Related papers: Entanglement Barriers from Computational Complexit…
We construct a tensor network that delivers an unnormalized quantum state whose coefficients are the solutions to a given instance of 3SAT, an NP-complete problem. The tensor network contraction that corresponds to the norm of the state…
Efficiently entangling pairs of qubits is essential to fully harness the power of quantum computing. Here, we devise an exact protocol that simultaneously entangles arbitrary pairs of qubits on a trapped-ion quantum computer. The protocol…
A promising paradigm of quantum computing for achieving practical quantum advantages is quantum annealing or quantum approximate optimization algorithm, where the classical problems are encoded in Ising interactions. However, it is…
We present an approach to parameterized reachability for communicating finite-state threads that formulates the analysis as a satisfiability problem. In addition to the unbounded number of threads, the main challenge for SAT/SMT-based…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
Quantum information theory is plagued by the problem of regularisations, which require the evaluation of formidable asymptotic quantities. This makes it computationally intractable to gain a precise quantitative understanding of the…
Nonstabilizerness, or `magic', is a critical quantum resource that, together with entanglement, characterizes the non-classical complexity of quantum states. Here, we address the problem of quantifying the average nonstabilizerness of…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
Describing non-equilibrium properties of quantum many-body systems is challenging due to high entanglement in the wavefunction. We describe evolution of local observables via the influence matrix (IM), which encodes the effects of a…
This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is precisely characterized by EXP, the class…
Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy…
Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the…
Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic…
Complex numbers are central to the formulation of quantum mechanics, yet their role as a genuine resource is only beginning to be understood. In this work, we demonstrate that quantum states with intrinsically complex amplitudes provide a…
This paper explores the Boolean Satisfiability Problem (SAT) in the context of Kolmogorov complexity theory. We present three versions of the distinguishability problem-Boolean formulas, Turing machines, and quantum systems-each focused on…
In recent years, efficient quantum circuit simulations incorporating ideal noise assumptions have relied on tensor network simulators, particularly leveraging the matrix product density operator (MPDO) framework. However, experiments on…
In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. They…
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…
We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical"…
A conceptual difficulty in the foundations of quantum mechanics is the quantum measurement problem (QMP), essentially concerned with the apparent non-unitarity of the measurement process and the classicality of macroscopic systems. In an…