Related papers: Classical vs Quantum Advice and Proofs under Class…
Yes, we show that they are. We initiate the study of languages that necessarily need uncloneable quantum proofs and advice. We define strictly uncloneable versions of the classes QMA, BQP/qpoly and FEQP/qpoly (which is the class of…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…
One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the…
Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can…
We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model…
We construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) commitments and QCCC multiparty non-interactive key exchange exist. We also construct a unitary oracle…
Near-term quantum computers are likely to have small depths due to short coherence time and noisy gates, and thus a potential way to use these quantum devices is using a hybrid scheme that interleaves them with classical computers. For…
The class MA consists of languages that can be efficiently verified by classical probabilistic verifiers using a single classical certificate, and the class QMA consists of languages that can be efficiently verified by quantum verifiers…
Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
We show that a simple eavesdropper listening in on classical communication between potentially entangled quantum parties will eventually be able to impersonate any of the parties. Furthermore, the attack is efficient if one-way puzzles do…
Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and…
Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…
We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function $f$, and present $f$ in…
Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications…