An optimal oracle separation of classical and quantum hybrid schemes

• URL: http://arxiv.org/abs/2205.04633v2
• Date: Mon, 8 Aug 2022 05:23:10 GMT
• Title: An optimal oracle separation of classical and quantum hybrid schemes
• Authors: Atsuya Hasegawa and Fran\c{c}ois Le Gall
• Abstract summary: We show that for any depth parameter $d$, there exists an oracle that separates quantum depth $d$ and $2d+1$, when computation-time classical is allowed. This gives an optimal oracle separation of classical and quantum hybrid schemes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, Chia, Chung and Lai (STOC 2020) and Coudron and Menda (STOC 2020) have shown that there exists an oracle $\mathcal{O}$ such that $\mathsf{BQP}^\mathcal{O} \neq (\mathsf{BPP^{BQNC}})^\mathcal{O} \cup (\mathsf{BQNC^{BPP}})^\mathcal{O}$. In fact, Chia et al. proved a stronger statement: for any depth parameter $d$, there exists an oracle that separates quantum depth $d$ and $2d+1$, when polynomial-time classical computation is allowed. This implies that relative to an oracle, doubling quantum depth gives classical and quantum hybrid schemes more computational power. In this paper, we show that for any depth parameter $d$, there exists an oracle that separates quantum depth $d$ and $d+1$, when polynomial-time classical computation is allowed. This gives an optimal oracle separation of classical and quantum hybrid schemes. To prove our result, we consider $d$-Bijective Shuffling Simon's Problem (which is a variant of $d$-Shuffling Simon's Problem considered by Chia et al.) and an oracle inspired by an "in-place" permutation oracle.

Related papers

• Quantum-Computable One-Way Functions without One-Way Functions [0.6349503549199401]
  We construct a classical oracle relative to which $mathsfP = mathsfNP$ but quantum-computable quantum-secure trapdoor one-way functions exist. Our result implies multi-copy pseudorandom states and pseudorandom unitaries, but also classical-communication public-key encryption, signatures, and oblivious transfer schemes.
  arXiv  Detail & Related papers  (2024-11-04T19:40:01Z)
• Classical versus quantum queries in quantum PCPs with classical proofs [0.3004066195320147]
  We generalize quantum-classical PCPs to allow for $q$ quantum queries to a classical proof. Surprisingly, this shows that we can amplify the promise gap from inverse to constant for constant query quantum-classicals. Even though we can achieve promise gap, our result also gives strong evidence that there exists no constant query quantum-classical PCP for $mathsfQCMA$.
  arXiv  Detail & Related papers  (2024-11-01T18:00:56Z)
• Oracle Separations for the Quantum-Classical Polynomial Hierarchy [0.0]
  We study the quantum-classical hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers. We give a new switching lemma for quantum algorithms which may be of independent interest.
  arXiv  Detail & Related papers  (2024-10-24T18:12:03Z)
• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• Quantum Depth in the Random Oracle Model [57.663890114335736]
  We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. For some problems, the ability to perform adaptive measurements in a single shallow quantum circuit is more useful than the ability to perform many shallow quantum circuits without adaptive measurements.
  arXiv  Detail & Related papers  (2022-10-12T17:54:02Z)
• Exponential Separation between Quantum and Classical Ordered Binary Decision Diagrams, Reordering Method and Hierarchies [68.93512627479197]
  We study quantum Ordered Binary Decision Diagrams($OBDD$) model. We prove lower bounds and upper bounds for OBDD with arbitrary order of input variables. We extend hierarchy for read$k$-times Ordered Binary Decision Diagrams ($k$-OBDD$) of width.
  arXiv  Detail & Related papers  (2022-04-22T12:37:56Z)
• Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-calculus [55.2480439325792]
  Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. We refine the PBS-calculus, a graphical language for coherent control inspired by quantum optics.
  arXiv  Detail & Related papers  (2022-02-10T18:59:52Z)
• Oracle separations of hybrid quantum-classical circuits [68.96380145211093]
  Two models of quantum computation: CQ_d and QC_d. CQ_d captures the scenario of a d-depth quantum computer many times; QC_d is more analogous to measurement-based quantum computation. We show that, despite the similarities between CQ_d and QC_d, the two models are intrinsically, i.e. CQ_d $nsubseteq$ QC_d and QC_d $nsubseteq$ CQ_d relative to an oracle.
  arXiv  Detail & Related papers  (2022-01-06T03:10:53Z)
• Quantum search-to-decision reductions and the state synthesis problem [0.4248594146171025]
  We show that a quantum algorithm makes queries to a classical decision oracle to output a desired quantum state. We also show that there exists a quantum-time algorithm that can generate a witness for a $mathsfQMA$ problem up to inverse precision. We also explore the more general $textitstate synthesis problem$, in which the goal is to efficiently synthesize a target state.
  arXiv  Detail & Related papers  (2021-11-04T16:52:58Z)
• An Optimal Separation of Randomized and Quantum Query Complexity [67.19751155411075]
  We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $ellsqrtbinomdell (1+log n)ell-1,$ sum to at most $cellsqrtbinomdell (1+log n)ell-1,$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant.
  arXiv  Detail & Related papers  (2020-08-24T06:50:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.