of the Hamiltonian are non-positive. If we choose $\beta$ small enough, all entries of $I-\beta H$ are non-negative. ...
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### Efficient method to find square root of a Hamiltonian

I'm working with a Hamiltonian $H$ represented as a linear combination of Pauli strings: $$H = \sum_j \alpha_j P_j,$$ where $P_j \in \{I, X, Y, Z\}^{\otimes n}$ are tensor products of Pauli matrices ...
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### Reference for a proof of QMA-completeness of sparse Hamiltonian

It is well-known that the $k$-local Hamiltonian problem is QMA-complete for $k$ constants over $n$ qubits, $||{H}|| \in \text{poly}(n)$ under a reasonably large promise gap. See e.g. these notes. ...
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### Cosine of an operator (a+a.dag()).cosm() in Qutip does not work as it should

As mentioned in the title, the .cosm() method in QuTip fails to give the correct evolution under the Hamiltonian. I am trying to define the Hamiltonian of a non-linear LCJ circuit as follows: ...
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### What is the intuition behind achieving Quantum advantage in simulating non-hermitian dynamics using Quantum computer?

There have been several works on simulating ODE for classical systems like here and here. They are quantum techniques to solve the ODE related to classical systems. A generic methodology is: To solve ...
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### Do some Hamiltonian simulations require an irreversible process?

I just stumbled upon this research paper https://arxiv.org/abs/2309.16596. They claim to have found a problem which is easy to solve quantumly but hard classically: to find local minima of 2D ...
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### Entanglement generation for commuting Hamiltonian

Consider an $n$ qubit Hamiltonian $H$ given by $$H = \sum_{i=1}^{m} H_i,$$ where each $H_i$ is a $k$-local term and it holds that e^{H} = e^{H_m} \cdot e^{...
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### Time-derivatives of Observables over Hamiltonian evolution

I am reading about algorithms to simulate Hamiltonian evolution by means of quantum computers, e.g. a transverse field Ising model. As far as I see one is interested in getting expectation values of ...
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### What work has been done on hamiltonian simulation of operators that are integrals instead of sums?

I'm looking at a problem where I want to do hamiltonian simulation of an operator integral. That is, I want to implement the unitary $$\mathrm U = \exp[-i \mathrm H t]$$ where $\mathrm H$ is of the ...
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### Spin Hamiltonian to Quantum Circuits and are there any group theory associated with the quantum circuits?

Can we think of Quantum Circuits as another representation to describe the dynamics of a system other than its Hamiltonian? How can we go from the spin Hamiltonian version (for eg: SSH Model ...
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### Deriving circuit templates for Hamiltonian simulation

Background I've been reading the paper entitled Some improvements to product formula circuits for Hamiltonian simulation. The authors propose three improvements motivated by phase estimation type ...
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### How useful is it to know the ground state energy of an arbitrary $k$-local Hamiltonian, if Nature herself can never find such energy?

We know that the $2$-local Hamiltonian problem is (promise) QMA-complete, which under the reasonable assumption that BQP$\subsetneq$QMA implies that no fast quantum algorithm exists to determine the ...
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### The no fast forwarding theorem and exponential advantage for many body Hamiltonians

When simulating Hamiltonians in first quantization there are $\eta$ particles occupying a grid of $N$ grid points. In the first quantization, you directly discretize the differential operators onto a ...
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### time evolution of Hamiltonian and observables

I am given the following Hamiltonian on 4 qubits. $$H = - J_x (X_0 X_1 + X_2 X_3) - J_z (Z_0 Z_2 + Z_1 Z_3) - h\sum_{j=0}^3 X_j + Z_j$$ I have already implemented the time evolution of this ...
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### How is implemented the hamiltonian simulation of Hermitian operator multiplied by projection

The article "Quantum Topological Data Analysis with Linear Depth and Exponential Speedup" (Ubaru et al) discusses the implementation of the Hamiltonian $\Delta_\Gamma$, named the ...
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### How to model the transtition part of dispersive frequency shift in dispersive readout?

The phenomenon of interest is the resonance frequency shift and the larger noise in the measurements inside the intermediate-powered region as shown below (from Fig. 3.3 of Characterisation of ...
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### Efficient gate executing the time evolution of a Hamiltonian using Runge-Kutta method

You can find a minimal working example below. In particular, I want to replace the scipy.linalg.expm() matrix exponential by a Runge Kutta time evolution method as ...
I'm new to Qiskit. I am trying to construct a gate from HamiltonianGate(), available on Qiskit. The Hamiltonian in question is: H = - \pi\delta(Z_1 - Z_2) + 2\pi J ~ \mathbf{I}_1 \cdot \...