laura cui
@reionize.bsky.social
phd student @ caltech | interested in quantum info, math education, watercolors, marine bio
https://reionize.github.io
https://reionize.github.io
happy to share some examples privately if that'd be helpful!
November 5, 2025 at 6:53 PM
happy to share some examples privately if that'd be helpful!
that's fair! it's possible I've just been lucky to have people (friends, mentors, parents) close to me go through this successfully
November 5, 2025 at 6:52 PM
that's fair! it's possible I've just been lucky to have people (friends, mentors, parents) close to me go through this successfully
interesting, maybe I have a lower bar but I wouldn't say it's particularly uncommon or frowned upon in my circles
November 4, 2025 at 1:07 AM
interesting, maybe I have a lower bar but I wouldn't say it's particularly uncommon or frowned upon in my circles
+ in the non-adaptive setting, there exist ensembles w/ natural spectral distributions whose dynamics look random in O(1) time ⌛
These results complement each other & highlight subtleties in formulating random models which capture the properties of physical dynamics 🔎 ✨
8/8
These results complement each other & highlight subtleties in formulating random models which capture the properties of physical dynamics 🔎 ✨
8/8
October 10, 2025 at 2:11 AM
+ in the non-adaptive setting, there exist ensembles w/ natural spectral distributions whose dynamics look random in O(1) time ⌛
These results complement each other & highlight subtleties in formulating random models which capture the properties of physical dynamics 🔎 ✨
8/8
These results complement each other & highlight subtleties in formulating random models which capture the properties of physical dynamics 🔎 ✨
8/8
However, when this constraint is relaxed, we show it is possible to construct ensembles of quasi-local time-independent Hamiltonians which generate pseudorandom dynamics!
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
October 10, 2025 at 2:11 AM
However, when this constraint is relaxed, we show it is possible to construct ensembles of quasi-local time-independent Hamiltonians which generate pseudorandom dynamics!
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
These ensembles can also be efficiently simulated assuming the existence of quantum-secure OWFs 💻
7/8
On the other hand, in [2] we consider time evolution dynamics when factoring in uncertainty in H 🤔
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
October 10, 2025 at 2:11 AM
On the other hand, in [2] we consider time evolution dynamics when factoring in uncertainty in H 🤔
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
When the connectivity of the system is known, we show that the dynamics of any ensemble of local Hamiltonians, at any time scale, can be distinguished from a random unitary.
6/8
To prove this, we construct Hamiltonians which embed arbitrary Turing machines.
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
October 10, 2025 at 2:11 AM
To prove this, we construct Hamiltonians which embed arbitrary Turing machines.
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
Under standard cryptographic assumptions, there exist Hamiltonians whose long-time dynamics perform computations that are out of reach for (& can be distinguished from) any efficient circuit 🤖
5/8
While some models admit energy-conserving PRUs, we show that in general no efficient construction exists even for local 1D spin chains ⛓️
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
October 10, 2025 at 2:11 AM
While some models admit energy-conserving PRUs, we show that in general no efficient construction exists even for local 1D spin chains ⛓️
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
Not only that, determining if there exist energy-conserving PRUs for a given family of local 1D Hamiltonians is in general undecidable!
4/8
This leads us to define energy-conserving ensembles [1] which are maximally random w/ the constraint [U, H] = 0. In general, this is the same as averaging over all times.
We then ask, when can we efficiently construct energy-conserving pseudorandom unitaries (PRUs)? 🔋
3/8
We then ask, when can we efficiently construct energy-conserving pseudorandom unitaries (PRUs)? 🔋
3/8
October 10, 2025 at 2:11 AM
This leads us to define energy-conserving ensembles [1] which are maximally random w/ the constraint [U, H] = 0. In general, this is the same as averaging over all times.
We then ask, when can we efficiently construct energy-conserving pseudorandom unitaries (PRUs)? 🔋
3/8
We then ask, when can we efficiently construct energy-conserving pseudorandom unitaries (PRUs)? 🔋
3/8
We first observe that for any time-independent Hamiltonian H, the dynamics are diagonal in the energy eigenbasis.
If H is local, we can also efficiently distinguish it from random unitary dynamics by preparing states with non-zero energy and checking if H is conserved ⚡
2/8
If H is local, we can also efficiently distinguish it from random unitary dynamics by preparing states with non-zero energy and checking if H is conserved ⚡
2/8
October 10, 2025 at 2:11 AM
We first observe that for any time-independent Hamiltonian H, the dynamics are diagonal in the energy eigenbasis.
If H is local, we can also efficiently distinguish it from random unitary dynamics by preparing states with non-zero energy and checking if H is conserved ⚡
2/8
If H is local, we can also efficiently distinguish it from random unitary dynamics by preparing states with non-zero energy and checking if H is conserved ⚡
2/8
some of us are also too young to understand the myspace vs facebook analogy...
September 18, 2025 at 3:47 PM
some of us are also too young to understand the myspace vs facebook analogy...
I don't have anything against it in principle! but you could argue that working with instead of against community norms is better for visibility & communication of your results
August 27, 2025 at 11:33 PM
I don't have anything against it in principle! but you could argue that working with instead of against community norms is better for visibility & communication of your results
according to other sources commercial panels were only at around 15% a decade ago (when I was learning about energy science in high school the quoted number was around 10%)
July 14, 2025 at 6:11 PM
according to other sources commercial panels were only at around 15% a decade ago (when I was learning about energy science in high school the quoted number was around 10%)