6 research outputs found
Exponential Separation between Quantum Communication and Logarithm of Approximate Rank
Chattopadhyay, Mande and Sherif (ECCC 2018) recently exhibited a total
Boolean function, the sink function, that has polynomial approximate rank and
polynomial randomized communication complexity. This gives an exponential
separation between randomized communication complexity and logarithm of the
approximate rank, refuting the log-approximate-rank conjecture. We show that
even the quantum communication complexity of the sink function is polynomial,
thus also refuting the quantum log-approximate-rank conjecture.
Our lower bound is based on the fooling distribution method introduced by Rao
and Sinha (ECCC 2015) for the classical case and extended by Anshu, Touchette,
Yao and Yu (STOC 2017) for the quantum case. We also give a new proof of the
classical lower bound using the fooling distribution method.Comment: The same lower bound has been obtained independently and
simultaneously by Anurag Anshu, Naresh Goud Boddu and Dave Touchett
Exponential separation between quantum communication and logarithm of approximate rank
Chattopadhyay, Mande and Sherif (ECCC 2018) recently exhibited a total Boolean function, the sink function, that has polynomial approximate rank and polynomial randomized communication complexity. This gives an exponential separation between randomized communication complexity and logarithm of the approximate rank, refuting the log-approximate-rank conjecture. We show that even the quantum communication complexity of the sink function is polynomial, thus also refuting the quantum log-approximate-rank conjecture. Our lower bound is based on the fooling distribution method introduced by Rao and Sinha (ECCC 2015) for the classical case and extended by Anshu, Touchette, Yao and Yu (STOC 2017) for the quantum case. We also give a new proof of the classical lower bound using the fooling distribution method.</p
Quantum Computing: Lecture Notes
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in subsequent years. The first 10 chapters cover the circuit model and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are followed by 2 chapters about complexity, 4 chapters about distributed ("Alice and Bob") settings, and a final chapter about quantum error correction. Appendices A and B give a brief introduction to the required linear algebra and some other mathematical and computer science background. All chapters come with exercises, with some hints provided in Appendix C
Quantum Computing: Lecture Notes
This is a set of lecture notes suitable for a Master's course on quantum
computation and information from the perspective of theoretical computer
science. The first version was written in 2011, with many extensions and
improvements in subsequent years. The first 10 chapters cover the circuit model
and the main quantum algorithms (Deutsch-Jozsa, Simon, Shor, Hidden Subgroup
Problem, Grover, quantum walks, Hamiltonian simulation and HHL). They are
followed by 3 chapters about complexity, 4 chapters about distributed ("Alice
and Bob") settings, and a final chapter about quantum error correction.
Appendices A and B give a brief introduction to the required linear algebra and
some other mathematical and computer science background. All chapters come with
exercises, with some hints provided in Appendix C.Comment: 184 pages. Version 2: added a new chapter about QMA and local
Hamiltonian, more exercises in several chapters, and some small
corrections/clarification