Can you explain why an ideal reversible device avoiding erasure costs wouldn’t reduce the energy cost of reliable erasure?
The Mike Frank quote mentioned previously seems to limit itself to irreversible devices :
As long as it’s a reliable, irreversible device, it will have to dissipate at least on the order of 1 electron volt (about 40 kT) per bit-operation in a room-temperature envronment, full stop, end of story.
Erasure is not reversible so this is a non question. An irreversible computer is then one that uses irreversible logic and gates at all levels, so it’s erasing bits everywhere just to compute everything, even though that is not required in theory. So a reversible computer doesn’t save energy by reducing the cost of each bit erasure, it saves energy by reducing the large quantity of unnecessary bit erasures. (But that turns out to be very hard to do and comes at a price)
It may be possible to still use reversible computation to even save the amount of energy required per bit deletion. It will be possible to use reversible computation to transform an unreliable but energy efficient bit deletion device into a reliable and energy efficient bit deletion device. We first need to take the random garbage data and send it through the efficient but unreliable bit deletion process. For example, if we have 10^9 bits of random data, then after the bit deletion process, 90% of those bits will be 1′s and the rest will be 0′s. One can then send this data through a data compression algorithm, and after compression, one will have about 0.47*10^9 bits of random data.
But I do not know if this is the best way of getting the energy efficiency of deletion close to Landauer’s limit.
We first need to take the random garbage data and send it through the efficient but unreliable bit deletion process.
I don’t actually see a way of doing this. The problem is that storing a bit reliably requires that it is in a deep low energy potential well, lower by about 1eV than the local neighborhood.
So if you try to use only 0.1 eV to eject the bit, you only get a tiny probability of success, and you need to apply about 1eV for 50% success, > 1eV to eject it reliably, etc.
So the problem is that a reliable bit is—by requirement—one that requires large energy on order 1eV to move out of it’s stable low energy local minimum (as otherwise it wouldn’t persist reliably against noise).
I am a mathematician and not a physicist, so I am not confident in my ability to look for weaknesses in my own reasoning about physics.
It seems like we need to be able to move a bit from an irreversible low reliability high efficiency mode with a low barrier to a reversible mode with a high barrier where we can perform reliable reversible computation. It looks like we need a way of reversibly lowering the barrier when we need to perform the unreliable deletion process followed by reversibly raising the barrier when we need to perform the reversible operations. Is there a way to reversibly raise and lower the barrier from 0.1 eV to 1eV or higher?
I am pretty sure that it should not be too difficult to make a good enough simulation of this to verify that everything works out correctly and is reversible except for the bit deletion.
Lowering the barrier just punts the problem to a new system component. See the long comment exchange with DaemonicSignal, where he ends up using a flywheel mechanism which is only capable of erasing non-bits (ie it doesn’t implement actual bit erasure).
Yes. A flywheel seems like a reasonable idea for a mechanism for raising and lowering a potential barrier. We just need to make sure that the flywheel is completely reversible. I was thinking about having a flywheel that hooks up to cams and followers that can mechanically raise and lower a physical barrier. This is probably an engineering challenge that will be about as difficult as the problem of making reversible computing hardware in the first place. It therefore seems like there are at least two problems of reversible computation that need to be overcome:
The most obvious problem is the problem of doing energy efficient purely reversible calculations.
The other problem is the problem of deleting a large quantity of bits in a way that does not consume much more than k*T*ln(2) energy per bit deleted. This will likely include the problem of reversibly raising and lowering an energy barrier so that we have a high energy barrier for reversible operations and so that we have a low energy barrier for bit deletions.
It seems like the few people who are working on reversible computation are focused on (1) while I have not heard anything on (2). I am a mathematician and not a researcher in these kinds of mechanisms, so I should end this post by saying that more research on this topic is needed. I would like for there to be research backed up by simulations that show that k*T*ln(2) per bit deletion is possible. I would be satisfied if these simulations were classical, mechanical simulations but which are reversible (you can run the simulation in reverse) and they incorporate thermal noise and the laws of thermodynamics.
5/21/2023 I just checked the 1970 paper ‘Minimal Energy Dissipation in Logic’ by Keyes and Landauer, and that gives another way of getting the energy efficiency of computation close to k*T*ln(2). This paper also uses the raising and lowering of a potential barrier.
Can you explain why an ideal reversible device avoiding erasure costs wouldn’t reduce the energy cost of reliable erasure?
The Mike Frank quote mentioned previously seems to limit itself to irreversible devices :
Erasure is not reversible so this is a non question. An irreversible computer is then one that uses irreversible logic and gates at all levels, so it’s erasing bits everywhere just to compute everything, even though that is not required in theory. So a reversible computer doesn’t save energy by reducing the cost of each bit erasure, it saves energy by reducing the large quantity of unnecessary bit erasures. (But that turns out to be very hard to do and comes at a price)
It may be possible to still use reversible computation to even save the amount of energy required per bit deletion. It will be possible to use reversible computation to transform an unreliable but energy efficient bit deletion device into a reliable and energy efficient bit deletion device. We first need to take the random garbage data and send it through the efficient but unreliable bit deletion process. For example, if we have 10^9 bits of random data, then after the bit deletion process, 90% of those bits will be 1′s and the rest will be 0′s. One can then send this data through a data compression algorithm, and after compression, one will have about 0.47*10^9 bits of random data.
But I do not know if this is the best way of getting the energy efficiency of deletion close to Landauer’s limit.
I don’t actually see a way of doing this. The problem is that storing a bit reliably requires that it is in a deep low energy potential well, lower by about 1eV than the local neighborhood.
So if you try to use only 0.1 eV to eject the bit, you only get a tiny probability of success, and you need to apply about 1eV for 50% success, > 1eV to eject it reliably, etc.
So the problem is that a reliable bit is—by requirement—one that requires large energy on order 1eV to move out of it’s stable low energy local minimum (as otherwise it wouldn’t persist reliably against noise).
I am a mathematician and not a physicist, so I am not confident in my ability to look for weaknesses in my own reasoning about physics.
It seems like we need to be able to move a bit from an irreversible low reliability high efficiency mode with a low barrier to a reversible mode with a high barrier where we can perform reliable reversible computation. It looks like we need a way of reversibly lowering the barrier when we need to perform the unreliable deletion process followed by reversibly raising the barrier when we need to perform the reversible operations. Is there a way to reversibly raise and lower the barrier from 0.1 eV to 1eV or higher?
I am pretty sure that it should not be too difficult to make a good enough simulation of this to verify that everything works out correctly and is reversible except for the bit deletion.
Lowering the barrier just punts the problem to a new system component. See the long comment exchange with DaemonicSignal, where he ends up using a flywheel mechanism which is only capable of erasing non-bits (ie it doesn’t implement actual bit erasure).
Yes. A flywheel seems like a reasonable idea for a mechanism for raising and lowering a potential barrier. We just need to make sure that the flywheel is completely reversible. I was thinking about having a flywheel that hooks up to cams and followers that can mechanically raise and lower a physical barrier. This is probably an engineering challenge that will be about as difficult as the problem of making reversible computing hardware in the first place. It therefore seems like there are at least two problems of reversible computation that need to be overcome:
The most obvious problem is the problem of doing energy efficient purely reversible calculations.
The other problem is the problem of deleting a large quantity of bits in a way that does not consume much more than k*T*ln(2) energy per bit deleted. This will likely include the problem of reversibly raising and lowering an energy barrier so that we have a high energy barrier for reversible operations and so that we have a low energy barrier for bit deletions.
It seems like the few people who are working on reversible computation are focused on (1) while I have not heard anything on (2). I am a mathematician and not a researcher in these kinds of mechanisms, so I should end this post by saying that more research on this topic is needed. I would like for there to be research backed up by simulations that show that k*T*ln(2) per bit deletion is possible. I would be satisfied if these simulations were classical, mechanical simulations but which are reversible (you can run the simulation in reverse) and they incorporate thermal noise and the laws of thermodynamics.
5/21/2023 I just checked the 1970 paper ‘Minimal Energy Dissipation in Logic’ by Keyes and Landauer, and that gives another way of getting the energy efficiency of computation close to k*T*ln(2). This paper also uses the raising and lowering of a potential barrier.