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<jats:title>Abstract</jats:title> <jats:p>We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any classical–quantum feedback loop, bypass the barren plateau problem and does not necessitate any complicated measurements such as the Hadamard test. We introduce the notion of the hybrid density matrix, which allows us to disentangle the different steps of our algorithm and delegate classically demanding tasks to the quantum computer. Our algorithm proceeds in three disjoint steps. First, we select the ansatz, followed by measuring overlap matrices on a quantum computer. The final step involves classical post-processing data from the second step. Our algorithm has potential applications in solving the Navier–Stokes equation, plasma hydrodynamics, quantum Boltzmann training, quantum signal processing and linear systems. Our entire framework is compatible with current experiments and can be implemented immediately.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We present a robust protocol for implementing high-fidelity multiqubit controlled phase gates (<jats:italic>C</jats:italic> <jats:sup> <jats:italic>k</jats:italic> </jats:sup> <jats:italic>Z</jats:italic>) on neutral atom qubits coupled to highly excited Rydberg states. Our approach is based on extending adiabatic rapid passage to two-photon excitation via a short-lived intermediate excited state common to alkali-atom Rydberg experiments, accounting for the full impact of spontaneous decay and differential AC Stark shifts from the complete manifold of hyperfine excited states. We evaluate and optimise gate performance, concluding that for Cs and currently available laser frequencies and powers, a <jats:italic>CCZ</jats:italic> gate with fidelity <jats:inline-formula> <jats:tex-math><?CDATA $\mathcal{F} > 0.995$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">F</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0.995</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac823aieqn1.gif" xlink:type="simple" /> </jats:inline-formula> for three qubits and <jats:italic>CCCZ</jats:italic> with <jats:inline-formula> <jats:tex-math><?CDATA $\mathcal{F} > 0.99$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">F</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0.99</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac823aieqn2.gif" xlink:type="simple" /> </jats:inline-formula> for four qubits is attainable in <jats:inline-formula> <jats:tex-math><?CDATA $\sim 1.8$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>∼</mml:mo> <mml:mn>1.8</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="qstac823aieqn3.gif" xlink:type="simple" /> </jats:inline-formula> <jats:italic>μ</jats:italic>s via this protocol. Higher fidelities are accessible with future technologies, and our results highlight the utility of neutral atom arrays for the native implementation of multiqubit unitaries.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Optical downconversion is a key resource for generating nonclassical states. Very recently, direct nondegenerate triple-photon spontaneous downconversion (NTPSD) with bright photon triplets and strong third-order correlations has been demonstrated in a superconducting device (2020 <jats:italic>Phys. Rev.</jats:italic> X <jats:bold>10</jats:bold> 011011). Besides, linear and nonlinear tripartite entanglement in this process have also been predicted (2018 <jats:italic>Phys. Rev. Lett</jats:italic>. <jats:bold>120</jats:bold> 043601; 2020 <jats:italic>Phys. Rev. Lett.</jats:italic> <jats:bold>125</jats:bold> 020502). In this paper, we consider the generation of nonclassical optical quantum superpositions and investigate nonlinear quantum steering effects in NTPSD. We find that large-size Schrödinger cat states of one downconverted mode can be achieved when the other two modes are subjected to homodyne detection. Also, a two-photon Bell entangled state can be generated when only one mode is homodyned. We further reveal that such ability of remote state steering originates from nonlinear quantum steerable correlations among the triplets. This is specifically embodied by the seeming violation of the Heisenberg uncertainty relation for the inferred variances of two noncommutating higher-order quadratures of downconverted modes, based on the outcomes of homodyne detection on the other mode, i.e., nonlinear quantum steering, compared to original Einstein–Podolsky–Rosen steering. Our results demonstrate non-Gaussian nonclassical features in NTPSD and would be useful for the fundamental tests of quantum physics and implementations of optical quantum technologies.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Entanglement is a universal resource in quantum networks, yet entangled photon sources are typically custom-made for a specific use case. Versatility, both in terms of state modulation and tunability of the temporal properties of the photons, is the key to flexible network architectures and cryptographic primitives that go beyond quantum key distribution. Here, we report on a flexible source design that produces high-quality entanglement in continuous-wave and GHz-rate-pulsed operation modes. Utilizing off-the-shelf optical components, our approach uses a fiber-based Sagnac loop to generate polarization-entangled photons at telecom wavelength with high efficiency and fidelities above 0.99. Phase modulation up to GHz before entangled state generation is also possible for fast entangled state switching. We show phase modulation at 100 MHz with an average fidelity of 0.95. Furthermore, the source 60 nm spectral bandwidth is entirely compatible with fully reconfigurable wavelength-multiplexed quantum networks.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Quantum architecture search (QAS) is the process of automating architecture engineering of quantum circuits. It has been desired to construct a powerful and general QAS platform which can significantly accelerate current efforts to identify quantum advantages of error-prone and depth-limited quantum circuits in the NISQ era. Hereby, we propose a general framework of differentiable quantum architecture search (DQAS), which enables automated designs of quantum circuits in an end-to-end differentiable fashion. We present several examples of circuit design problems to demonstrate the power of DQAS. For instance, unitary operations are decomposed into quantum gates, noisy circuits are re-designed to improve accuracy, and circuit layouts for quantum approximation optimization algorithm are automatically discovered and upgraded for combinatorial optimization problems. These results not only manifest the vast potential of DQAS being an essential tool for the NISQ application developments, but also present an interesting research topic from the theoretical perspective as it draws inspirations from the newly emerging interdisciplinary paradigms of differentiable programming, probabilistic programming, and quantum programming.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate the issue of assisted coherence distillation in the asymptotic limit, by coordinately performing the identical local operations on the auxiliary systems of each copy. When we further restrict the coordinate operations to projective measurements, the distillation process branches into many sub-processes. Finally, a computable measure of the assisted distillable coherence is derived as the maximal average coherence of the residual states with the maximization taken over all the projective measurements on the auxiliary. The measure can be conveniently used to evaluate the assisted distillable coherence in experiments, especially suitable for the case that the system and its auxiliary are in mixed states. By using the measure, we for the first time study the assisted coherence distillation in multipartite systems. Monogamy-like inequalities are derived to constrain the distribution of the assisted distillable coherence in the subsystems. Taking a three-qubit system for example, we experimentally prepare two types of tripartite correlated states, i.e., the <jats:italic>W</jats:italic>-type and GHZ-type states in a linear optical setup, and experimentally test the assisted distillable coherence. Theoretical and experimental results agree well to verify the distribution inequalities given by us. Three measures of multipartite quantum correlation are also considered. The close relationship between the assisted coherence distillation and the multipartite correlation is revealed.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The rapid development in hardware for quantum computing and simulation has led to much interest in problems where these devices can exceed the capabilities of existing classical computers and known methods. Approaching this for problems that go beyond testing the performance of a quantum device is an important step, and quantum simulation of many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum simulators with neutral atoms in optical lattices and trapped ions. Considering the primary sources of error in analogue devices and how they propagate after a quench in studies of the Hubbard or long-range transverse field Ising model, we identify the level of error expected in quantities we extract from experiments. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators. We also identify the hardware requirements to reach the same level of accuracy with future fault-tolerant digital quantum simulation. Verification techniques are already available to test the assumptions we make here, and demonstrating these in experiments will be an important next step.</jats:p>