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Abstract Although molecular vibronic spectra generation is pivotal for chemical analysis, tackling such exponentially complex tasks on classical computers remains inefficient. Quantum simulation, though theoretically promising, faces technological challenges in experimentally extracting vibronic spectra for molecules with multiple modes. Here, we propose a nontrivial algorithm to generate the vibronic spectra using states with zero displacements (squeezed vacuum states) coupled to a linear optical network, offering ease of experimental implementation. We also fabricate an integrated quantum photonic microprocessor chip as a versatile simulation platform containing 16 modes of single-mode squeezed vacuum states and a fully programmable interferometer network. Molecular vibronic spectra of formic acid and thymine under the Condon approximation are simulated using the quantum microprocessor chip with high reconstructed fidelity ( > 92%). Furthermore, vibronic spectra of naphthalene, phenanthrene, and benzene under the non-Condon approximation are also experimentally simulated. Such demonstrations could pave the way for solving complicated quantum chemistry problems involving vibronic spectra and computational tasks beyond the reach of classical computers.

Abstract Self-testing allows one to characterise quantum systems under minimal assumptions. However, existing schemes rely on quantum nonlocality and cannot be applied to systems that are not entangled. Here, we introduce a robust method that achieves self-testing of individual systems by taking advantage of contextuality. The scheme is based on the simplest contextuality witness for the simplest contextual quantum system—the Klyachko-Can-Binicioğlu-Shumovsky inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements as a function of the value of the witness under a pragmatic assumption on the measurements. We apply the method in an experiment on a single trapped 40Ca+ using randomly chosen measurements and perfect detection efficiency. Using the observed statistics, we obtain an experimental demonstration of self-testing of a single quantum system.

Abstract Recent years have witnessed significant progress in quantum communication and quantum internet with the emerging quantum photonic chips, whose characteristics of scalability, stability, and low cost, flourish and open up new possibilities in miniaturized footprints. Here, we provide an overview of the advances in quantum photonic chips for quantum communication, beginning with a summary of the prevalent photonic integrated fabrication platforms and key components for integrated quantum communication systems. We then discuss a range of quantum communication applications, such as quantum key distribution and quantum teleportation. Finally, the review culminates with a perspective on challenges towards high-performance chip-based quantum communication, as well as a glimpse into future opportunities for integrated quantum networks.

Abstract Quantum logic gates are backbones of quantum information processing (QIP), wherein the typical three-qubit Fredkin and Toffoli gates are essential in quantum computation and communication. So far, the quantum Fredkin gate has only been demonstrated with pre-entangled input states in free-space optics, which limits its usage for independent input photons. Here, we put forward an exquisite scheme and experimentally perform a proof-of-principle demonstration of three-qubit Fredkin and Toffoli gates on a programmable quantum photonic chip. Our scheme can also be used to realize a series of other two-qubit quantum gates. Our work sheds light on the merits of quantum photonic chip in implementing quantum logic gates, and paves the way for advanced quantum chip processors.

Abstract In this short review article, we aim to provide physicists not working within the quantum computing community a hopefully easy-to-read introduction to the state of the art in the field, with minimal mathematics involved. In particular, we focus on what is termed the Noisy Intermediate Scale Quantum era of quantum computing. We describe how this is increasingly seen to be a distinct phase in the development of quantum computers, heralding an era where we have quantum computers that are capable of doing certain quantum computations in a limited fashion, and subject to certain constraints and noise. We further discuss the prominent algorithms that are believed to hold the most potential for this era, and also describe the competing physical platforms on which to build a quantum computer that have seen the most success so far. We then talk about the applications that are most feasible in the near-term, and finish off with a short discussion on the state of the field. We hope that as non-experts read this article, it will give context to the recent developments in quantum computers that have garnered much popular press, and help the community understand how to place such developments in the timeline of quantum computing.

The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian without explicitly preparing its eigenstates. By means of numerical simulations we show that this approach finds many of the matrix elements for the one and two qubits cases. Specifically, while in the first case, one can initialize the ansatz parameters over a broad interval, in the latter the optimization landscape can significantly slow down the speed of convergence and one should therefore be careful to restrict the initialization to a smaller range of parameters.

Integrated photonics provides a versatile platform for encoding and processing quantum information. However, the encoded quantum states are sensitive to noise, which limits their capability to perform complicated quantum computations. Here, we use a five-qubit linear cluster state on a silicon photonic chip to implement a quantum error-correction code and demonstrate its capability of identifying and correcting a single-qubit error. The encoded quantum information is reconstructed from a single-qubit error and an average state fidelity of 0.863±0.032 is achieved for different input states. We further extend the scheme to demonstrate a fault-tolerant measurement-based quantum computation (MBQC) on stabilizer formalism that allows us to redo the qubit operation against the failure of the teleportation process. Our work provides a proof-of-concept working prototype of error correction and MBQC in an integrated photonic chip.

It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.

Abstract Quantum key distribution is a matured quantum science and technology. Over the last 20 years, there has been substantial research and development in this area. Recently, silicon technology has offered tremendous promise in the field for improved miniaturization of quantum key distribution through integrated photonic chips. We expect further progress in this area both in terms of protocols, photon sources, and photon detectors. This review captures some of the recent advances in this area.

Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose using classical and quantum Fisher information (FI) as alternative metrics to detect and measure quantum synchronization. We establish the connection between FI and quantum synchronization, demonstrating that both classical and quantum FI can be deployed as more general indicators of quantum phase synchronization in some regimes where all other existing measures fail to provide reliable results. We show advantages in FI-based measures, especially in 2-to-1 synchronization. Furthermore, we analyze the impact of noise on the synchronization measures, revealing the robustness and susceptibility of each method in the presence of dissipation and decoherence. Our results open up new avenues for understanding and exploiting quantum synchronization.

Existing low-temperature thermometers can only perform with high precision within a narrow range. Here, the authors provide a bound for global thermometry across a wide range, including the design of optimal thermometers with the state-of-the-art quantum technologies.

Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e., the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here, we study how to simulate such open quantum dynamics in a digital quantum computer, for which we use an IBM hardware. We consider in particular how accurate different implementations of the evolution result as a function of the level of noise in the hardware and of the parameters of the open dynamics. For the regimes studied, we show that the key aspect is to simulate the unitary portion of the dynamics, while the dissipative part can lead to a more noise-resistant simulation. We consider both a single spin coupled to a harmonic oscillator, and also two spins coupled to the oscillator. In the latter case, we show that it is possible to simulate the emergence of correlations between the spins via the oscillator.

Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set B_{Q} of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, B_{Q} is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that B_{Q} is strictly contained in an easy-to-characterize set associated with a graph, Θ(G). Therefore, whenever the optimum over B_{Q} and the optimum over Θ(G) coincide, self-testing can be demonstrated by simply proving self-testability with Θ(G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araújo et al., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovász theta number for a family of graphs called the Möbius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1), this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.

Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our algorithm does not have any classical-quantum feedback loop and bypasses the barren plateau problem by construction. The classical part in our hybrid quantum-classical algorithm corresponds to a quadratically constrained quadratic program (QCQP) with a single quadratic equality constraint, which admits a semidefinite relaxation. The QCQP based classical optimization was recently introduced as the classical step in quantum assisted eigensolver (QAE), a NISQ algorithm for the Hamiltonian ground state problem. Thus, our work provides a conceptual unification between the NISQ algorithms for the Hamiltonian ground state problem and the Hamiltonian simulation. We recover differential equation-based NISQ algorithms for Hamiltonian simulation such as quantum assisted simulator (QAS) and variational quantum simulator (VQS) as particular cases of our algorithm. We test our algorithm on some toy examples on current cloud quantum computers. We also provide a systematic approach to improve the accuracy of our algorithm.

We study the persistent current in a system of SU($N$) fermions with repulsive interaction confined in a ring-shaped potential and pierced by an effective magnetic flux. By applying a combination of Bethe ansatz and numerical analysis, we demonstrate that, as a combined effect of spin correlations, interactions and applied flux a specific phenomenon can occur in the system: spinon creation in the ground state. As a consequence, peculiar features in the persistent current arise. The elementary flux quantum, which fixes the persistent current periodicity, is observed to evolve from a single particle one to an extreme case of fractional flux quantum, in which one quantum is shared by all the particles. We show that the persistent current depends on the number of spin components $N$, number of particles and interaction in a specific way that in certain physical regimes has universality traits. At integer filling fractions, the persistent current is suppressed above a threshold of the repulsive interaction by the Mott spectral gap. Despite its mesoscopic nature, the current displays a clear finite size scaling behavior. Specific parity effects in the persistent current landscape hold.

We study a Rabi type Hamiltonian system in which a qubit and a d-level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is found to be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppresses the bipartite entanglement. We analyze the system dynamics under quenching and adiabatic switching of the qubit-resonator and qudit-resonator couplings. In the quench case, we found that the non-adiabatic generation of photons in the resonator is enhanced by the number of levels in the qudit. The adiabatic control represents a possible route for preparation of GHZ states. Our analysis provides relevant information for future studies on coherent state transfer in qubit-qudit systems.

The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Recently it was shown [A. Coladangelo, K. T. Goh, and V. Scarani, Nat. Commun. 8, 15485 (2017)10.1038/ncomms15485] that all pure bipartite entangled states can be self-tested in the device-independent scenario by employing subspace methods introduced by Yang and Navascués [Phys. Rev. A 87, 050102(R) (2013)10.1103/PhysRevA.87.050102]. Here, we have adapted their method to show that any bipartite pure entangled state can be certified in the semi-device-independent scenario through quantum steering. Analogous to the tilted Clauser-Horne-Shimony-Holt inequality, we use a steering inequality called the tilted steering inequality for certifying any pure two-qubit entangled state. Furthermore, we use this inequality to certify any bipartite pure entangled state by certifying two-dimensional subspaces of the qudit state by observing the structure of the set of assemblages obtained on the trusted side after measurements are made on the untrusted side. As a feature of quantum state certification via steering, we use the notion of assemblage-based robust state certification to provide robustness bounds for the certification result in the case of pure maximally entangled states of any local dimension.

A fundamental problem in quantum computation and quantum information is finding the minimum quantum dimension needed for a task. For tasks involving state preparation and measurements, this problem can be addressed using only the input–output correlations. This has been applied to Bell, prepare-and-measure, and Kochen–Specker contextuality scenarios. Here, we introduce a novel approach to quantum dimension witnessing for scenarios with one preparation and several measurements, which uses the graphs of mutual exclusivity between sets of measurement events. We present the concepts and tools needed for graph-theoretic quantum dimension witnessing and illustrate their use by identifying novel quantum dimension witnesses, including a family that can certify arbitrarily high quantum dimensions with few events.

The design, accurate preparation, and manipulation of quantum states in quantum circuits are essential operational tasks at the heart of quantum technologies. Nowadays, circuits can be designed with physical parameters that can be controlled with unprecedented accuracy and flexibility. However, the generation of well-controlled current states is still a nagging bottleneck, especially when different circuit elements are integrated together. In this work, we show how machine learning can effectively address this challenge and outperform the current existing methods. To this end, we exploit deep reinforcement learning to prepare prescribed quantum current states in circuits composed of lumped elements. To highlight our method, we show how to engineer bosonic persistent currents as they are relevant in different quantum technologies as cold atoms and superconducting circuits. We demonstrate the use of deep reinforcement learning to rediscover established protocols, as well as solving configurations that are difficult to treat with other methods. With our approach, quantum current states characterized by a single winding number or entangled currents of multiple winding numbers can be prepared in a robust manner, superseding the existing protocols.

We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure allows us to discuss synchronization of disparate physical systems such as coupled hybrid quantum systems and coupled systems undergoing mutual synchronization that are also driven locally. In many cases of interest, we find a closed-form expression for the proposed measure.

Contextuality is one way of capturing the nonclassicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of noncontextuality inequalities—certain linear inequalities involving probabilities of measurement events. Using the exclusivity graph approach (one of the two main graph theoretic approaches for studying contextuality), it was shown [Cabello et al. Phys. Rev. A 88, 032104 (2013)10.1103/PhysRevA.88.032104; Chudnovsky et al. Ann. Math. 164, 51 (2006)10.4007/annals.2006.164.51] that a necessary and sufficient condition for witnessing contextuality is the presence of an odd number of events (greater than three) which are either cyclically or anticyclically exclusive. Thus, the noncontextuality inequalities the underlying exclusivity structure of which is as stated, either cyclic or anticyclic, are fundamental to quantum theory. We show that there is a unique noncontextuality inequality for each nontrivial cycle and anticycle. In addition to the foundational interest, we expect this to aid the understanding of contextuality as a resource to quantum computing and its applications to local self-testing.

Quantum networks provide a prominent platform for realizing quantum information processing and quantum communication, with entanglement being a key resource in such applications. Here we describe the dissipative transport protocol for entangled states, where entanglement stored in the first node of a quantum network can be transported with high fidelity to the second node via a one-dimensional chiral waveguide. In particular, we exploit the directional asymmetry in chirally coupled single-mode ring resonators to transport entangled states. For the fully chiral waveguide, Bell states, multipartite W states, and and Dicke states can be transported with fidelity as high as 0.954, despite the fact that the communication channel is noisy. Our proposal can be utilized for the long-distance distribution of multipartite entangled states between the quantum nodes of an open quantum network.