The idea of the out-of-time-order correlator (OTOC) has recently emerged in study both condensed matter systems and gravitational systems. It not only plays a key role investigating holographic duality between strongly interacting quantum system system, it also diagnoses chaotic behavior many-body characterizes information scrambling. Based on OTOCs, three different concepts—quantum chaos, duality, scrambling—are found to be intimately related each other. Despite its theoretical importance,...

Entanglement is an important evidence that a quantum device can potentially solve problems intractable for classical computers. In this paper, we prepare connected graph states involving 8 to 16 qubits on ibmqx5, 16-qubit superconducting processor accessible via IBM cloud,using low-depth circuits. We demonstrate the prepared state fully entangled, i.e. inseparable with respect any fixed partition.

Logic gates can be performed on data encoded in quantum code blocks such that errors introduced by faulty corrected. The important class of transversal acts bitwise between corresponding qubits and thus limits error propagation. If any gate could implemented using gates, the set would universal. We study structure <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GF</i> (4)-additive codes prove no universal logic exists for these codes. This result...

This is the draft version of a textbook, which aims to introduce quantum information science viewpoints on condensed matter physics graduate students in (or interested researchers). We keep writing self-consistent way, requiring minimum background science. Basic knowledge undergraduate and assumed. start slowly from basic ideas theory, but wish eventually bring readers frontiers research physics, including topological phases matter, tensor networks, symmetry-protected phases.

The problem of determining whether a given quantum state is entangled lies at the heart information processing. Despite many methods---such as positive partial transpose criterion and $k$-symmetric extendibility criterion---to tackle this problem, none them enables general, practical solution due to problem's NP-hard complexity. Explicitly, separable states form high-dimensional convex set vastly complicated structures. In work, we build different separability-entanglement classifier...

In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying orders corresponds to gapped quantum states. We show such a statement is not precise. introduce the concept \emph{gapped liquid} as special kind states can "dissolve" any product on additional sites. Topologically ordered actually correspond liquids with stable ground-state degeneracy. Symmetry-breaking for on-site symmetry are also liquids, but unstable (2)...

This paper proves that the remote-state preparation (RSP) scheme in real Hilbert space can only be implemented when dimension of is 2, 4, or 8. fact shown to related parallelizability $(n\ensuremath{-}1)$-dimensional sphere ${S}^{n\ensuremath{-}1}.$ When 4 and 8 generalized explicitly presented. It also for a given state with components having same norm, RSP arbitrary case.

The concept of a qudit (a d-level system) cluster state is proposed by generalizing the qubit [Phys. Rev. Lett. 86, 910 (2001)] to higher-dimensional Hilbert space according finite-dimensional representations quantum plane algebra. We demonstrate their correlations and prove theorem which guarantees availability states in computation. explicitly construct network show universality one-way computer based on defined single-qudit measurement. A protocol implementing suggested using...

The definition of entanglement in identical-particle system is introduced. separability criterion two-identical particle given. physical meaning the analysed. Applications to two-boson and two-fermion systems are made. It found new correlation phenomena identical-boson exist, they may have applications field quantum information.

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well all known examples of nonadditive codes with good parameters. use this framework generate new superior parameters any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. also show how construct encoding circuits for within our framework.

Accurate and efficient control of quantum systems is one the central challenges for information processing. Current state-of-the-art experiments rarely go beyond 10 qubits in most cases demonstrate only limited control. Here we a 12-qubit system, show that system can be employed as processor to optimize its own sequence by using measurement-based feedback (MQFC). The final product complex task: preparation 12-coherent state. about 10% more accurate than generated standard (classical)...

Abstract Quantum state tomography is a daunting challenge of experimental quantum computing, even in moderate system size. One way to boost the efficiency via local measurements on reduced density matrices, but reconstruction full thereafter hard. Here, we present machine-learning method recover ground states $$k$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math> -local Hamiltonians from just information, where fully connected neural network built...

The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due various unnatural ingredients of the SYK Hamiltonian such as strong randomness fully nonlocal fermion interaction. At present, constructing exploring dynamics is best through digital simulation, where state-of-the-art techniques can already...

Abstract The quantum imaginary time evolution is a powerful algorithm for preparing the ground and thermal states on near-term devices. However, algorithmic errors induced by Trotterization local approximation severely hinder its performance. Here we propose deep reinforcement learning-based method to steer mitigate these errors. In our scheme, well-trained agent can find subtle path where most cancel out, enhancing fidelity significantly. We verified method’s validity with transverse-field...

Many-body entangled quantum states studied in condensed matter physics can be primary resources for information, allowing any computation to realized using measurements alone, on the state. Such a universal state would remarkably valuable, if only it were thermodynamically stable and experimentally accessible, by virtue of being unique ground physically reasonable Hamiltonian made two-body, nearest-neighbor interactions. We introduce such state, composed six-state particles hexagonal...

We discuss the uniqueness of quantum states compatible with given results for measuring a set observables. For pure state, we consider two different types uniqueness: (1) no other state is same measurement and (2) or mixed, results. case (1), it known that d-dimensional Hilbert space, there exists 4d-5 observables uniquely determines any state. show (2), 5d-7 suffice to determine Thus gap between give some examples illustrate this. The corresponding reduced density matrices (RDMs)...

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global be uniquely determined (UD) by its reduced density matrices (RDMs). In this work, we demonstrate first time a class of states are UD their RDMs under assumption pure, but fail to in absence assumption. This discovery allows us classify according properties, with requirement each treated distinctly practice simplifying tomography. Additionally,...

We experimentally simulate the spin networks -- a fundamental description of quantum spacetime at Planck level. achieve this by simulating tetrahedra and their interactions. The tensor product these comprises networks. In initial attempt to study information processing, on four-qubit nuclear magnetic resonance simulator, we basic module comprising five interactions spacetime. By measuring geometric properties corresponding interactions, our experiment serves as that represents Feynman...

As quantum technology rapidly advances, the need for efficient scalable methods to characterize systems intensifies. Quantum state tomography and Hamiltonian learning are essential interpreting optimizing systems, yet a unified approach remains elusive. Such an integration could enhance our understanding of complex relationship between states Hamiltonians, contributing development more methodologies. In this paper, we present method that integrates learning, drawing inspiration from machine...

Abstract In the 1970s, Wiesner introduced concept of quantum money, where states serve as currency, offering physical-level unforgeability through mechanics. Yet, traditional proposals often unrealistically assume personal computing access for each user. To address these issues, we propose a cloud-based semi-quantum money (CSQM) scheme. This approach only requires semi-honest third-party clouds, while rest system, including transactions and banks, remains fully classical. We also estimate...

The tensor product representation of quantum states leads to a promising variational approach study phase and transitions, especially topological ordered phases which are impossible handle with conventional methods due their long range entanglement. However, an important issue arises when we use (TPS) as find the ground state Hamiltonian: can arbitrary variations in tensors that represent Hamiltonian be induced by local perturbations Hamiltonian? Starting from is exact $\mathbb{Z}_2$ order,...