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Quantum Algorithms for solving differential equations

Home Page: https://quantumbfs.github.io/QuDiffEq.jl/latest/

License: MIT License

Julia 100.00%

qudiffeq.jl's Introduction

QuDiffEq

Quantum algorithms for solving differential equations.

This project is part of Julia's Season of Contribution 2019.

For an introduction to the algorithms and an overview of the features, you can take a look at the blog posts: #1, #2.

Installation

QuDiffEq is a Julia Language package. To install QuDiffEq, please open Julia's interactive session (known as REPL) and press ] key in the REPL to use the package mode, then type the following command

pkg> add QuDiffEq

Algorithms

Quantum Algorithms for Linear Differential Equations,
- Based on truncated Taylor series
- Based on HHL.
Quantum Algorithms for Non Linear Differential Equations.

Built With

Yao - A framework for Quantum Algorithm Design
QuAlgorithmZoo - A repository for Quantum Algorithms

Authors

See the list of contributors who participated in this project.

License

This project is licensed under the MIT License - see the LICENSE.md file for details

References

D. W. Berry. High-order quantum algorithm for solving linear differential equations (https://arxiv.org/abs/1010.2745)
Tao Xin et al. A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment (https://arxiv.org/abs/1807.04553)
Sarah K. Leyton, Tobias J. Osborne. A quantum algorithm to solve nonlinear differential equations(https://arxiv.org/abs/0812.4423)
P. C.S. Costa et al. Quantum Algorithm for Simulating the Wave Equation (https://arxiv.org/abs/1711.05394)

qudiffeq.jl's People

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stjordanis stanescuuw shilpi1958 olgok daradarry

qudiffeq.jl's Issues

The solve method doe not work

It seem solve does not work independently in QuDiffEq. It required using OrdinaryDiffEq

using  QuDiffEq

# dx/dt = 3*x + 4

M = hcat(3.0)
b = [4.0]
x_0 = [2.0]
tspan = (0.0, 1.0)

qprob = QuLDEProblem(M, b, x_0, tspan)
sol = solve(qprob, QuLDE(5))

ERROR: UndefVarError: solve not defined

using  QuDiffEq
using OrdinaryDiffEq

# dx/dt = 3*x + 4

M = hcat(3.0)
b = [4.0]
x_0 = [2.0]
tspan = (0.0, 1.0)

qprob = QuLDEProblem(M, b, x_0, tspan)
sol = solve(qprob, QuLDE(5))

Prints result

1-element Vector{ComplexF64}:
 59.999999999999986 + 0.0im

register package

A few things to do before we release this:

finish docs
fix examples

[Tutorials] More examples

Hello! Thank you for your wonderful work on solving DE on quantum device.

I have never had experience with Julia, so I use Python JuliaCall. Could you please provide more examples how to submit DE to the QuDiffEq solver? I tried a really straightforward example such as dx/dt = 3x+4, but could not figure out a correct way of creating the M, b and x_initial matrices (I follow the notation dx/dt=Mx+b). What data types should I use for this matrices if M, x,b are numbers?

Why the QuDiffEq can not be precomplied?

ERROR: LoadError: Failed to precompile QuDiffEq [c02438fe-7edc-11e9-0a49-b5c5aafabe04] to C:\Users\35321.juliapro\JuliaPro_v1.4.2-1\compiled\v1.4\QuDiffEq\hei7O_TPJID.ji.
Stacktrace:
[1] error(::String) at .\error.jl:33
[2] compilecache(::Base.PkgId, ::String) at .\loading.jl:1272
[3] _require(::Base.PkgId) at .\loading.jl:1029
[4] require(::Base.PkgId) at .\loading.jl:927
[5] require(::Module, ::Symbol) at .\loading.jl:922

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Inputs for HHL-based linear differential equation solvers

At the moment, HHL based linear differential equation solvers take inputs as time dependent functions alone i.e.

# for solving M x = b

A(t) = M
b(t) = v

qprob = QuLDEProblem(A, b, x, tspan)
res = solve(qprob, QuEuler(), dt = h)  # alg is HHL based

Therefore, solve throws an error if we input constant matrices. We need to update solve to accomodate constant inputs, keeping in line with the input scheme for the other linear differential equation solver, QuLDE.