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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Can we use quantum phase estimation to learn anything about the dynamics of puzzles like the Rubik's cube?

Introduction Consider a state $\vert\psi\rangle$ as below, which is in a superposition of a difference between a Rubik's cube in a solved state and a Rubik's cube in the "superflip" state. ...
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Trotter error for bosons in various encodings

Mapping second-quantized bosonic modes onto qubits can be done using various encodings. Each of those have their pro et contra. Fewer qubits — more gates, and vice versa. Encoding an $N$-level bosonic ...
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Is there a systematic way how to generate the Hamiltonian from a given circuit?

If I have a designed circuit to solve a particular problem. Is there a systematic way how to generate the Hamiltonian from it?
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What is the usefulness of the Suzuki-Trotter formula?

I can't seem to wrap my head around the suzuki-trotter formula. I have seen This answer but I am still confused of the applicability of the formula. Let me explain: As I understand it Trotterization ...
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How to convert a qubit hamiltonian to QUBO and vice versa?

This is my hamiltonian. Solving this by hand, Numpy Python package and VQE algorithm gives the minimum energy eigenvalue -2. If we want to find the minimum energy of this hamiltonian with Quantum ...
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Numerical approximation to eigenstates and their differentials

I am working in Adiabatic Quantum Computing and I have a $6\times6$ Hamiltonian. I have only the symbolic expression for its eigenstates which have complicated expressions in solutions of degree $6$ ...
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How to find minimum time needed for Hamiltonian evolution?

Database search can be looked upon as Hamiltonian evolution, with kinetic and potential energy operators. Let the evolution follow the Schrodinger equation: $$i\frac{d}{dt}|\psi⟩= H|ψ⟩$$ with $H = E|s⟩...
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What type of tasks it is possible to solve on a quantum simulator?

In this article, the author claimed that researches from Harvard and MIT created 256 qubits quantum simulator. However, we are not talking about piece of software on a classical computer but actual ...
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Reducing cost of Phase Estimation for Trotterization

Even though Trotterized Hamiltonians have polynomial time scaling directly, the process of quantum phase estimation means that the controlled unitaries $ CU$ scale exponentially with number of ...
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86 views

How close is the history state to the ground state in the Kitaev clock construction?

Consider a standard circuit to Hamiltonian reduction in QMA. For example, refer here (Vazirani's lecture notes) or page 235 of here (survey by Gharibian et al). The history state of the Kitaev clock ...
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XX, YY, ZZ circuit representations?

Is there a good primer or set of lectures\examples that show entirely how to take a given matrix and developing a circuit that represents it. I am trying to implement a program to find the lowest ...
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Estimating errors in Hamiltonian Simulation paper

I am looking at the paper: Simulating Hamiltonian dynamics with a truncated Taylor series and I am explicitly interested in Eq (15) and (16). These read $$ ||PA |0\rangle |\psi \rangle - |0\rangle ...
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Quantum Optimization via Quantum Label Classification in Quantum Circuits

I have been reading Farhi and Neven's paper on quantum neural networks on quantum circuits. I also found an example - albeit not ideal as pointed out by a couple of users - thank you - in here. ...
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Could the Hamiltonian of a Rubik's Cube be simulated with a NISQ device?

Consider the four cells on each of the six faces of the 2x2x2 Rubik's cube (the pocket cube), with front, up, and right twists being labelled as $\langle F,U,R\rangle$. Each move uses fifteen SWAP ...
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Eigenvalues and energy levels of 1D Heisenberg model using real Quantum Computers?

The 1D Quantum Heisenberg model is $$H_\textrm{Heisenberg} = -~J \sum_{\langle i\ j\rangle} \hat{S}_{i} \cdot \hat{S}_{j}$$ where each spin is an operator. For simple cases, for example, a system with ...
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QAOA for Binary Optimization

I have reduced an optimization problem to a Binary Integer Linear Programming model as follows: $$\sum_{j=1}^{2^n-1} f(C_j)x_j \rightarrow \max$$ $$\text{subject to} \sum_{j=1}^{2^n-1} S_{i,j}x_j=1\,\,...
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Matrix multiplication through Block Encodings

For a project, I want to simulate a matrix multiplication on a simulated quantum circuit. Assuming that we have a matrix $A\in \mathbb{R}^{m\times n}$ stored in a quantum superposition, i.e. $$|A\...
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How to implement the Mixer of Quantum Alternating Operator Ansatz for Max-Independent-Set

I am trying to implement the Mixer of the Max-Independent Set from The Quantum Alternating Operator Ansatz. From this paper: https://arxiv.org/pdf/1709.03489.pdf in Chapter 4.2 page 15 to 17. For ...
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How precise are BQPSPACE measurements?

This is in a similar spirit to another question I asked here. Let's say I am given a $k$-local Hamiltonian $H$. We know that $||H|| \leq 1$. Let the ground state be $|\psi_{0}\rangle$, with energy $E_{...
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What Are The Most Promising Real-World Applications For Quantum Machine Learning

I know this has been asked before in different ways, however, I am interested in something with a degree of clarity and focus not found in other questions. What I am looking to get is a list of the ...
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VQE Cirq example

Is my understanding correct that in this example the Hamiltonian measurement is not performed through measuring individual Pauli operators because all its terms are mutually commuting? So, for each ...
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Openfermion to qiskit

Is there a direct way to go from an object generated in openfermion to objects usable in Qiskit. I can't find anything about any plugin. It's not too hard to translate into pyQuil and then to Qiskit ...
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Paradox on the evolution direction in controlled Hamiltonian simulation for Quantum Phase Estimation

Suppose we want to perform Quantum Phase Estimation over a Linear Combination of Unitaries Hamiltonian. One of the most efficient ways to do so is to use qubitization: \begin{equation} Q=(2|0\rangle\...
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Applying QPE on a large matrix on amazon-braket

I'm running a QPE algorithm on the amazon-braket but it can only apply on a 22 or 44 matrix, when I want to expand it into a 5*5 or more, it will come an error. As I know, there is no theoretical ...
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Implementation of the Phase Estimation algorithm

I've been working on implementing quantum phase estimation in Qiskit for a $2^n \times 2^n$ Hamiltonian as part of my bachelor project, I'm using Trotterization as my Hamiltonian simulation of choice ...
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Are inconsistent results between different VQE runs justified?

I made this post a while ago, where I learned I could use qiskit's VQE to calculate (or approximate) the Transverse Field Ising Hamiltonian and other similar Hamiltonians. After working with my code ...
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Has any analogue quantum simulator showed quantum advantage yet?

Quantum advantage/supremacy was achieved by Google using a quantum computer and more recently by Pan Jianwei's group using photons. So I was wondering, has any analog quantum simulator showed quantum ...
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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 ...
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Primer for Quantum Circuits and Optimization

I am interested in studying physical systems and trying to build circuits to simulate them. Now, of course, all the systems I could try to work with at simple, toy, systems - and that's fine. ...
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102 views

Exponentiating Hermitian Matrix for use in QPE/HHL

I am currently trying to understand HHL by implementing a very inefficient Qiskit simulation script that performs HHL on an arbitrary hermitian matrix $A$ and a vector $b$. Because I am currently ...
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Encoding Binary Data into Quantum Basis

I am working on implementing a paper on QNNs. I have successfully been able to resize a MNIST digit to be able to meet the size of quantum circuit. But I am not clear of how to convert the resized ...
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Ansatz Techniques to Multi-Body Physics Problems

I have been reading this paper: https://arxiv.org/abs/1906.01563v1. I am wondering: is it possible to use the idea behind quantum circuits to build classical Hamiltonians represented in the same way?...
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In the HHL algorithm, does the controlled unitary depend on the Hermitian matrix coefficients?

In HHL algorithm, does the controlled unitary (Hamiltonian simulation part of Quantum phase estimation) depend on Hermitian matrix coefficients and how?
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How can extract reduced dynamics of a bipartite system from unitary evolution in quite

Let us assume that I have a bipartite system $A\otimes B$ and an initial product state undergoing some evolution $H^{AB} = H^A+H^B+V^{AB}$, which is time independent. I want to simulate the reduced ...
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How does Qiskit's VQE encode binary digits into a solution from a given Hamiltonian?

So far I have been working with the VQE on different Hamiltonians that happened to have degeneracies, that is there were always at least two different global minima, because the Hamiltonians I was ...