Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation

Purifying Quantum States: Quantum and Classical Algorithms

vi

Hybrid classical-quantum dynamics

A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of interaction, the correspondence principle is violated. PACS numbers: 03.65.Bz, 03.65.Sq ∗ Electronic mail: [email protected], [email protected]

Unbounded-Error Classical and Quantum Communication Complexity

Since the seminal work of Paturi and Simon [26, FOCS’84 & JCSS’86], the unboundederror classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently, [14, ICALP’07] found that the unboundederror quantum communication complexity in the one-way communication model can also be investigated using the arrangement, and showed th...

Quantum Error-Correction Codes on Abelian Groups

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.

Isomorphism and Factorization- Classical and Quantum Algorithms