Related papers: BQP and the Polynomial Hierarchy
The computational complexity of simulating the dynamics of physical quantum systems is a central question at the interface of quantum physics and computer science. In this work, we address this question for the simulation of exponentially…
There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical…
Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
We generalize quantum-classical PCPs, first introduced by Weggemans, Folkertsma and Cade (TQC 2024), to allow for $q$ quantum queries to a polynomially-sized classical proof ($\mathsf{QCPCP}_{Q,c,s}[q]$). Exploiting a connection with the…
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant…
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…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not…
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…
In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…
Distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for QIP, the class of problems having quantum interactive proof systems. Circuits in this model can represent arbitrary quantum processes, and thus…
In this work, we propose a new way to (non-interactively, verifiably) demonstrate Quantum Advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) multivariate quadratic…
We propose a new method for evaluating NISQ devices. This paper has three distinct parts. First, we present a new quantum algorithm that solves a two hundred year old problem of finding quadratic nonresidues (QNR) in polynomial time. We…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…