Related papers: Achieving perfect completeness in classical-witnes…
We introduce a basis-restricted variant of the Quantum-k-SAT problem, in which each term in the input Hamiltonian is required to be diagonal in either the standard or Hadamard basis. Our main result is that the Quantum-6-SAT problem with…
We discuss and experimentally demonstrate a probabilistic Hadamard gate for coherent state qubits. The scheme is based on linear optical components, non-classical resources and the joint projective action of a photon counter and a homodyne…
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 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…
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…
QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the ``Local Hamiltonian'' problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems.…
Authentication provides the trust people need to engage in transactions. The advent of physical keys that are impossible to copy promises to revolutionize this field. Up to now, such keys have been verified by classical challenge-response…
We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap with a product state is 1-epsilon, the test passes with…
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…
As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized…
We study two kinds of different problems. One is the multiple independence testing, which can be considered as a kind of generalization of quantum Stein's lemma. We test whether the quantum system is correlated to the classical system or is…
We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits…
We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets…
The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer. Here we revisit this theorem and extend it to quantum circuits composed of Clifford and T gates,…
Quantum zero-knowledge proofs and quantum proofs of knowledge are inherently difficult to analyze because their security analysis uses rewinding. Certain cases of quantum rewinding are handled by the results by Watrous (SIAM J Comput, 2009)…
The question of whether quantum real-time one-counter automata (rtQ1CAs) can outperform their probabilistic counterparts has been open for more than a decade. We provide an affirmative answer to this question, by demonstrating a…
BellQMA protocols are a subclass of multi-prover quantum Merlin-Arthur protocols in which the verifier is restricted to perform nonadaptive,unentangled measurements on the quantum states received from each Merlin. In this paper, we prove…
We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…
A single-shot Toffoli, or controlled-controlled-NOT, gate is desirable for classical and quantum information processing. The Toffoli gate alone is universal for reversible computing and, accompanied by the Hadamard gate, forms a universal…
We perform Bell's measurement and perform quantum Fourier transform with the classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the…