In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. [1] . It is the quantum analogue to the complexity class BPP.

2015年2月2日 · A $BQP$ machine can also compute $L$, with the $BPP$ strategy. An $EQP$ machine can use Grover's algorithm to solve $L$ with certainty. (Also works for BQP, but overkill.) The Oracle. So we have a decision problem $L(B, n)$ that separates $P^{NP}$ and $BQP$, but relying crucially on the assumption that the machine is limited to querying $B$.

计算机科学家们已经证明，bqp包含在pspace中，且bqp包含p。 但是他们不知道BQP是否包含在NP中，但是他们相信这两类是不可比的：存在NP中的问题但不是BQP，反之亦然。

BQP is a class of languages L ⊆ (0, 1)∗, decidable with bounded error probability ( say 1/3 ) by a uniform family of polynomial-size quantum circuit over some universal family of gate. In today’s lecture, we will see where this BQP sits in inclusion diagram of complexity classes.

We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to topics in circuit complexity, pseudorandomness, and Fourier analysis. First, we show that there exists an oracle relation problem (i.e., a problem with many valid outputs) that is solvable in BQP, but not in PH.

2023年3月4日 · 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 proof before.

2022年9月19日 · Here, I provide the proof of a stronger result that implies this result: BQP contains problems that lie beyond the much larger classical computing class NP. This proves that quantum computation is able to efficiently solve problems which are far beyond the capabilities of classical computers.

bqp 和 np 之间的关系是量子复杂性理论研究的一个活跃领域。 开放性问题包括 BQP 是否包含在 NP 中、BQP 完全问题的存在性以及 BQP 是否等于 P 或 NP。 解决这些问题将加深我们对量子计算的能力和局限性的理解，并对包括密码学在内的各个领域产生影响。

It is unlikely that the current under-review proof of P != NP will allow you to seperate BQP and QMA (or BQP and P, or BQP and NP, or even BPP and NP...). Deolalikar's proof uses descriptive complexity, in particular it uses a correspondence between statements expressible in certain logics and the complexity classes P and NP.

Watrous says that an intuitive approach for proving the containment BQP ⊆ PP B Q P ⊆ P P is along the lines of: unbounded error probabilistic computations can simulate interference in quantum computations (e.g. run two probabilistic processes, and …