Comments for The Quantum Pontiff http://dabacon.org/pontiff A College of Quantum Cardinals Mon, 14 May 2012 20:57:52 +0000 hourly 1 http://wordpress.org/?v=3.3 Comment on A jack of two trades and a master of both by John Sidles http://dabacon.org/pontiff/?p=6279#comment-644436 John Sidles Mon, 14 May 2012 20:57:52 +0000 http://dabacon.org/pontiff/?p=6279#comment-644436 In further news, the <i>Theoretical Physics StackExchange</i> has closed down. On a planet of 7x10^9 people, the single-citizen interval between visits to the site was 96 thousand years, and the mean interval between questions was 27 million years. <b>Summary:</b> The inhabitants of this planet show no substantial interest in theoretical physics. In further news, the Theoretical Physics StackExchange has closed down. On a planet of 7×10^9 people, the single-citizen interval between visits to the site was 96 thousand years, and the mean interval between questions was 27 million years.

Summary: The inhabitants of this planet show no substantial interest in theoretical physics.

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]]> Comment on 300 by Quantum Refutations and Reproofs « Gödel’s Lost Letter and P=NP http://dabacon.org/pontiff/?p=6251#comment-644418 Quantum Refutations and Reproofs « Gödel’s Lost Letter and P=NP Sat, 12 May 2012 14:32:59 +0000 http://dabacon.org/pontiff/?p=6251#comment-644418 [...] mentioned some new papers and articles beginning here. On the technological side, Steve Flammia noted on the Quantum Pontiff blog that ion-trap technology has taken a big leap upward in scale for [...] [...] mentioned some new papers and articles beginning here. On the technological side, Steve Flammia noted on the Quantum Pontiff blog that ion-trap technology has taken a big leap upward in scale for [...]

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]]> Comment on 300 by John Sidles http://dabacon.org/pontiff/?p=6251#comment-644394 John Sidles Tue, 08 May 2012 15:09:49 +0000 http://dabacon.org/pontiff/?p=6251#comment-644394 "They want to prepare the ground state …" Hmmm … it's not clear this system (or any similar system) affords methods for preparing a ground state that are general, natural, and robust. However, it's a system well-suited to studying thermodynamical equations of state and/or transport coefficients … and these are the properties that one generally wishes to know. “They want to prepare the ground state …”

Hmmm … it’s not clear this system (or any similar system) affords methods for preparing a ground state that are general, natural, and robust.

However, it’s a system well-suited to studying thermodynamical equations of state and/or transport coefficients … and these are the properties that one generally wishes to know.

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]]> Comment on 300 by Steve http://dabacon.org/pontiff/?p=6251#comment-644390 Steve Mon, 07 May 2012 17:54:40 +0000 http://dabacon.org/pontiff/?p=6251#comment-644390 Thanks for the clarification; I had indeed misunderstood your question. Let us abstract away the details of the experiment, and suppose that they are working with n spins. They want to prepare the ground state of, and observe the dynamics of, a system with an Ising-type interaction that decays with distance, a homogeneous single-qubit control field, and single-qubit measurements in the computational basis. Then I believe you are asking whether there is a constant-depth quantum circuit to simulate the distribution of measurement outcomes. My guess in that case is <i>no</i>, but I can't be certain. The so-called "no fast-forwarding theorem" (Thm. 3 in <a href="http://arxiv.org/abs/quant-ph/0508139" rel="nofollow">quant-ph/0508139</a>) is a no-go theorem which is relevant in the general case, but since this is a specific instance I don't know that we can say anything definitive. Thanks for the clarification; I had indeed misunderstood your question. Let us abstract away the details of the experiment, and suppose that they are working with n spins. They want to prepare the ground state of, and observe the dynamics of, a system with an Ising-type interaction that decays with distance, a homogeneous single-qubit control field, and single-qubit measurements in the computational basis. Then I believe you are asking whether there is a constant-depth quantum circuit to simulate the distribution of measurement outcomes. My guess in that case is no, but I can’t be certain. The so-called “no fast-forwarding theorem” (Thm. 3 in quant-ph/0508139) is a no-go theorem which is relevant in the general case, but since this is a specific instance I don’t know that we can say anything definitive.

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]]> Comment on 300 by Gil Kalai http://dabacon.org/pontiff/?p=6251#comment-644388 Gil Kalai Mon, 07 May 2012 11:54:17 +0000 http://dabacon.org/pontiff/?p=6251#comment-644388 Hi Steve, Of course we need to be careful if we try to apply computational complexity terminology and insights for real life situation. Everything we do is with finite input size so your type of reasoning make every real life application of computational complexity meaningless including your question from the post "Whether or not there is an efficient way to replicate all of the observations from this experiment on a classical computer is not entirely clear. " My question is about a small number of quantum computer cycles (2, 3, 5) which will NOT scale up when you replace 300 by, say, 3,000. Of course if by "bounded" we allow 2^300 or even 300^2 we miss the entire point. Hi Steve,

Of course we need to be careful if we try to apply computational complexity terminology and insights for real life situation.

Everything we do is with finite input size so your type of reasoning make every real life application of computational complexity meaningless including your question from the post “Whether or not there is an efficient way to replicate all of the observations from this experiment on a classical computer is not entirely clear. ”

My question is about a small number of quantum computer cycles (2, 3, 5) which will NOT scale up when you replace 300 by, say, 3,000. Of course if by “bounded” we allow 2^300 or even 300^2 we miss the entire point.

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]]> Comment on 300 by Steve http://dabacon.org/pontiff/?p=6251#comment-644376 Steve Wed, 02 May 2012 19:54:28 +0000 http://dabacon.org/pontiff/?p=6251#comment-644376 Hi Gil, I'm quite confident that the answer is "yes", the experiment can be simulated on a quantum computer in a bounded number of steps. At the very worst case, experiments like these always fit inside of PSPACE (once you suitably abstract them), hence for a fixed input size you only need a bounded number of computational steps to simulate everything. Hi Gil,
I’m quite confident that the answer is “yes”, the experiment can be simulated on a quantum computer in a bounded number of steps. At the very worst case, experiments like these always fit inside of PSPACE (once you suitably abstract them), hence for a fixed input size you only need a bounded number of computational steps to simulate everything.

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]]> Comment on 300 by John Sidles http://dabacon.org/pontiff/?p=6251#comment-644368 John Sidles Tue, 01 May 2012 14:32:31 +0000 http://dabacon.org/pontiff/?p=6251#comment-644368 A class of questions related to Gil's (to which I don't know the answer) is: How might one use quantum simulation algorithms to speed-up the simulation of non-equilibrium and/or finite-temperature dynamics, so as to estimate (for example) the spin system's heat conductivity? A class of questions related to Gil’s (to which I don’t know the answer) is: How might one use quantum simulation algorithms to speed-up the simulation of non-equilibrium and/or finite-temperature dynamics, so as to estimate (for example) the spin system’s heat conductivity?

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]]> Comment on 300 by Gil Kalai http://dabacon.org/pontiff/?p=6251#comment-644366 Gil Kalai Tue, 01 May 2012 13:02:37 +0000 http://dabacon.org/pontiff/?p=6251#comment-644366 Hi Steve, This is indeed exciting. As you mentioned, the question if observations from this or similar experiments can be replicated by classical computers leads us to notorious computational complexity issues, perhaps a better question is if this or similar experiments can be simulated by a quantum computer running a bounded number of computer cycles. Is it? Hi Steve,
This is indeed exciting. As you mentioned, the question if observations from this or similar experiments can be replicated by classical computers leads us to notorious computational complexity issues, perhaps a better question is if this or similar experiments can be simulated by a quantum computer running a bounded number of computer cycles. Is it?

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]]> Comment on 300 by John Sidles http://dabacon.org/pontiff/?p=6251#comment-644365 John Sidles Mon, 30 Apr 2012 19:48:42 +0000 http://dabacon.org/pontiff/?p=6251#comment-644365 It's good to see smoke coming from the Pontiffs' Vatican chimney  and thank you, Steve, for this fine summary of some outstandingly interesting research. From a simulationist/geometer point-of-view, this experiment has intriguing aspects beyond those mentioned in the article. Let us suppose that we simulate the experiment's wave-function as the (numerically computed) integral curve of a Hamiltonian trajectory. For reason of numerical efficiency, we can pullback the physics onto a rank-$latex r$ <a href="http://faculty.washington.edu/sidles/ENC_2011/index.html#burningArrow" rel="nofollow">secant variety of a Segre variety</a> (that is, a matrix product state of rank-$latex r$). For systems of 300 spins, it is numerically feasible to integrate curves for ranks $latex r \sim 100$ or so. A natural question is, how large a state-space rank is required to accurately simulate the experiment? The answer (it seems to me) is likely to depend upon a key parameter of the experiment, namely, the (parasitic) noise operations that act upon the qubits … because these operations generically act to compress the system's dynamical trajectories onto the above-mentioned varietal state-spaces. It might perhaps be the case — and it is a fundamentally important question to investigate — that the condensed matter regimes that are hardest to simulate numerically, are precisely the regimes that are most sensitive to (parasitic) noise operations. Thus this experiment opens a new world not only to fundamental quantum physics experiments, but also (and essentially equivalently) to the fundamental validation of <i>algorithms</i>. It's exciting! It’s good to see smoke coming from the Pontiffs’ Vatican chimney  and thank you, Steve, for this fine summary of some outstandingly interesting research.

From a simulationist/geometer point-of-view, this experiment has intriguing aspects beyond those mentioned in the article. Let us suppose that we simulate the experiment’s wave-function as the (numerically computed) integral curve of a Hamiltonian trajectory. For reason of numerical efficiency, we can pullback the physics onto a rank-r secant variety of a Segre variety (that is, a matrix product state of rank-r). For systems of 300 spins, it is numerically feasible to integrate curves for ranks r \sim 100 or so.

A natural question is, how large a state-space rank is required to accurately simulate the experiment? The answer (it seems to me) is likely to depend upon a key parameter of the experiment, namely, the (parasitic) noise operations that act upon the qubits … because these operations generically act to compress the system’s dynamical trajectories onto the above-mentioned varietal state-spaces.

It might perhaps be the case — and it is a fundamentally important question to investigate — that the condensed matter regimes that are hardest to simulate numerically, are precisely the regimes that are most sensitive to (parasitic) noise operations.

Thus this experiment opens a new world not only to fundamental quantum physics experiments, but also (and essentially equivalently) to the fundamental validation of algorithms. It’s exciting!

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]]> Comment on Ghost Paper Dance! by John Sidles http://dabacon.org/pontiff/?p=6237#comment-644271 John Sidles Wed, 18 Apr 2012 14:29:27 +0000 http://dabacon.org/pontiff/?p=6237#comment-644271 <i>Quantum Pontiff</i> and <i>Shtetl Optimized</i> both have fallen silent ... and so (by default) Wally's vision for quantum computing — see yesterday's <i>Dilbert</i> cartoon "<a href="http://www.dilbert.com/2012-04-17/" rel="nofollow"><i>How's your quantum computer prototype coming along?</i></a>" — is emerging as the dominant cultural narrative … is this really what we want? :( Quantum Pontiff and Shtetl Optimized both have fallen silent … and so (by default) Wally’s vision for quantum computing — see yesterday’s Dilbert cartoon “How’s your quantum computer prototype coming along?“ — is emerging as the dominant cultural narrative … is this really what we want? :(

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]]> Comment on Ghost Paper Dance! by John Sidles http://dabacon.org/pontiff/?p=6237#comment-644165 John Sidles Thu, 05 Apr 2012 09:58:24 +0000 http://dabacon.org/pontiff/?p=6237#comment-644165 Whoops ... I had not entirely grasped (on first reading) the final point your post makes ... still a fine analysis of an important class of problems. Whoops … I had not entirely grasped (on first reading) the final point your post makes … still a fine analysis of an important class of problems.

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