For questions about the quantum complexity class referring to problems that can be solved by a quantum computer in polynomial time (the quantum equivalent of the classical complexity class P). You may also wish to tag with [complexity-theory].
Questions tagged [bqp]
43 questions
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Why is a quantum computer in some ways more powerful than a nondeterministic Turing machine?
The standard popular-news account of quantum computing is that a quantum computer (QC) would work by splitting into exponentially many noninteracting parallel copies of itself in different universes and having each one attempt to verify a different…
tparker
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33
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What is postselection in quantum computing?
A quantum computer can efficiently solve problems lying in the complexity class BQP. I have seen a claim that one can (potentially, because we don't know whether BQP is a proper subset or equal to PP) increase the efficiency of a quantum computer by…
Sir Cornflakes
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What are examples of Hamiltonian simulation problems that are BQP-complete?
Many papers assert that Hamiltonian simulation is BQP-complete
(e.g.,
Hamiltonian simulation with nearly optimal dependence on all parameters and Hamiltonian Simulation by Qubitization).
It is easy to see that Hamiltonian simulation is BQP-hard…
groupsgroupsgroups
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23
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What does Google's claim of "Quantum Supremacy" mean for the question of BQP vs BPP vs NP?
Google recently announced that they have achieved "Quantum Supremacy": "that would be practically impossible for a classical machine."
Does this mean that they have definitely proved that BQP ≠ BPP ? And if that is the case, what are the…
Alex Kinman
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Jones Polynomial
There are many fairly standard quantum algorithms that can all be understood within a very similar framework, from Deutsch's algorithm Simon's problem, Grover's search, Shor's algorithm and so on.
One algorithm that seems to be completely different…
DaftWullie
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Is HHL still BQP-complete when the matrix entries are only in {0,1}?
I'm studying BQP-completeness proofs of a number of interesting problems of Janzing and Wocjan, and Wocjan and Zhang. Janzing and Wocjan show that estimating entries of matrix powers $(A^m)_{ij}$ with $A_{ij}\in\{-1,0,1\}$ is (promise) BQP-complete.…
Mark Spinelli
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What is stopping FACTORING from being BQP-complete?
Classical complexity theory makes much of the study of so-called intermediate problems - that is, problems that are in $\mathsf{NP}$ but are nonetheless not known to be in $\mathsf{P}$ and further not expected to be $\mathsf{NP}$-complete.
Commonly…
Mark Spinelli
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What is recursive Fourier sampling and how does it prove separations between BQP and NP in the black-box model?
Context:
I was going through John Watrous' lecture Quantum Complexity Theory (Part 1) - CSSQI 2012. Around 48 minutes into the lecture, he presents the following:
No relationship is known between $\mathsf{BQP}$ and $\mathsf{NP}$...they are…
Sanchayan Dutta
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Is BQP only about time? Is this meaningful?
The complexity class BQP (bounded-error quantum polynomial time) seems to be defined only considering the time factor. Is this always meaningful? Do algorithms exist where computational time scales polynomially with the input size but other…
Daniel Tordera
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Consequences of SAT ∈ BQP
"Quantum magic won't be enough" (Bennett et al. 1997)
If you throw away the problem structure, and just consider the space of $2^n$ possible solutions, then even a quantum computer needs about $\sqrt{2^n}$ steps to find the correct one (using…
Didix
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Is there a BQP algorithm for each level of the polynomial hierarchy PH?
This question is inspired by thinking about quantum computing power with respect to games, such as chess/checkers/other toy games. Games fit naturally into the polynomial hierarchy $\mathrm{PH}$; I'm curious about follow-up questions.
Every Venn…
Mark Spinelli
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Why doesn't Deutsch-Jozsa Algorithm show that P ≠ BQP?
To my understanding, Deutsch-Jozsa algorithm solves a specific problem in constant time, using a fixed circuit depth, compared to a classical deterministic algorithm, which would require time exponential to the number of bits used to store the…
3yakuya
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Is APPROX-QCIRCUIT-PROB a BQP-complete problem?
I've read contradictory information: on the Wikipedia page for BQP, it is written without proof that "APPROX-QCIRCUIT-PROB is a BQP-complete problem", while I have read elsewhere (don't remember) that "it is usually assumed that are no BQP-complete…
9
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Is it known that BQP is not contained within NP?
I recently stumbled upon this paper here and here on the "deep ai" website that claims "BQP is not in NP."
I thought that this result would be huge (as a corollary would be that $BQP \neq P$), so I find it strange that I haven't heard about the…
wavosa
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Query regarding BQP belonging to PP
I found the following proof of BQP belonging to PP (the original document is here). There is a part of the proof that I have trouble understanding. First, the structure is given below.
We try to simulate a polynomial-time generated quantum circuit
…
BlackHat18
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