Is there any online Bloch sphere simulator?

Is there any online Bloch sphere simulator? Ask Question Asked 6 years, 10 months ago Modified 5 days ago Viewed 10k times 17 While writing this answer I realized it would be really helpful if I could show the OP a video or .gif of how qubit states in Bloch spheres transform under certain unitary operations. I googled up a bit and could find only these two simulators: Bloch Sphere Simulation (Stephen Shary and Dr. Marc Cahay) Wolfram Demonstration Project: Qubits on the Poincaré (Bloch) Sphere Both involve some messy software installations and I don't really want to do that. The second one apparently doesn't even allow the user to input arbitrary 2×2 operators! P.S: It would be great if Craig Gidney could add a full-fledged Bloch sphere simulator within Quirk at some point (ideally, by making the already existing Bloch sphere views of the qubit states clickable and enlargeable). :) resource-requestsimulationbloch-sphere Share Improve this question Follow edited May 20, 2019 at 19:23 asked May 20, 2019 at 13:21 Sanchayan Dutta 18.2k9 9 gold badges 56 56 silver badges 118 118 bronze badges Add a comment 7 Answers Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 10 This doesn't really answer the question as it's not an online simulator. It might still be relevant though as it is a way to produce this sort of gifs if one has access to the software. It is relatively easy to do this sort of things using Wolfram Mathematica. As a quick and dirty example, if we just define a couple of relevant helper functions: pauliX = PauliMatrix[1]; pauliY = PauliMatrix[2]; pauliZ = PauliMatrix[3]; ClearAll@decomposeInPauliBasis; decomposeInPauliBasis[matrix_?MatrixQ] := { Tr[matrix.pauliX], Tr[matrix.pauliY], Tr[matrix.pauliZ] }/2; decomposeInPauliBasis[vec_?VectorQ] := Re@{ Dot[Conjugate@vec, pauliX, vec], Dot[Conjugate@vec, pauliY, vec], Dot[Conjugate@vec, pauliZ, vec] }; ClearAll[simulateStateEvolution, smallestEigenvectors]; smallestEigenvectors[matrix_, howmany_Integer] := With[ {nn = Norm@Flatten@matrix}, Eigenvalues[matrix - nn IdentityMatrix[Dimensions@matrix], howmany] + nn ]; simulateStateEvolution[H : (_Symbol | _Function | _CompiledFunction), time_: 1., initialState_: None] := Module[{t}, Module[{\[DiamondSuit]initialState, \[DiamondSuit]H}, If[initialState === None, \[DiamondSuit]initialState = First@smallestEigenvectors[H[0], 1], \[DiamondSuit]initialState = initialState ]; (* protect from symbolic evaluation *) \[DiamondSuit]H[ t_?NumericQ] := H[t]; NDSolveValue[{ \[Psi][0] == \[DiamondSuit]initialState, \[Psi]'[t] == -I \[DiamondSuit]H[t].\[Psi][t] }, \[Psi], {t, 0, time} ][time] ] ]; we can then visualise the evolution in the Bloch sphere with hamiltonian[t_] := pauliZ + 2 pauliX; initialState = {1, 0}; With[{points = Table[ decomposeInPauliBasis@ simulateStateEvolution[hamiltonian, t, initialState], {t, 0, 1, 0.01} ]}, Graphics3D[{ {Orange, Opacity@0.2, Sphere[{0, 0, 0}, 1]}, {Red, PointSize@0.02, Point@points[[1]]}, {Blue, PointSize@0.02, Point@points[[-1]]}, Dashed, Thickness@0.005, Arrow@points }, Axes -> True, AxesOrigin -> {0, 0, 0}, AxesStyle -> Black, Ticks -> None, Boxed -> False] ] which gives We can also use a time-dependent Hamiltonian, for example: hamiltonian[t_] := pauliZ + t pauliX; initialState = {1, 0}; With[{points = Table[ decomposeInPauliBasis@ simulateStateEvolution[hamiltonian, t, initialState], {t, 0, 4, 0.01} ]}, Graphics3D[{ {Orange, Opacity@0.2, Sphere[{0, 0, 0}, 1]}, {Red, PointSize@0.02, Point@points[[1]]}, {Blue, PointSize@0.02, Point@points[[-1]]}, Dashed, Thickness@0.005, Arrow@points }, Axes -> True, AxesOrigin -> {0, 0, 0}, AxesStyle -> Black, Ticks -> None, Boxed -> False] ] If you want something a bit more fancy, you can take the code I used in this answer to draw a better looking Bloch sphere, which would give something like the following: Finally, if you want some animation, you can try something like the following (where I'm also adding the green line to denote the instantaneous eigenvector of the Hamiltonian): hamiltonian[t_] := pauliZ + t pauliX; initialState = {1, 0}; timesList = Range[0, 4, 0.01]; With[{points = Table[ decomposeInPauliBasis@ simulateStateEvolution[hamiltonian, t, initialState], {t, timesList} ]}, Animate[ Graphics3D[{ {Orange, Opacity@0.2, Sphere[{0, 0, 0}, 1]}, {Red, PointSize@0.02, Point@points[[1]]}, {Purple, PointSize@0.02, Point@points[[idx]]}, {Darker@Green, Thickness@0.01, InfiniteLine@{-#, #} &@ decomposeInPauliBasis@ First@Eigenvectors@hamiltonian@timesList[[idx]]}, {Dashed, Thickness@0.005, Tube@points[[;; idx]]} }, Axes -> True, AxesOrigin -> {0, 0, 0}, AxesStyle -> Black, Ticks -> None, Boxed -> False], {idx, 1, Length@points, 1} ] ] (quality and smoothness can definitely be improved here) Share Improve this answer Follow edited May 23, 2019 at 14:08 answered May 22, 2019 at 14:09 glS♦ 28k7 7 gold badges 43 43 silver badges 139 139 bronze badges Add a comment 7 Have you tried the Bloch Sphere Playground Application? It just might be what you are looking for. Bloch Sphere Playground Application https://javafxpert.github.io/grok-bloch/ Share Improve this answer Follow answered Jan 15, 2020 at 1:34 ProfVersaggi 2132 2 silver badges 5 5 bronze badges This link, unlike the other Block sphere simulator's google was giving me, finally helped me to understand what I missing about phase. (Well there are tonnes and tonnes of other things I'm still missing, but at least I'm over one hump thanks to you. –  Joel Roberts Commented Jun 10, 2024 at 0:58 Add a comment 7 Let me plug my pet project: https://attilakun.net/bloch It allows you to enter arbitrary 2x2 matrices and visualize how the quantum state is affected by them. In the below example the red arc shows how the H matrix transforms the |0⟩ | 0 ⟩ state (yellow arrow) into |+⟩ | + ⟩ : Also, it's open source if you want to play around with the code: https://github.com/attila-kun/bloch Share Improve this answer Follow answered Jan 23, 2021 at 22:23 Attila Kun 5995 5 silver badges 10 10 bronze badges Add a comment 6 I used this last time I needed to look up something about Bloch sphere. It's not perfect, since it doesn't allow entering the exact values of angles, let alone 2x2 matrices, but it has the benefit of being available online. This one looks promising in that it allows to enter matrices (and is also online), but I haven't tried it. Share Improve this answer Follow edited May 20, 2019 at 17:08 Sanchayan Dutta 18.2k9 9 gold badges 56 56 silver badges 118 118 bronze badges answered May 20, 2019 at 16:00 Mariia Mykhailova 9,3451 1 gold badge 14 14 silver badges 41 41 bronze badges Erm, tried the second one. Not sure how it works. Ticked "active" for Ψ 1 Ψ 1 , entered 0,0 corresponding to θ 𝜃 and ϕ 𝜙 and tried with the pre-defined unitaries. The top display shows an empty Bloch sphere. –  Sanchayan Dutta Commented May 20, 2019 at 16:13 None of the links worked for me. Up-to-date Firefox (67.0) on Linux. I don't know if Chrome users or Mac/Windows users had more chance. –  Adrien Suau Commented May 23, 2019 at 12:13 @Nelimee Odd, the first one worked for me (Firefox on Ubuntu). –  Mariia Mykhailova Commented May 23, 2019 at 15:58 Add a comment 4 I see this thread is a little old but if folks are still looking, here's my pet project showing 2 Bloch spheres. In addition to the full array of standard gates (1 and 2 qubit), the simulation also generates Q# code (and output) on the fly which you can paste and run directly into a Q# program. Given there are 2 qubits, you can also see when they get entangled. It's all written in Javascript and a link to the code is provided. Enjoy! https://renniedatascience.com/Bloch Share Improve this answer Follow answered Oct 10, 2022 at 22:23 Rob Rennie 412 2 bronze badges Add a comment 2 I am the developer of unbloched.xyz, it is an open source project I've been working on for the last year while studying quantum related topics. The website is a Bloch sphere simulator with a lot of features and a nice user interface. It has L A T E X 𝐿 𝐴 𝑇 𝐸 𝑋 support to input arbitrary density matrices and gates. It supports noise simulation and can export nice images for hand-outs and similar (I put and example below). With the help of other students we also built an interactive tutorial that introduces the general concepts of quantum information. Share Improve this answer Follow edited Mar 11 at 9:31 answered Mar 3 at 11:50 gamberoillecito 212 2 bronze badges Add a comment 1 I use very regularly this site: https://bloch.kherb.io It is useful to understand and engineer quantum control sequences as well as to generate plots for talks. Share Improve this answer Follow answered Aug 19, 2023 at 10:12 P. Egli 1111 1 bronze badge Very good tool, +1. –  Martin Vesely Commented Aug 19, 2023 at 20:09 Add a comment Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions resource-requestsimulationbloch-sphere See similar questions with these tags. 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