5 papers
On the dynamical Lie algebras of quantum approximate optimization algorithms
Jonathan Allcock, Miklos Santha, Pei Yuan +1
Dynamical Lie algebras (DLAs) have emerged as a valuable tool in the study of parameterized quantum circuits, helping to characterize both their expressiveness and trainability. In…
Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
Jonathan Allcock, Joao F. Doriguello, Gábor Ivanyos +1
Bell sampling is a simple yet powerful tool based on measuring two copies of a quantum state in the Bell basis, and has found applications in a plethora of problems related to stab…
On generating direct powers of dynamical Lie algebras
Jonathan Allcock, Miklos Santha, Pei Yuan +1
The expressibility and trainability of parameterized quantum circuits has been shown to be intimately related to their associated dynamical Lie algebras (DLAs). From a quantum algo…
Quasi-quantum states and the quasi-quantum PCP theorem
Itai Arad, Miklos Santha
We introduce -local quasi-quantum states: a superset of the regular quantum states, defined by relaxing the positivity constraint. We show that a -local quasi-quantum state o…
Constant-depth circuits for Boolean functions and quantum memory devices using multi-qubit gates
Jonathan Allcock, Jinge Bao, Joao F. Doriguello +2
We explore the power of the unbounded Fan-Out gate and the Global Tunable gates generated by Ising-type Hamiltonians in constructing constant-depth quantum circuits, with particula…