<p>tricky question! there is some diverse crosscutting research into this question, and will attempt to outline it, but will in the end take the position here that the question is <em>contradictory/ impossible</em> at heart (and anticipating some this may be a controversial conclusion). here are two key recent references from a physics pov addressing your question. </p>

<ul>
<li><p><a href="http://arxiv.org/pdf/1312.1695v3.pdf" rel="nofollow">Gate count estimates for performing quantum chemistry
on small quantum computers</a> / Wecker et al</p></li>
<li><p><a href="http://arxiv.org/abs/1111.3633" rel="nofollow">Quantum Algorithms for Quantum Field Theories</a> / Jordan, Lee, Preskill</p></li>
</ul>

<p>a rough complexity theory estimate of "simulating particle physics" is to count the number of particles, and there are about $O(n^2)$ interactions between particles, and many supercomputer simulations of particle dynamics fit this. so as a rough bound, one would pick the smallest particles, but, wait! the standard model has many <em>subatomic</em> particles! so one might use neutrinos, one of the smallest known stable particles, as an estimate... but then what about unstable particles such as quarks/ leptons?</p>

<p>there is also the whole other problematic accuracy/ precision problem of <a href="https://en.wikipedia.org/wiki/Butterfly_effect" rel="nofollow">the butterfly effect</a> long known in computational physics aka "sensitive dependence on initial conditions".</p>

<p>Aaronson write in his essay <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/is-there-anything-beyond-quantum-computing/" rel="nofollow">Is There Anything Beyond Quantum Computing?</a>:</p>

<blockquote>
  <p>Is there any such problem that couldn’t be solved efficiently by a quantum computer, but could be solved efficiently by some other computer allowed by the laws of physics?</p>
</blockquote>

<p>so he sketches out weird physics such as black holes or quantum gravity that might not be simulable by a quantum computer. but flipping this whole essay on its head (in a manner it which it was unintended), what he is describing are frontier areas of physics that currently do not have <em>complete/ definite physical theories known by humans</em> (at best, only plausible candidates/ approximations floating around.) eg: </p>

<ul>
<li>black holes</li>
<li>time curves</li>
<li>quantum gravity</li>
</ul>

<p>(adding to his list) </p>

<ul>
<li>dark matter/ energy</li>
<li>virtual particles, vacuum energy</li>
</ul>

<p>so the problem comes in your title that you literally want to <em><strong>fully</strong> simulate</em> a cubic meter of space. but the standard model is actually ultimately/ technically widely acknowledged/ conceded by physicists themselves (if pressed!) as an <em>incomplete</em> model of reality due to all the extreme/ problematic "edge cases" listed above, and others not known. even the standard model itself is problematic in that new particles/ tiny forces and revisions are added/ modified all the time, nearly "regularly", even the famous/ celebrated <a href="https://en.wikipedia.org/wiki/Higgs_boson" rel="nofollow">Higgs particle</a> recently.</p>

<p>so actually its a major open question of physics whether the basic rules of reality are computable. this ties in with the <a href="https://en.wikipedia.org/wiki/Digital_physics" rel="nofollow">digital physics</a> research agenda.</p>

<p>so physicists generally regard the idea that physics of reality is computable as something of an "approximation" that physical theories are in the continual process of evolving/ finetuning but "very thorough/ precise models" are ultimately not to be confused with <em>accurate simulations.</em></p>

<p>also relevant to this question/ impinging is that there is new "cutting edge/ borderline" physics theory/ research and experiments to attempt detect if we are "living in a hologram" ie some kind of "simulation". it is theorized that cosmic rays might have detectable properties indicating this, or other very sensitive experiments could reveal kinds of "digitization artifacts", etc.; one example:</p>

<ul>
<li><a href="http://www.technologyreview.com/view/429561/the-measurement-that-would-reveal-the-universe-as-a-computer-simulation/" rel="nofollow">The Measurement That Would Reveal The Universe As A Computer Simulation</a> / MIT tech review</li>
</ul>

CC BY-SA 3.0
2015-09-28T17:24:12.463Z
see also the [fallacy of Laplace's demon](https://en.wikipedia.org/wiki/Laplace%27s_demon) and [limitations of reductionism](https://en.wikipedia.org/wiki/Reductionism#Criticism)
vzn
CC BY-SA 3.0
2015-09-28T17:21:18.013Z
2015-09-28T17:21:18.013Z
vzn
<p>Imagine you want to simulate a cubic meter down to the particle. By following the <a href="https://en.wikipedia.org/wiki/Standard_Model" rel="nofollow noreferrer">Standard Model</a> and other basic physical equations, how much computing power would be required to do this, in say, a day?</p>

<p>Would a quantum computer help you in this task? Could you somehow directly simulate the particles?</p>

<p>Thanks</p>

CC BY-SA 3.0
2015-09-17T12:48:39.473Z
Seems like a question for https://what-if.xkcd.com/
Denis
CC BY-SA 3.0
2015-09-19T00:32:44.713Z
This article touches on the issue, if anyone's interested http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/is-there-anything-beyond-quantum-computing/
APCoding
CC BY-SA 3.0
2015-09-19T00:36:38.517Z
A wiki article https://en.wikipedia.org/wiki/Quantum_simulator
APCoding
CC BY-SA 3.0
2015-09-19T13:46:18.117Z
Cross-posted to physics.se: http://physics.stackexchange.com/questions/207796/how-much-computing-power-would-be-required-to-fully-simulate-a-cubic-meter
Norbert Schuch
CC BY-SA 3.0
2015-09-20T14:21:20.333Z
The answers at Physics.SE are fairly complete.  In short: it is not likely to be feasible in the foreseeable future, no, and no.
András Salamon
CC BY-SA 3.0
2015-09-21T02:47:48.467Z
somewhat related wikipedia on [limits to computation](https://en.wikipedia.org/wiki/Limits_to_computation). one way to estimate this would be to estimate the max # of smallest particles per unit of space and the amt of cost of particle simulation. but note that "real" physics simulation is far more complex eg QFT involving virtual particles. the quantity seems finite but nearly inestimable. note that in a sense it is not even really possible to simulate a unit of space due to the complexity of interactions of virtual particles etc.; physics gets more nondeterministic the deeper the theory.
vzn
CC BY-SA 3.0
2015-09-21T04:12:42.423Z
so, there is some problem with the phrase _"fully simulate"._ one could use the standard model which is indeed a computational/ algorithmic process, but it is widely admitted even by physicists to be _incomplete_ wrt some crucial derivable elements of reality that are at the boundaries of known physics eg black holes, virtual particles, dark matter, large scale vs small scale theories/ incompatibility ie GR vs QM, etc.! also note the Higgs particle was "newly" discovered only within the last few years, and physicists do not rule out new particle discoveries, some even expect them, etc!
vzn
CC BY-SA 4.0
2024-06-16T13:12:10.063Z
An infinitely infinite amount!
someonewhohasasanota
<quantum-computing><physics>
How Much Computing Power would be Required to Fully Simulate a Cubic Meter?
APCoding
# How Much Computing Power would be Required to Fully Simulate a Cubic Meter?

(Asked by: username_0 on 2015-09-17)

Imagine you want to simulate a cubic meter down to the particle. By following the [Standard Model](https://en.wikipedia.org/wiki/Standard_Model) and other basic physical equations, how much computing power would be required to do this, in say, a day?

Would a quantum computer help you in this task? Could you somehow directly simulate the particles?

Thanks

**Tags:** quantum-computing, physics
> **Comments:**
> **username_1**: Seems like a question for https://what-if.xkcd.com/  
> **username_0**: This article touches on the issue, if anyone's interested http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/is-there-anything-beyond-quantum-computing/  
> **username_0**: A wiki article https://en.wikipedia.org/wiki/Quantum_simulator  
> **username_2**: Cross-posted to physics.se: http://physics.stackexchange.com/questions/207796/how-much-computing-power-would-be-required-to-fully-simulate-a-cubic-meter  
> **username_3**: The answers at Physics.SE are fairly complete.  In short: it is not likely to be feasible in the foreseeable future, no, and no.  
> **username_4**: somewhat related wikipedia on [limits to computation](https://en.wikipedia.org/wiki/Limits_to_computation). one way to estimate this would be to estimate the max # of smallest particles per unit of space and the amt of cost of particle simulation. but note that "real" physics simulation is far more complex eg QFT involving virtual particles. the quantity seems finite but nearly inestimable. note that in a sense it is not even really possible to simulate a unit of space due to the complexity of interactions of virtual particles etc.; physics gets more nondeterministic the deeper the theory.  
> **username_4**: so, there is some problem with the phrase _"fully simulate"._ one could use the standard model which is indeed a computational/ algorithmic process, but it is widely admitted even by physicists to be _incomplete_ wrt some crucial derivable elements of reality that are at the boundaries of known physics eg black holes, virtual particles, dark matter, large scale vs small scale theories/ incompatibility ie GR vs QM, etc.! also note the Higgs particle was "newly" discovered only within the last few years, and physicists do not rule out new particle discoveries, some even expect them, etc!  
> **username_5**: An infinitely infinite amount!  

---

## 1 answers

### Answer by username_4 on 2015-09-28. Score: 1

tricky question! there is some diverse crosscutting research into this question, and will attempt to outline it, but will in the end take the position here that the question is *contradictory/ impossible* at heart (and anticipating some this may be a controversial conclusion). here are two key recent references from a physics pov addressing your question.

* [Gate count estimates for performing quantum chemistry
  on small quantum computers](http://arxiv.org/pdf/1312.1695v3.pdf) / Wecker et al
* [Quantum Algorithms for Quantum Field Theories](http://arxiv.org/abs/1111.3633) / Jordan, Lee, Preskill

a rough complexity theory estimate of "simulating particle physics" is to count the number of particles, and there are about $O(n^2)$ interactions between particles, and many supercomputer simulations of particle dynamics fit this. so as a rough bound, one would pick the smallest particles, but, wait! the standard model has many *subatomic* particles! so one might use neutrinos, one of the smallest known stable particles, as an estimate... but then what about unstable particles such as quarks/ leptons?

there is also the whole other problematic accuracy/ precision problem of [the butterfly effect](https://en.wikipedia.org/wiki/Butterfly_effect) long known in computational physics aka "sensitive dependence on initial conditions".

Aaronson write in his essay [Is There Anything Beyond Quantum Computing?](http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/is-there-anything-beyond-quantum-computing/):

> Is there any such problem that couldn’t be solved efficiently by a quantum computer, but could be solved efficiently by some other computer allowed by the laws of physics?

so he sketches out weird physics such as black holes or quantum gravity that might not be simulable by a quantum computer. but flipping this whole essay on its head (in a manner it which it was unintended), what he is describing are frontier areas of physics that currently do not have *complete/ definite physical theories known by humans* (at best, only plausible candidates/ approximations floating around.) eg:

* black holes
* time curves
* quantum gravity

(adding to his list)

* dark matter/ energy
* virtual particles, vacuum energy

so the problem comes in your title that you literally want to ***fully** simulate* a cubic meter of space. but the standard model is actually ultimately/ technically widely acknowledged/ conceded by physicists themselves (if pressed!) as an *incomplete* model of reality due to all the extreme/ problematic "edge cases" listed above, and others not known. even the standard model itself is problematic in that new particles/ tiny forces and revisions are added/ modified all the time, nearly "regularly", even the famous/ celebrated [Higgs particle](https://en.wikipedia.org/wiki/Higgs_boson) recently.

so actually its a major open question of physics whether the basic rules of reality are computable. this ties in with the [digital physics](https://en.wikipedia.org/wiki/Digital_physics) research agenda.

so physicists generally regard the idea that physics of reality is computable as something of an "approximation" that physical theories are in the continual process of evolving/ finetuning but "very thorough/ precise models" are ultimately not to be confused with *accurate simulations.*

also relevant to this question/ impinging is that there is new "cutting edge/ borderline" physics theory/ research and experiments to attempt detect if we are "living in a hologram" ie some kind of "simulation". it is theorized that cosmic rays might have detectable properties indicating this, or other very sensitive experiments could reveal kinds of "digitization artifacts", etc.; one example:

* [The Measurement That Would Reveal The Universe As A Computer Simulation](http://www.technologyreview.com/view/429561/the-measurement-that-would-reveal-the-universe-as-a-computer-simulation/) / MIT tech review

> **Comments:**
> **username_4**: see also the [fallacy of Laplace's demon](https://en.wikipedia.org/wiki/Laplace%27s_demon) and [limitations of reductionism](https://en.wikipedia.org/wiki/Reductionism#Criticism)  

---

