50 ms·

[Note: I am a master student doing my thesis in this area] Ok, I'm going to go out on a limb here and call bullshit, based on the meta-reason that they cite a

[Note: I am a master student doing my thesis in this area] Ok, I'm going to go out on a limb here and call bullshit, based on the meta-reason that they cite a paper of theirs which already claims to show that NP is contained in BQP using a different NP-complete problem, published in may 2015 (which is basically the same groundbreaking result as this paper), but this somehow completely failed to make waves in the community. Additionally, on a superficial reading of the paper nothing seems wrong with it, except that it has this air of everything being too easy, too novel, not building on any widely recognized partial results. Considering this problem has been attacked by hundreds (?) of researchers over the years, it seems highly implausible that they just happened to find this one weird trick nobody had thought of before. Anyway, those are just heuristics, and I'd love to be wrong on this occasion, but life is too short to give my full attention to a dubious paper for more than 15 minutes. I could attempt to whip up this algorithm in a quantum simulator, but that would take a considerable amount of time to do right, so I'll let somebody else do the work of debunking/confirming the result.

yread 11y ago
Why comment when you don't have the time for more than superficial analysis?
- algorias 11y ago
  According to that criterion, no one should comment on HN ever, unless they are writing at the level of a peer reviewed journal. I supposed it would be interesting for people here for me to at least point out some obvious red flags.
- gjm11 11y ago
  Because even the superficial analysis provides more than zero useful information. (Nothing super-obviously wrong. Nothing that looks clever enough to overcome the guess that, none the less, something's probably wrong.)
- Anderkent 11y ago
  'This relies on their earlier paper from May 2015, and if that paper was correct it would have made big waves' is valuable context.
- Steuard 11y ago
  Because experts with domain-specific knowledge tend to have better heuristics for this sort of thing than the average interested outsider. (They have to, or else they'd get nothing done except debunking flawed claim after flawed claim. Which might be worthwhile, but doesn't move the field forward.) I've seen plenty of "theories of particle physics" that evidently look fairly plausible to non-physicists (and maybe even to non-specialists) that I can recognize immediately as crackpottery by my own heuristics (but that would take at least a weekend's work to convincingly demonstrate as such, if I wanted to invest that kind of time: I've done that, too). I'm not saying that anyone should take anyone's heuristic guesses in such cases as gospel (once or twice a century we might actually get a delightful surprise), but they can serve as a useful restraining influence if you're tempted to get excited about a headline.
  - anfedorov 11y ago
    Nope. An expert would be able to skim it, recognize the path of reasoning as something he's seen a before, and narrow down on the error quickly. Reasoning about something by how many "waves in the community" it has made is a deference of personal judgement to the social network an individual is embedded in, which is a useful shortcut when you are not an expert relative to your peers, but dangerous set of mind to operate in for any lengthy amount of time, as it can be the basis of cults and the like.
  - anfedorov 11y ago
    An expert would be able to skim it, recognize the path of reasoning as something he's seen a before, and narrow down on the error quickly. Reasoning about something by how many "waves in the community" it has made is a deference of personal judgement to the social network an individual is embedded in, which is a useful shortcut when you are not an expert relative to your peers, but dangerous set of mind to operate in for any lengthy amount of time, as it can be the basis of cults and the like.
    - evanpw 11y ago
      > An expert would be able to skim it, recognize the path of reasoning as something he's seen a before, and narrow down on the error quickly. This is almost exactly equivalent to saying that an expert programmer should be able to determine whether an unfamiliar, complicated code base contains a bug by skimming the source. The hard bugs are going to be subtle.
MathsOX 11y ago
Could you provide a link to this paper?
- yk 11y ago
  I think he means this one: http://arxiv.org/abs/1505.06284 http://arxiv.org/abs/1505.06284
- sanxiyn 11y ago
  Sure. May 2015 paper is http://arxiv.org/abs/1505.06284 http://arxiv.org/abs/1505.06284, as easily found by reading the paper. (It is reference 13.) As for "but this somehow completely failed to make waves in the community", I think "but life is too short to give my full attention to a dubious paper for more than 15 minutes" is an enough explanation.
outworlder 11y ago
> I could attempt to whip up this algorithm in a quantum simulator This is the first time I've heard of a quantum simulator. How expensive would be to run the algorithm in one?
- sanxiyn 11y ago
  Quantum computer can be simulated by classical computer with exponential slowdown. Here are some quantum computer simulators: http://www.quantiki.org/wiki/List_of_QC_simulators http://www.quantiki.org/wiki/List_of_QC_simulators
  - jackfoxy 11y ago
    No mention of LIQUi|> (pronounced liquid) in this list. http://research.microsoft.com/en-us/projects/liquid/ http://research.microsoft.com/en-us/projects/liquid/ MSR claims to have the most advanced / fastest quantum computer simulator.
    - sanxiyn 11y ago
      As I understand, LIQUi|> is not publicly available. Is it?
      - jackfoxy 11y ago
        I believe you are correct, so you cannot just hobby hack on it, but it you have a serious purpose I think the team will listen to you. In any event "List of QC simulators" appears to be just that, a list, with no stipulation that it contains only open source software, etc.
  - gghh 11y ago
    another one that seems missing is this one http://www.quantumplayground.net http://www.quantumplayground.net which runs in a browser and has tutorials on how to write programs. EDIT: spelling
- algorias 11y ago
ThePhysicist 11y ago
After quickly reading through the paper it seems that the algorithm they employ is very similar to Grover search [1], which provides a quadratic/square-root speed-up for generic search problems, so O(2^m) -> O(2^(n/2)). Basically, they perform the following three steps: 1) Generate an even superposition of all possible solution states using a Hadamard transform (so go from |000000...> to 1/sqrt(N)*(|00000..0>+|000...1>+|1111...1>). This is pretty standard and used in almost all quantum algorithms. 2) Evaluate each clause of their Boolean E3-CNF function on the superposed input state and transfer the results to a register of control qubits, which yields an entangled state of the input state qubits with these control qubits (akin to the Oracle operator in the Grover search algorithm that performs the operation |x>|0> -> |x>|f(x)>, only here they use multiple Oracle functions and control qubits [which is fine of course]). This is a classical operation which we can implement in reversible computing btw, so no quantum magic involved here yet (apart from applying it to a superposed input state). 3) Increase the amplitude of the states that contain the solution to the search problem, very much akin to the rotation operator employed in Grover search that transfers amplitude from non-solution states to the solution state. <- The problem might be here. So where I have trouble understanding the algorithm is when they apply the operator M_x to increase "the amplitude of the truth vector of clauses with maximum number of satisfied clauses using a partial negation and iterative measurement technique" (page 6 ff.). They seem to want to repeatedly apply that operator to the same state in order to maximize the amplitude transfer to the correct solution states. However, there is a rather simple proof that shows that the maximum amount of amplitude which you can transfer from one component of a quantum state to another using a control qubit is fundamentally limited by the Unitarian nature of quantum operations. This also limits the efficiency of quantum search in the general case and is the reason that we cannot achieve arbitrary speed-up in the Grover algorithm (see e.g. my PhD thesis for a simple explanation [2] or Grover's original paper to get the full picture [3]). Basically this proof states that although we can generate the quantum information about the answer that we're looking for, we cannot get that information out of the quantum system in an (exponentially) efficient way. It would be very exciting if this algorithm was correct of course, I just can't imagine that someone would publish such an important finding on Arxiv.org without having it cross-checked and backed by some other people in the field first (which does not seem to be the case judging from the text). That being said, I think it should be not too difficult to simulate this algorithm and see if all of their transformations are actually unitary and possible to implement in reversible computing and if they correctly take into account the entanglement of individual control qubits and the corresponding wave function collapse due to the qubit measurements they perform. [1] Grover Search Algorithm - https://en.wikipedia.org/wiki/Grover%27s_algorithm https://en.wikipedia.org/wiki/Grover%27s_algorithm [2] My PhD thesis on an Experimental Realization of Grover's Algorithm - see page 136 ff. for a simple explanation of the effiency of quantum searching http://iramis.cea.fr/spec/Pres/Quantro/static/wp-content/uploads/2013/09/thesis_Dewes_web.pdf http://iramis.cea.fr/spec/Pres/Quantro/static/wp-content/upl... [3] Grover's Algorithm - Original Paper http://arxiv.org/abs/quant-ph/9605043 http://arxiv.org/abs/quant-ph/9605043 [4] The No-Cloning Theorem: https://en.wikipedia.org/wiki/No-cloning_theorem https://en.wikipedia.org/wiki/No-cloning_theorem
deleted 11y ago
[deleted]
anfedorov 11y ago
Heuristics like that are a dangerous thing. Have you seen the line of reasoning used in the paper before, and what is the error?
deleted 11y ago
[deleted]
sim_man 11y ago
V=[0.75+0.4330127018922193i 0.24999999999999994-0.4330127018922193i , 0.24999999999999994-0.4330127018922193i 0.75+0.4330127018922193i ] qubit_0="x0" qubit_1="x1" qubit_2="x2" qubit_3="c0" qubit_4="c1" qubit_5="d0" qubit_6="ax" gateproperty("group_gate10gate11gate12gate13gate14_6068",reps=10.0) gate0={H:-:-:-:-:-:-} gate1={-:H:-:-:-:-:-} gate2={-:-:H:-:-:-:-} gate3={1:1:1:NOT:-:-:-} gate4={NOT:-:-:-:-:-:-} gate5={-:NOT:-:-:-:-:-} gate6={-:-:NOT:-:-:-:-} gate7={1:1:1:-:NOT:-:-} gate8={-:-:NOT:-:-:-:-} gate9={-:NOT:-:-:-:-:-} group_gate10gate11gate12gate13gate14_6068.gate10={-:-:-:1:-:-:V} group_gate10gate11gate12gate13gate14_6068.gate11={-:-:-:-:1:-:V} group_gate10gate11gate12gate13gate14_6068.gate12={-:-:-:-:-:1:V} group_gate10gate11gate12gate13gate14_6068.gate13={-:-:-:-:-:-:!} group_gate10gate11gate12gate13gate14_6068.gate14_6068={-:-:-:-:-:-:NOT} gate17={-:-:-:!:-:-:-} gate14={-:-:-:-:!:-:-}
sim_man 11y ago
algorias: I finally managed to simulate the algorithm on a handy quantum simulator jaQuzzi 0.1(http://www.eng.buffalo.edu/~phygons/jaQuzzi/ http://www.eng.buffalo.edu/~phygons/jaQuzzi/). As I can see, the algorithm really works. Below is the code for the example shown in Fig 5, (x0 v x1 v x2)&(~x0 v ~x1 v ~x2). You can try it by yourself and here are the steps: 1- copy the below code to a text editor and save it with extension .jaq. 2- open the file with jaQuzzi. 3- set |c0>=|1>,|c1>=|1>,|d0>=|1> 4- run the circuit. 5- select |c0> and |c1> and press on "plot probability chart" to open the "chart center" and see the correct answer for c's. 6- select |x0>, |x1> and |x2> and press on "plot probability chart" to open the "chart center" and see the probability for the superposition of the correct answer of x's. Hints: -You can trace the circuit by selecting |c0> and |c1> and press on "plot probability chart" to open the "chart center", reset the circuit and start pressing on "step forward" to watch the probability of the solution increases during the loop. -Don't forget to select auto in the "chart center". If you want to play around, 1-set the number of x’s and c’s as required. 2-add the dummy qubits. 3-initialize c’s and d’s to |1> (required number of d’s calculated using equations in the paper) 4- set V = [0.5(1+exp((ipi)/k)),0.5(1-exp((ipi)/k));0.5(1-exp((ipi)/k)),0.5(1+exp((ipi)/k))], where k is the number of c’s and d’s. (you have to ungroup the set of gates before you modify V, and group again) 5- set the number of iterations in the properties of the group. The code in another comment...have fun!!!
- sim_man 11y ago
  V=[0.75+0.4330127018922193i 0.24999999999999994-0.4330127018922193i , 0.24999999999999994-0.4330127018922193i 0.75+0.4330127018922193i ] qubit_0="x0" qubit_1="x1" qubit_2="x2" qubit_3="c0" qubit_4="c1" qubit_5="d0" qubit_6="ax" gateproperty("group_gate10gate11gate12gate13gate14_6068",reps=10.0) gate0={H:-:-:-:-:-:-} gate1={-:H:-:-:-:-:-} gate2={-:-:H:-:-:-:-} gate3={1:1:1:NOT:-:-:-} gate4={NOT:-:-:-:-:-:-} gate5={-:NOT:-:-:-:-:-} gate6={-:-:NOT:-:-:-:-} gate7={1:1:1:-:NOT:-:-} gate8={-:-:NOT:-:-:-:-} gate9={-:NOT:-:-:-:-:-} group_gate10gate11gate12gate13gate14_6068.gate10={-:-:-:1:-:-:V} group_gate10gate11gate12gate13gate14_6068.gate11={-:-:-:-:1:-:V} group_gate10gate11gate12gate13gate14_6068.gate12={-:-:-:-:-:1:V} group_gate10gate11gate12gate13gate14_6068.gate13={-:-:-:-:-:-:!} group_gate10gate11gate12gate13gate14_6068.gate14_6068={-:-:-:-:-:-:NOT} gate17={-:-:-:!:-:-:-} gate14={-:-:-:-:!:-:-}

yread 11y ago

Why comment when you don't have the time for more than superficial analysis?

algorias 11y ago
According to that criterion, no one should comment on HN ever, unless they are writing at the level of a peer reviewed journal. I supposed it would be interesting for people here for me to at least point out some obvious red flags.
gjm11 11y ago
Because even the superficial analysis provides more than zero useful information. (Nothing super-obviously wrong. Nothing that looks clever enough to overcome the guess that, none the less, something's probably wrong.)
Anderkent 11y ago
'This relies on their earlier paper from May 2015, and if that paper was correct it would have made big waves' is valuable context.
Steuard 11y ago
Because experts with domain-specific knowledge tend to have better heuristics for this sort of thing than the average interested outsider. (They have to, or else they'd get nothing done except debunking flawed claim after flawed claim. Which might be worthwhile, but doesn't move the field forward.) I've seen plenty of "theories of particle physics" that evidently look fairly plausible to non-physicists (and maybe even to non-specialists) that I can recognize immediately as crackpottery by my own heuristics (but that would take at least a weekend's work to convincingly demonstrate as such, if I wanted to invest that kind of time: I've done that, too). I'm not saying that anyone should take anyone's heuristic guesses in such cases as gospel (once or twice a century we might actually get a delightful surprise), but they can serve as a useful restraining influence if you're tempted to get excited about a headline.
- anfedorov 11y ago
  Nope. An expert would be able to skim it, recognize the path of reasoning as something he's seen a before, and narrow down on the error quickly. Reasoning about something by how many "waves in the community" it has made is a deference of personal judgement to the social network an individual is embedded in, which is a useful shortcut when you are not an expert relative to your peers, but dangerous set of mind to operate in for any lengthy amount of time, as it can be the basis of cults and the like.
- anfedorov 11y ago
  An expert would be able to skim it, recognize the path of reasoning as something he's seen a before, and narrow down on the error quickly. Reasoning about something by how many "waves in the community" it has made is a deference of personal judgement to the social network an individual is embedded in, which is a useful shortcut when you are not an expert relative to your peers, but dangerous set of mind to operate in for any lengthy amount of time, as it can be the basis of cults and the like.
  - evanpw 11y ago
    > An expert would be able to skim it, recognize the path of reasoning as something he's seen a before, and narrow down on the error quickly. This is almost exactly equivalent to saying that an expert programmer should be able to determine whether an unfamiliar, complicated code base contains a bug by skimming the source. The hard bugs are going to be subtle.

MathsOX 11y ago

Could you provide a link to this paper?

yk 11y ago
I think he means this one: http://arxiv.org/abs/1505.06284 http://arxiv.org/abs/1505.06284
sanxiyn 11y ago
Sure. May 2015 paper is http://arxiv.org/abs/1505.06284 http://arxiv.org/abs/1505.06284, as easily found by reading the paper. (It is reference 13.) As for "but this somehow completely failed to make waves in the community", I think "but life is too short to give my full attention to a dubious paper for more than 15 minutes" is an enough explanation.

outworlder 11y ago

> I could attempt to whip up this algorithm in a quantum simulator This is the first time I've heard of a quantum simulator. How expensive would be to run the algorithm in one?

sanxiyn 11y ago
Quantum computer can be simulated by classical computer with exponential slowdown. Here are some quantum computer simulators: http://www.quantiki.org/wiki/List_of_QC_simulators http://www.quantiki.org/wiki/List_of_QC_simulators
- jackfoxy 11y ago
  No mention of LIQUi|> (pronounced liquid) in this list. http://research.microsoft.com/en-us/projects/liquid/ http://research.microsoft.com/en-us/projects/liquid/ MSR claims to have the most advanced / fastest quantum computer simulator.
  - sanxiyn 11y ago
    As I understand, LIQUi|> is not publicly available. Is it?
    - jackfoxy 11y ago
      I believe you are correct, so you cannot just hobby hack on it, but it you have a serious purpose I think the team will listen to you. In any event "List of QC simulators" appears to be just that, a list, with no stipulation that it contains only open source software, etc.
- gghh 11y ago
  another one that seems missing is this one http://www.quantumplayground.net http://www.quantumplayground.net which runs in a browser and has tutorials on how to write programs. EDIT: spelling
algorias 11y ago

ThePhysicist 11y ago

After quickly reading through the paper it seems that the algorithm they employ is very similar to Grover search [1], which provides a quadratic/square-root speed-up for generic search problems, so O(2^m) -> O(2^(n/2)). Basically, they perform the following three steps: 1) Generate an even superposition of all possible solution states using a Hadamard transform (so go from |000000...> to 1/sqrt(N)*(|00000..0>+|000...1>+|1111...1>). This is pretty standard and used in almost all quantum algorithms. 2) Evaluate each clause of their Boolean E3-CNF function on the superposed input state and transfer the results to a register of control qubits, which yields an entangled state of the input state qubits with these control qubits (akin to the Oracle operator in the Grover search algorithm that performs the operation |x>|0> -> |x>|f(x)>, only here they use multiple Oracle functions and control qubits [which is fine of course]). This is a classical operation which we can implement in reversible computing btw, so no quantum magic involved here yet (apart from applying it to a superposed input state). 3) Increase the amplitude of the states that contain the solution to the search problem, very much akin to the rotation operator employed in Grover search that transfers amplitude from non-solution states to the solution state. <- The problem might be here. So where I have trouble understanding the algorithm is when they apply the operator M_x to increase "the amplitude of the truth vector of clauses with maximum number of satisfied clauses using a partial negation and iterative measurement technique" (page 6 ff.). They seem to want to repeatedly apply that operator to the same state in order to maximize the amplitude transfer to the correct solution states. However, there is a rather simple proof that shows that the maximum amount of amplitude which you can transfer from one component of a quantum state to another using a control qubit is fundamentally limited by the Unitarian nature of quantum operations. This also limits the efficiency of quantum search in the general case and is the reason that we cannot achieve arbitrary speed-up in the Grover algorithm (see e.g. my PhD thesis for a simple explanation [2] or Grover's original paper to get the full picture [3]). Basically this proof states that although we can generate the quantum information about the answer that we're looking for, we cannot get that information out of the quantum system in an (exponentially) efficient way. It would be very exciting if this algorithm was correct of course, I just can't imagine that someone would publish such an important finding on Arxiv.org without having it cross-checked and backed by some other people in the field first (which does not seem to be the case judging from the text). That being said, I think it should be not too difficult to simulate this algorithm and see if all of their transformations are actually unitary and possible to implement in reversible computing and if they correctly take into account the entanglement of individual control qubits and the corresponding wave function collapse due to the qubit measurements they perform. [1] Grover Search Algorithm - https://en.wikipedia.org/wiki/Grover%27s_algorithm https://en.wikipedia.org/wiki/Grover%27s_algorithm [2] My PhD thesis on an Experimental Realization of Grover's Algorithm - see page 136 ff. for a simple explanation of the effiency of quantum searching http://iramis.cea.fr/spec/Pres/Quantro/static/wp-content/uploads/2013/09/thesis_Dewes_web.pdf http://iramis.cea.fr/spec/Pres/Quantro/static/wp-content/upl... [3] Grover's Algorithm - Original Paper http://arxiv.org/abs/quant-ph/9605043 http://arxiv.org/abs/quant-ph/9605043 [4] The No-Cloning Theorem: https://en.wikipedia.org/wiki/No-cloning_theorem https://en.wikipedia.org/wiki/No-cloning_theorem

deleted 11y ago

[deleted]

anfedorov 11y ago

Heuristics like that are a dangerous thing. Have you seen the line of reasoning used in the paper before, and what is the error?

deleted 11y ago

[deleted]

sim_man 11y ago

V=[0.75+0.4330127018922193i 0.24999999999999994-0.4330127018922193i , 0.24999999999999994-0.4330127018922193i 0.75+0.4330127018922193i ] qubit_0="x0" qubit_1="x1" qubit_2="x2" qubit_3="c0" qubit_4="c1" qubit_5="d0" qubit_6="ax" gateproperty("group_gate10gate11gate12gate13gate14_6068",reps=10.0) gate0={H:-:-:-:-:-:-} gate1={-:H:-:-:-:-:-} gate2={-:-:H:-:-:-:-} gate3={1:1:1:NOT:-:-:-} gate4={NOT:-:-:-:-:-:-} gate5={-:NOT:-:-:-:-:-} gate6={-:-:NOT:-:-:-:-} gate7={1:1:1:-:NOT:-:-} gate8={-:-:NOT:-:-:-:-} gate9={-:NOT:-:-:-:-:-} group_gate10gate11gate12gate13gate14_6068.gate10={-:-:-:1:-:-:V} group_gate10gate11gate12gate13gate14_6068.gate11={-:-:-:-:1:-:V} group_gate10gate11gate12gate13gate14_6068.gate12={-:-:-:-:-:1:V} group_gate10gate11gate12gate13gate14_6068.gate13={-:-:-:-:-:-:!} group_gate10gate11gate12gate13gate14_6068.gate14_6068={-:-:-:-:-:-:NOT} gate17={-:-:-:!:-:-:-} gate14={-:-:-:-:!:-:-}

sim_man 11y ago

algorias: I finally managed to simulate the algorithm on a handy quantum simulator jaQuzzi 0.1(http://www.eng.buffalo.edu/~phygons/jaQuzzi/ http://www.eng.buffalo.edu/~phygons/jaQuzzi/). As I can see, the algorithm really works. Below is the code for the example shown in Fig 5, (x0 v x1 v x2)&(~x0 v ~x1 v ~x2). You can try it by yourself and here are the steps: 1- copy the below code to a text editor and save it with extension .jaq. 2- open the file with jaQuzzi. 3- set |c0>=|1>,|c1>=|1>,|d0>=|1> 4- run the circuit. 5- select |c0> and |c1> and press on "plot probability chart" to open the "chart center" and see the correct answer for c's. 6- select |x0>, |x1> and |x2> and press on "plot probability chart" to open the "chart center" and see the probability for the superposition of the correct answer of x's. Hints: -You can trace the circuit by selecting |c0> and |c1> and press on "plot probability chart" to open the "chart center", reset the circuit and start pressing on "step forward" to watch the probability of the solution increases during the loop. -Don't forget to select auto in the "chart center". If you want to play around, 1-set the number of x’s and c’s as required. 2-add the dummy qubits. 3-initialize c’s and d’s to |1> (required number of d’s calculated using equations in the paper) 4- set V = [0.5(1+exp((ipi)/k)),0.5(1-exp((ipi)/k));0.5(1-exp((ipi)/k)),0.5(1+exp((ipi)/k))], where k is the number of c’s and d’s. (you have to ungroup the set of gates before you modify V, and group again) 5- set the number of iterations in the properties of the group. The code in another comment...have fun!!!

sim_man 11y ago
V=[0.75+0.4330127018922193i 0.24999999999999994-0.4330127018922193i , 0.24999999999999994-0.4330127018922193i 0.75+0.4330127018922193i ] qubit_0="x0" qubit_1="x1" qubit_2="x2" qubit_3="c0" qubit_4="c1" qubit_5="d0" qubit_6="ax" gateproperty("group_gate10gate11gate12gate13gate14_6068",reps=10.0) gate0={H:-:-:-:-:-:-} gate1={-:H:-:-:-:-:-} gate2={-:-:H:-:-:-:-} gate3={1:1:1:NOT:-:-:-} gate4={NOT:-:-:-:-:-:-} gate5={-:NOT:-:-:-:-:-} gate6={-:-:NOT:-:-:-:-} gate7={1:1:1:-:NOT:-:-} gate8={-:-:NOT:-:-:-:-} gate9={-:NOT:-:-:-:-:-} group_gate10gate11gate12gate13gate14_6068.gate10={-:-:-:1:-:-:V} group_gate10gate11gate12gate13gate14_6068.gate11={-:-:-:-:1:-:V} group_gate10gate11gate12gate13gate14_6068.gate12={-:-:-:-:-:1:V} group_gate10gate11gate12gate13gate14_6068.gate13={-:-:-:-:-:-:!} group_gate10gate11gate12gate13gate14_6068.gate14_6068={-:-:-:-:-:-:NOT} gate17={-:-:-:!:-:-:-} gate14={-:-:-:-:!:-:-}