Related papers: Quantum proofs can be verified using only single q…
This paper studies multiple-proof quantum Merlin-Arthur (QMA) proof systems in the setting when the completeness-soundness gap is small. Small means that we only lower-bound the gap with an inverse-exponential function of the input length,…
Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve $\NP$-complete problems given a "short" quantum proof; more precisely, $\NP\subseteq…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
We present a simple quantum interactive proof (QIP) protocol using the quantum state teleportation (QST) and quantum energy teleportation (QET) protocols. QET is a technique that allows a receiver at a distance to extract the local energy…
Deterministic quantum computation with one quantum bit (DQC1) is a restricted model of quantum computing where the input state is the completely mixed state except for a single clean qubit, and only a single output qubit is measured at the…
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it…
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 consider the problem of testing and learning from data in the presence of resource constraints, such as limited memory or weak data access, which place limitations on the efficiency and feasibility of testing or learning. In particular,…
We propose a simple protocol for the verification of quantum computation after the computation has been performed. Our construction can be seen as an improvement on previous results in that it requires only a single prover, who is…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
QMA is the class of languages that can be decided by an efficient quantum verifier given a quantum witness, whereas QCMA is the class of such languages where the efficient quantum verifier only is given a classical witness. A challenging…
Valiant-Vazirani showed in 1985 [VV85] that solving NP with the promise that "yes" instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions). We are interested in extending this result to…
We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There…
With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation…
Measurement-based quantum computing enables universal quantum computing with only adaptive single-qubit measurements on certain many-qubit states, such as the graph state, the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, and several…
We introduce a simple sub-universal quantum computing model, which we call the Hadamard-classical circuit with one-qubit (HC1Q) model. It consists of a classical reversible circuit sandwiched by two layers of Hadamard gates, and therefore…
In computer science, many search problems are reducible to decision problems, which implies that finding a solution is as hard as deciding whether a solution exists. A quantum analogue of search-to-decision reductions would be to ask…
We prove a deterministic exponential time upper bound for Quantum Merlin-Arthur games with k unentangled provers. This is the first non-trivial upper bound of QMA(k) better than NEXP and can be considered an exponential improvement, unless…