arXiv subjects

David Miloschewsky

Publications and source records attributed to David Miloschewsky.

5 recordsLinked to original sources

arXiv2026

Promises should be taken seriously: On relativization with promise problems

Relativization is concerned with comparing computational models with black-box access to an oracle. For promise problems, black-box access is not canonical due to inputs outside of the promise being unconstrained. We study two semantics for such access. Under robust queries, a machine must correctly answer regardless of the completion of the problem,, while loose access requires that the internal choices of a machine do not change based on off-promise queries. Our first result separates the language and promise settings. Namely, we construct an oracle $O$ such that $\mathsf{P}^O = \mathsf{BQP}^O = \mathsf{AWPP}^O$, but $\mathsf{PromiseBQP}^O\not\subseteq\mathsf{PromiseP}^O_{\mathsf{/poly}}$. In particular, $\mathsf{BPP}^O = \mathsf{BQP}^O$, but $\mathsf{PromiseBQP}^O \neq \mathsf{PromiseBPP}^O$, showing that results for languages need not transfer to promises. Next, we use loose queries to strengthen the upper bound on the Quantum-Classical Polynomial Hierarchy from $\mathsf{P}^{\mathsf{PP}^{\mathsf{PP}}}$ to $\mathsf{QCPH} \subseteq \mathsf{BP\cdot PP} \subseteq \mathsf{PromiseBPP}^{\mathsf{PP}}$. The same proof also shows $\mathsf{PP}^\mathsf{PromiseBQP} = \mathsf{PP}$. Additionally, we show that $\mathsf{PromiseBQP}$, even when given quantum advice, is self-low under robust queries. Finally, we exhibit an obstruction to transferring language-level counting results to promise classes. Although $\mathsf{AWPP}$ and $\mathsf{APP}$ are low for $\mathsf{PP}$, a corresponding promise analogue would collapse the counting hierarchy as $\mathsf{GapP} \subseteq \mathsf{FP}^{\mathsf{PromiseAWPP}}$. This motivates the introduction of $\mathsf{PromisePostBQP^*}$, which restricts $\mathsf{PostBQP}$ to input-indepencent postselection. By showing that it is low for \PP, we obtain $\mathsf{PP}^{\mathsf{PromiseYQP^*}} = \mathsf{PP}$.

cs.CC↗

arXiv2026

En Route to a Standard QMA1 vs. QCMA Oracle Separation

We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in $\mathsf{QMA}_1$ but not in $\mathsf{QCMA}$ when the $\mathsf{QCMA}$ verifier is only allowed polynomially many adaptive rounds and exponentially many parallel queries per round. Additionally, we derandomize the permutation-oracle separation of Fefferman and Kimmel, obtaining an in-place oracle separation between $\mathsf{QMA}_1$ and $\mathsf{QCMA}$. Furthermore, we focus on $\mathsf{QCMA}$ and $\mathsf{QMA}$ with an exponentially small gap, where we show a separation assuming the gap is fixed, but not when it may be arbitrarily small. Finally, we derive consequences for approximate ground-state preparation from sparse Hamiltonian oracle access, including a bounded-adaptivity frustration-free variant.

quant-ph↗

arXiv2026

A Framework for Ruling Out Quantum Speedups

We study when partial Boolean functions can (and cannot) exhibit superpolynomial quantum query speedups, and develop a general framework for ruling out such speedups via two complementary lenses: promise-aware complexity measures and function completions. First, we introduce promise versions of standard combinatorial measures (including block sensitivity and related variants) and prove that if the relevant promise and completion measures ``collapse'', then deterministic and quantum query complexities are necessarily polynomially related, i.e. $D(f) = \mathrm{poly}(Q(f))$. We then analyze structured families of promises, including symmetric partial functions and promises supported on Hamming slices, obtaining sharp (up to polynomial factors) characterizations in terms of a single gap parameter for the symmetric case and refined slice-dependent bounds for $k$-slice domains. Next, we formalize completion complexity as the minimum of a measure over total completions of a partial function, and show that completability of a measure captures the possibility of superpolynomial quantum speedups. Finally, we apply this viewpoint to derive broad non-speedup criteria for some classes of functions admitting well-behaved completions, such as functions with low maximum influence on both the standard and $p$-biased hypercubes and functions with efficiently identifiable domains, and then show some hardness results for general completion techniques.

quant-ph↗

arXiv2025

Modifications of Quantum Computation and Adaptive Queries to PP

In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first, $\mathsf{CorrBQP}$, is a modification of $\mathsf{BQP}$ which has the power to perform correlated measurements, i.e. measurements that output the same value across a partition of registers. The second, $\mathsf{MajBQP}$, augments $\mathsf{BQP}$ with the ability to collapse a register to its most likely measurement outcome. Specifically, we consider two variants, $\mathsf{MajBQP}$ and $\mathsf{AdMajBQP}$, where the latter may perform intermediate measurements. We exactly characterize the computational power of the models, $\mathsf{CorrBQP} = \mathsf{AdMajBQP} = \mathsf{BPP}^{\mathsf{PP}}$ and $\mathsf{MajBQP} = \mathsf{P}^{\mathsf{PP}}$. In fact, we show that other metaphysical modifications of $\mathsf{BQP}$, such as $\mathsf{CBQP}$ (i.e. $\mathsf{BQP}$ with the ability to clone arbitrary quantum states), are also equal to $\mathsf{BPP}^{\mathsf{PP}}$. We show that $\mathsf{CorrBQP}$ and $\mathsf{MajBQP}$ are self-low with respect to classically-accessible queries. In contrast, if they were self-low under quantumly-accessible queries, the counting hierarchy would collapse. Furthermore, we introduce a variant of rational degree that lower-bounds the query complexity of $\mathsf{BPP}^{\mathsf{PP}}$. Lastly, we extend the adversary lower-bounding technique to $\mathsf{AdPDQP}$, $\mathsf{BQP}$ with the ability to sample the current state of an algorithm with collapsing it and adapt the computation based on the samples.

cs.CC↗

arXiv2024

New Lower-bounds for Quantum Computation with Non-Collapsing Measurements

Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without collapsing them. Although PDQP contains SZK, it still requires $\Omega(N^{1/4})$ queries to solve unstructured search. We formulate an alternative equivalent definition of PDQP, which we use to prove the positive weighted adversary lower-bounding method, establishing multiple tighter bounds and a trade-off between queries and non-collapsing measurements. We utilize the technique in order to analyze the query complexity of the well-studied majority and element distinctness problems. Additionally, we prove a tight $\Theta(N^{1/3})$ bound on search. Furthermore, we use the lower-bound to explore PDQP under query restrictions, finding that when combined with non-adaptive queries, we limit the speed-up in several cases.

quant-ph↗