In what way does quantum computing challenge the strong Church-Turing thesis, and what are the implications of this challenge for computational theory?
The strong Church-Turing thesis posits that any function which can be computationally realized can be computed by a Turing machine, given sufficient time and resources. This thesis extends the original Church-Turing thesis by suggesting that Turing machines can simulate any physical computational device with polynomial overhead. Quantum computing, however, presents a formidable challenge to this
What are the open questions regarding the relationship between BQP and NP, and what would it mean for complexity theory if BQP is proven to be strictly larger than P?
The relationship between BQP (Bounded-error Quantum Polynomial time) and NP (Nondeterministic Polynomial time) is a topic of great interest in complexity theory. BQP is the class of decision problems that can be solved by a quantum computer in polynomial time with a bounded error probability, while NP is the class of decision problems that can
What evidence do we have that suggests BQP might be more powerful than classical polynomial time, and what are some examples of problems believed to be in BQP but not in BPP?
One of the fundamental questions in quantum complexity theory is whether quantum computers can solve certain problems more efficiently than classical computers. The class of problems that can be efficiently solved by a quantum computer is known as BQP (Bounded-error Quantum Polynomial time), which is analogous to the class of problems that can be efficiently
- Published in Quantum Information, EITC/QI/QIF Quantum Information Fundamentals, Introduction to Quantum Complexity Theory, BQP, Examination review
How do we define a language L to be in BQP and what are the requirements for a quantum circuit solving a problem in BQP?
In the field of quantum complexity theory, the class BQP (Bounded Error Quantum Polynomial Time) is defined as the set of decision problems that can be solved by a quantum computer in polynomial time with a bounded probability of error. To define a language L to be in BQP, we need to show that there
- Published in Quantum Information, EITC/QI/QIF Quantum Information Fundamentals, Introduction to Quantum Complexity Theory, BQP, Examination review