Related papers: An exponential time upper bound for Quantum Merlin…
The quantum k-Local Hamiltonian problem is a natural generalization of classical constraint satisfaction problems (k-CSP) and is complete for QMA, a quantum analog of NP. Although the complexity of k-Local Hamiltonian problems has been well…
We prove that QMA where the verifier may also make a single non-collapsing measurement is equal to NEXP, resolving an open question of Aaronson. We show this is a corollary to a modified proof of QMA+ = NEXP [arXiv:2306.13247]. At the core…
We quantise the generalised Hawk-Dove Game. By restricting the strategy space available to the players, we show that every game of this type can be extended into the quantum realm to produce a Pareto optimal evolutionarily stable strategy.…
We study the algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a \emph{corrupted} set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
We prove an n-EXPTIME lower bound for the problem of deciding the winner in a reachability game on Higher Order Pushdown Automata (HPDA) of level n. This bound matches the known upper bound for parity games on HPDA. As a consequence the…
We consider the problem of unambiguous (error-free) discrimination of N linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive…
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the…
We study the problem of entanglement-assisted quantum state redistribution in the one-shot setting and provide a new achievability result on the quantum communication required. Our bounds are in terms of the max-relative entropy and the…
A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang's maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the…
Motivated by the success of bounded model checking framework for finite state machines, Ouaknine and Worrell proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for…
Dries Sels and Allan Gr{\o}nlund have demonstrated numerical algorithms that outperform the players of our Quantum Moves game and they call the conclusions of our article Exploring the Quantum Speed Limit with Computer Games, Nature, 532,…
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…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit $q$-state separation automaton implies an algorithm for parity games with running time polynomial in…
We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst…
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…