5 papers · 1 filter
Arts & crafts: Strong random unitaries and geometric locality
Marten Folkertsma, Lorenzo Grevink, Jonas Helsen +1
We study the problem of constructing strong approximate unitary -designs on -dimensional grids (and more generally on Cartesian products of graphs), building on the work of S…
Quantum Catalytic Space
Harry Buhrman, Marten Folkertsma, Ian Mertz +4
Space complexity is a key field of study in theoretical computer science. In the quantum setting there are clear motivations to understand the power of space-restricted computation…
State preparation by shallow circuits using feed forward
Harry Buhrman, Marten Folkertsma, Bruno Loff +1
In order to achieve fault-tolerant quantum computation, we need to repeat the following sequence of four steps: First, perform 1 or 2 qubit quantum gates (in parallel if possible).…
Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture
Jordi Weggemans, Marten Folkertsma, Chris Cade
We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem, which we call 'Guidable Local Hamiltonian' problems. Unlike their guided counterparts, thes…
Complexity of the Guided Local Hamiltonian Problem: Improved Parameters and Extension to Excited States
Chris Cade, Marten Folkertsma, Jordi Weggemans
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a -local Hamiltonian when provided with a description of a qua…