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<jats:title>Abstract</jats:title> <jats:p>Multi-particle interference is a key resource for quantum information processing, as exemplified by Boson Sampling. Hence, given its fragile nature, an essential desideratum is a solid and reliable framework for its validation. However, while several protocols have been introduced to this end, the approach is still fragmented and fails to build a big picture for future developments. In this work, we propose an operational approach to validation that encompasses and strengthens the state of the art for these protocols. To this end, we consider the Bayesian hypothesis testing and the statistical benchmark as most favorable protocols for small- and large-scale applications, respectively. We numerically investigate their operation with finite sample size, extending previous tests to larger dimensions, and against two adversarial algorithms for classical simulation: the mean-field sampler and the metropolized independent sampler. To evidence the actual need for refined validation techniques, we show how the assessment of numerically simulated data depends on the available sample size, as well as on the internal hyper-parameters and other practically relevant constraints. Our analyses provide general insights into the challenge of validation, and can inspire the design of algorithms with a measurable quantum advantage.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The quadratic reduction of query complexity of Grover’s search algorithm (GA), while significant, would not be enough to enjoy exponentially fast data searching in large-scale quantum computation. One of the ways to enhance the speedup in the framework of Grover’s algorithm is to employ a novel quantum operation, i.e., inversion against an unknown state; however, this is not possible at least in quantum theory. We thus extend the Grover algorithm assisted by closed timelike curves (CTCs), in which the unknown-state inversion is achievable by combining the superposition of two unknown states with cloning. We dubbed this refined algorithm CTC-assisted Grover algorithm (CTC-GA). We show that the CTC-GA can vastly reduce the query complexity compared to the original algorithm; remarkably, from polynomial to poly-logarithmic. These results will provide a broader intuition for exponential quantum speedup of data searching problems.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Quantum Darwinism is a compelling theory that describes the quantum-to classical transition as the emergence of objectivity of quantum systems. Spectrum broadcast structure and strong quantum Darwinism are two extensions of this theory with emphasis on state structure and information respectively. The complete experimental verification of these three frameworks, however, requires quantum state tomography over both the system and accessible environments, thus limiting the feasibility and scalability of experimental tests. Here, we introduce a subspace-dependent objectivity operation and construct a witness that detects non-objectivity by comparing the dynamics of the system-environment state with and without the objectivity operation. We then propose a photonic experimental simulation that implements the witnessing scheme. Our work proposes a route to further experimental exploration of the quantum to classical transition.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We analyze a scheme for preparation of magnetically ordered states of two-component bosonic atoms in optical lattices. We compute the dynamics during adiabatic and optimized time-dependent ramps to produce ground states of effective spin Hamiltonians, and determine the robustness to decoherence for realistic experimental system sizes and timescales. Ramping parameters near a phase transition point in both effective spin-1/2 and spin-1 models produces entangled spin-symmetric states that have potential future applications in quantum enhanced measurement. The preparation of these states and their robustness to decoherence is quantified by computing the quantum Fisher information (QFI) of final states. We identify that the generation of useful entanglement should in general be more robust to heating than it would be implied by the state fidelity, with corresponding implications for practical applications.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We give quantum speedups of several general-purpose numerical optimisation methods for minimising a function <jats:inline-formula> <jats:tex-math><?CDATA $f:{\mathbb{R}}^{n}\to \mathbb{R}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:mo>→</mml:mo> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstabb003ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>. First, we show that many techniques for global optimisation under a Lipschitz constraint can be accelerated near-quadratically. Second, we show that backtracking line search, an ingredient in quasi-Newton optimisation algorithms, can be accelerated up to quadratically. Third, we show that a component of the Nelder–Mead algorithm can be accelerated by up to a multiplicative factor of <jats:inline-formula> <jats:tex-math><?CDATA $O\left(\sqrt{n}\right)$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>O</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msqrt> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstabb003ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>. Fourth, we show that a quantum gradient computation algorithm of Gilyén <jats:italic>et al</jats:italic> can be used to approximately compute gradients in the framework of stochastic gradient descent. In each case, our results are based on applying existing quantum algorithms to accelerate specific components of the classical algorithms, rather than developing new quantum techniques.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We design a quantum repeater architecture using individual <jats:sup>167</jats:sup>Er ions doped into Y<jats:sub>2</jats:sub>SiO<jats:sub>5</jats:sub> crystal. This ion is a promising candidate for a repeater protocol because of its long hyperfine coherence time in addition to its ability to emit photons within the telecommunication wavelength range. To distribute entanglement over a long distance, we propose two different swapping gates between nearby ions using the exchange of virtual cavity photons and the electric dipole–dipole interaction. We analyze their expected performance, and discuss their strengths and weaknesses. Then, we show that a post-selection approach can be implemented to improve the gate fidelity of the virtual photon exchange scheme by monitoring cavity emission. Finally, we use our results for the swapping gates to estimate the end-to-end fidelity and distribution rate for the protocol.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Graph states are ubiquitous in quantum information with diverse applications ranging from quantum network protocols to measurement based quantum computing. Here we consider the question whether one graph (<jats:italic>source</jats:italic>) state can be transformed into another graph (<jats:italic>target</jats:italic>) state, using a specific set of quantum operations (LC + LPM + CC): single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. This question is of interest for effective routing or state preparation decisions in a quantum network or distributed quantum processor and also in the design of quantum repeater schemes and quantum error-correction codes. We first show that deciding whether a graph state |<jats:italic>G</jats:italic>⟩ can be transformed into another graph state |<jats:italic>G</jats:italic>′⟩ using LC + LPM + CC is <jats:inline-formula> <jats:tex-math><?CDATA $\mathbb{N}\mathbb{P}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="double-struck">N</mml:mi> <mml:mi mathvariant="double-struck">P</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstaba763ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>-complete, which was previously not known. We also show that the problem remains NP-complete even if |<jats:italic>G</jats:italic>′⟩ is restricted to be the GHZ-state. However, we also provide efficient algorithms for two situations of practical interest. Our results make use of the insight that deciding whether a graph state |<jats:italic>G</jats:italic>⟩ can be transformed to another graph state |<jats:italic>G</jats:italic>′⟩ is equivalent to a known decision problem in graph theory, namely the problem of deciding whether a graph <jats:italic>G</jats:italic>′ is a <jats:italic>vertex-minor</jats:italic> of a graph <jats:italic>G</jats:italic>. The computational complexity of the vertex-minor problem was prior to this paper an open question in graph theory. We prove that the vertex-minor problem is <jats:inline-formula> <jats:tex-math><?CDATA $\mathbb{N}\mathbb{P}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="double-struck">N</mml:mi> <mml:mi mathvariant="double-struck">P</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstaba763ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>-complete by relating it to a new decision problem on 4-regular graphs which we call the <jats:italic>semi-ordered Eulerian tour</jats:italic> problem.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>There is a growing interest in using cold-atom systems to explore the effects of strong interactions in topological band structures. Here we investigate interacting bosons in a Cruetz ladder, which is characterised by topological flat energy bands where it has been proposed that interactions can lead to the formation of bound atomic pairs giving rise to pair superfluidity. By investigating realistic experimental implementations, we understand how the lattice topology enhances the properties of bound pairs giving rise to relatively large effective pair-tunnelling in these systems which can lead to robust pair superfluidity, and we find lattice supersolid phases involving only pairs. We identify schemes for preparation of these phases via time-dependent parameter variation and look at ways to detect and characterise these systems in a lattice. This work provides a starting point for investigating the interplay between the effects of topology, interactions and pairing in more general systems, with potential future connections to quantum simulation of topological materials.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We propose a scheme to realize the active controlled dual-band unidirectional reflectionlessness at exceptional points by classical driving field in a non-Hermitian quantum system that consists of two Λ-type three-level quantum dots side coupled to a plasmonic waveguide. We demonstrate that the dual-band unidirectional reflectionlessness can be controlled by appropriately tuning classical driving field, phase shift between two quantum dots, dissipations of two quantum dots, and quantum dot-waveguide coupling strengths. Furthermore, the dual-band unidirectional reflectionlessness spectra with quality factors of ∼375.40 and ∼402.59 can be obtained in the forward and backward directions, respectively.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement <jats:italic>E</jats:italic> <jats:sub>R</jats:sub> is an outstanding quantity due to its clear geometric meaning, easy compatibility with different system sizes, and various applications in many other related quantity calculations. Lower bounds of <jats:italic>E</jats:italic> <jats:sub>R</jats:sub> were previously found based on distance to the set of positive partial transpose states. We propose a method to calculate upper bounds of <jats:italic>E</jats:italic> <jats:sub>R</jats:sub> based on active learning, a subfield in machine learning, to generate an approximation of the set of separable states. We apply our method to calculate <jats:italic>E</jats:italic> <jats:sub>R</jats:sub> for composite systems of various sizes, and compare with the previous known lower bounds, obtaining promising results. Our method adds a reliable tool for entanglement measure calculation and deepens our understanding for the structure of separable states.</jats:p>