Related papers: stateQIP = statePSPACE
We consider a hypothetical apparatus that implements measurements for arbitrary 4-local quantum observables A on n qubits. The apparatus implements the ``measurement algorithm'' after receiving a classical description of A. We show that a…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
Models of computations over the integers are equivalent from a computability and complexity theory point of view by the Church-Turing thesis. It is not possible to unify discrete-time models over the reals. The situation is unclear but…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
We consider the quantum complexity of computing Schatten $p$-norms and related quantities, and find that the problem of estimating these quantities is closely related to the one clean qubit model of computation. We show that the problem of…
We provide an alternative proof of \class{QIP}=\class{PSPACE} to the recent breakthrough result. Unlike solving some semidefinite programs that captures the computational power of quantum interactive proofs, our method starts with one…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
The performance of quantum algorithms for ground-state energy estimation is directly impacted by the quality of the initial state, where quality is traditionally defined in terms of the overlap of the input state with the target state. An…
We study the task of lifting arbitrary quantum states and channels to purifications and Stinespring dilations, respectively, in both the probabilistic exact and deterministic approximate settings. We formalize this task through a general…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…
Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…