Author
Seth Douglas
Recent research
- Physics & SpaceOpen access
A device that runs a quantum operation which does not respect time translation needs its own clock. This paper asks what owning that clock costs. Gates. The clock is paid for in capital, in the energy range of the heat baths, and in an energy that comes back only as a lottery, ea...
- Physics & SpaceOpen access
The work cost of answering in real time
Many devices must answer each request before the next one arrives, while remembering what came before. This paper determines how much work such a device must spend per episode, one complete run of the process, for every finite interactive quantum process whose outputs carry the s...
- Physics & SpaceOpen access
Only quantum channels save work by waiting
Faist, Berta and Brandão showed that n uses of a time-covariant quantum channel cost, to leading order, n times its thermodynamic capacity, when the device may collect all inputs before it releases any output. Many devices cannot wait: they must release each output before the nex...
- Physics & SpaceOpen access
A physical device acts in time: inputs arrive, outputs are released and can no longer be touched, some systems are kept, and some must come back. This paper shows that the optimal work rate of such a device, over many uses at vanishing error, is fixed by one quantity, the least e...
- AI & ComputingOpen access
No algorithm can tell how much memory a repeated quantum channel needs
A device that applies a quantum channel over and over must release each output before the next input arrives. How much memory does it need? Suppose every fresh qubit the device receives is maximally mixed. In companion work we showed that the answer then turns on one set: the cha...
- AI & ComputingOpen access
The memory and purity cost of immediate delivery
How much memory does a device need to apply one quantum channel n times, if each output must leave before the next input arrives? The paper counts the qubits the device keeps, the qubits it exchanges for fresh ones, and the purity it is given, with error measured on the whole exp...
- AI & ComputingOpen access
How far from finite can an amenable group be? Every finite piece of an amenable group can be imitated by permutations of a finite set, and Cornulier's sofic profile counts how many points such an imitation needs at accuracy 1/r. We build a finitely presented elementary amenable g...
- AI & ComputingOpen access
How far from finite can an amenable group be? Every finite piece of an amenable group can be imitated by permutations of a finite set, and Cornulier's sofic profile counts how many points such an imitation needs at accuracy 1/r. We build a finitely presented elementary amenable g...
- AI & ComputingOpen access
How far from finite can an amenable group be? Every finite piece of an amenable group can be imitated by permutations of a finite set, and Cornulier's sofic profile counts how many points such an imitation needs at accuracy 1/r. We build a finitely presented elementary amenable g...
- AI & ComputingOpen access
How far from finite can an amenable group be? Every finite piece of an amenable group can be imitated by permutations of a finite set, and Cornulier's sofic profile counts how many points such an imitation needs at accuracy 1/r. We build a finitely presented elementary amenable g...
- AI & ComputingOpen access
A rational quantum channel beyond finite tracial baths
A quantum channel on a finite system always has a finite realization with a pure environment. With a maximally mixed environment this can fail even approximately: since MIP* = RE, some factorizable channels lie outside the closure of the finite matrix-tracial factorizations (Haag...
- AI & ComputingOpen access
Houghton's group H_3 has superpolynomial sofic profile
How many points does a permutation model of a group need? Houghton's group H_3, which is finitely presented and elementary amenable, has a finite piece whose sofic profile lies between exp(Omega(r^c)), with c = 1/(log_2(107)+1), about 0.129, and exp(O(sqrt(r) log r)). So an amena...
- AI & ComputingOpen access
Houghton's group H_3 has superpolynomial sofic profile
How many points does a permutation model of a group need? Houghton's group H_3, which is finitely presented and elementary amenable, has a finite piece whose sofic profile lies between exp(Omega(r^c)), with c = 1/(log_2(107)+1), about 0.129, and exp(O(sqrt(r) log r)). So an amena...
- AI & ComputingOpen access
Houghton's group H_3 has superpolynomial sofic profile
Houghton's finitely presented elementary amenable group H_3 has a finite chunk with superpolynomial sofic profile. We prove a lower bound exp(Omega(r^c)), where c = 1/(log_2(107)+1), and an upper bound exp(O(sqrt(r) log r)). The upper bound holds for every fixed finite chunk of H...