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Efficient Quantum Pseudorandomness.
Fernando G S L Brandão1,2, Aram W Harrow3, Michał Horodecki4
1Quantum Architectures and Computation Group, Microsoft Research, Redmond 11728, Washington, USA.
Physical Review Letters
|May 14, 2016
Summary
Random quantum circuits offer a new way to create pseudorandomness efficiently. This breakthrough allows for polynomial-time constructions of quantum unitary designs, useful in quantum information science and cryptography.
Area of Science:
- Quantum Information Science
- Quantum Computing
- Theoretical Physics
Background:
- Randomness is crucial for modeling natural systems and for engineered applications like computation and control.
- While classical pseudorandom operations are well-understood, constructing similar pseudorandomness in quantum systems is challenging.
- Fully random quantum transformations are computationally expensive, requiring exponential time.
Purpose of the Study:
- To demonstrate that random quantum unitary time evolutions (circuits) can serve as a powerful source of quantum pseudorandomness.
- To provide the first polynomial-time construction for quantum unitary designs.
- To show that generic quantum dynamics are indistinguishable from truly random processes.
Main Methods:
- Utilizing random quantum unitary time evolutions (circuits) as a method for generating pseudorandomness.
- Developing a polynomial-time construction for quantum unitary designs.
- Analyzing the properties of generic quantum dynamics.
Main Results:
- Established random quantum circuits as a source of quantum pseudorandomness.
- Achieved the first polynomial-time construction of quantum unitary designs.
- Demonstrated that generic quantum dynamics cannot be distinguished from truly random processes.
Conclusions:
- Random quantum circuits provide an efficient method for creating quantum pseudorandomness.
- The developed quantum unitary designs can substitute for fully random operations in many applications.
- The findings have implications for quantum information science, cryptography, and the study of quantum system self-equilibration.
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