We obtain the first nontrivial time-space lower bound for quantum algorithms solving prob-lems related to satisfiability. Our bound applies to MajSAT and MajMajSAT, which are com-plete problems for the first and second levels of the counting hierarchy, respectively. We prove that for every real d and every positive real there exists a real c> 1 such that either: • MajMajSAT does not have a quantum algorithm with bounded two-sided error that runs in time nc, or • MajSAT does not have a quantum algorithm with bounded two-sided error that runs in time nd and space n1−. In particular, MajMajSAT cannot be solved by a quantum algorithm with bounded two-sided error running in time n1+o(1) and space n1− for any > 0. The key technical novelt...
AbstractWe use the powerful tools of counting complexity and generic oracles to help understand the ...
AbstractWe prove the following facts about the language recognition power of quantum Turing machines...
We use the powerful tools of counting complexity and generic oracles to help understand the limitati...
We give two time- and space-efficient simulations of quantum computations with intermediate measurem...
AbstractThis paper investigates the computational power of space-bounded quantum Turing machines. Th...
We present a number of results related to quantum algorithms with small error probability and quantu...
We explore the space “just above ” BQP by defining a complexity class PDQP (Product Dynamical Quantu...
Thesis (Ph.D.)--University of Washington, 2013Computational complexity is the field that studies the...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Comp...
It is well known that a straightforward application of Grover’s quantum search algorithm enables to ...
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In ...
We extend the lower bound techniques of [14], to the unbounded-error probabilistic model. A key step...
While quantum computers hold the promise of significant computational speedups, the limited size of ...
One of the major challenges in the field of complexity theory is the inability to prove unconditiona...
The usual method for studying run-times of quantum algorithms is via an asymptotic, worst-case analy...
AbstractWe use the powerful tools of counting complexity and generic oracles to help understand the ...
AbstractWe prove the following facts about the language recognition power of quantum Turing machines...
We use the powerful tools of counting complexity and generic oracles to help understand the limitati...
We give two time- and space-efficient simulations of quantum computations with intermediate measurem...
AbstractThis paper investigates the computational power of space-bounded quantum Turing machines. Th...
We present a number of results related to quantum algorithms with small error probability and quantu...
We explore the space “just above ” BQP by defining a complexity class PDQP (Product Dynamical Quantu...
Thesis (Ph.D.)--University of Washington, 2013Computational complexity is the field that studies the...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Comp...
It is well known that a straightforward application of Grover’s quantum search algorithm enables to ...
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In ...
We extend the lower bound techniques of [14], to the unbounded-error probabilistic model. A key step...
While quantum computers hold the promise of significant computational speedups, the limited size of ...
One of the major challenges in the field of complexity theory is the inability to prove unconditiona...
The usual method for studying run-times of quantum algorithms is via an asymptotic, worst-case analy...
AbstractWe use the powerful tools of counting complexity and generic oracles to help understand the ...
AbstractWe prove the following facts about the language recognition power of quantum Turing machines...
We use the powerful tools of counting complexity and generic oracles to help understand the limitati...