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In many natural and engineered systems, unknown quantum channels act on a subsystem that cannot be directly controlled and measured, but is instead learned through a controllable subsystem that weakly interacts with it. We study quantum channel discrimination (QCD) under these restrictions, which we call hidden system QCD. We find sequential protocols achieve perfect discrimination and saturate the Heisenberg limit. In contrast, depth-1 parallel and multishot protocols cannot solve hidden system QCD. This suggests sequential protocols are superior in experimentally realistic situations.

Classifying many-body quantum states with distinct properties and phases of matter is one of the most fundamental tasks in quantum many-body physics. However, due to the exponential complexity that emerges from the enormous numbers of interacting particles, classifying large-scale quantum states has been extremely challenging for classical approaches. Here, we propose a new approach called quantum neuronal sensing. Utilizing a 61-qubit superconducting quantum processor, we show that our scheme can efficiently classify two different types of many-body phenomena: namely the ergodic and localized phases of matter. Our quantum neuronal sensing process allows us to extract the necessary information coming from the statistical characteristics of the eigenspectrum to distinguish these phases of matter by measuring only one qubit and offers better phase resolution than conventional methods, such as measuring the imbalance. Our work demonstrates the feasibility and scalability of quantum neuronal sensing for near-term quantum processors and opens new avenues for exploring quantum many-body phenomena in larger-scale systems., (Copyright © 2023 Science China Press. Published by Elsevier B.V. All rights reserved.)

The Unruh effect can not only arise out of the entanglement between modes of left and right Rindler wedges, but also between modes of future and past light cones. We explore the geometric phase resulting from this timelike entanglement between the future and past, showing that it can be captured in a simple Λ system. This provides an alternative paradigm to the Unruh-deWitt detector. The Unruh effect has not been experimentally verified because the accelerations needed to excite a response from Unruh-deWitt detectors are prohibitively large. We demonstrate that a stationary but time-dependent Λ-system detects the timelike Unruh effect with current technology.

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that nontransverse operations, which are essential for universal quantum computation, lead to the spread of errors. Quantum gate teleportation has been proposed as an elegant solution for this. Here, one replaces these fragile, nontransverse inline gates with the generation of specific, highly entangled offline resource states that can be teleported into the circuit to implement the nontransverse gate. As the first important step, we create a maximally entangled state between a physical and an error-correctable logical qubit and use it as a teleportation resource. We then demonstrate the teleportation of quantum information encoded on the physical qubit into the error-corrected logical qubit with fidelities up to 0.786. Our scheme can be designed to be fully fault tolerant so that it can be used in future large-scale quantum technologies., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

Quantum walks are the quantum mechanical analog of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and fabricated an 8-by-8 two-dimensional square superconducting qubit array composed of 62 functional qubits. We used this device to demonstrate high-fidelity single- and two-particle quantum walks. Furthermore, with the high programmability of the quantum processor, we implemented a Mach-Zehnder interferometer where the quantum walker coherently traverses in two paths before interfering and exiting. By tuning the disorders on the evolution paths, we observed interference fringes with single and double walkers. Our work is a milestone in the field, bringing future larger-scale quantum applications closer to realization for noisy intermediate-scale quantum processors., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of matter appear in a variety of quantum technology applications. Such symmetries are normally broken in spatial dimension, however, they can also be broken temporally leading to the concept of discrete time symmetries and their associated crystals. Discrete time crystals (DTCs) are a novel state of matter emerging in periodically driven quantum systems. Typically, they have been investigated assuming individual control operations with uniform rotation errors across the entire system. In this work we explore a new paradigm arising from nonuniform rotation errors, where two dramatically different phases of matter coexist in well defined regions of space. We consider a quantum spin network possessing long-range interactions where different driving operations act on different regions of that network. What results from its inherent symmetries is a system where one region is a DTC, while the second is ferromagnetic. We envision our work to open a new avenue of research on chimeralike phases of matter where two different phases coexist in space.

Quantum random numbers distinguish themselves from others by their intrinsic unpredictability arising from the principles of quantum mechanics. As such they are extremely useful in many scientific and real-world applications with considerable efforts going into their realizations. Most demonstrations focus on high asymptotic generation rates. For this goal, a large number of repeated trials are required to accumulate a significant store of certifiable randomness, resulting in a high latency between the initial request and the delivery of the requested random bits. Here we demonstrate low-latency real-time certifiable randomness generation from measurements on photonic time-bin states. For this, we develop methods to certify randomness taking into account adversarial imperfections in both the state preparation and the measurement apparatus. Every 0.12 s we generate a block of 8192 random bits which are certifiable against all quantum adversaries with an error bounded by 2 -64 . Our quantum random number generator is thus well suited for realizing a continuously-operating, high-security and high-speed quantum randomness beacon.

Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate 5.47×10^{8} quantum-proof random bits while consuming 4.39×10^{8}  bits of entropy, expanding our store of randomness by 1.08×10^{8}  bits at a latency of about 13.1 h, with a total soundness error 4.6×10^{-10}. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.

We report the analog simulation of an ergodic-localized junction by using an array of 12 coupled superconducting qubits. To perform the simulation, we fabricated a superconducting quantum processor that is divided into two domains: one is a driven domain representing an ergodic system, while the second is localized under the effect of disorder. Because of the overlap between localized and delocalized states, for a small disorder there is a proximity effect and localization is destroyed. To experimentally investigate this, we prepare a microwave excitation in the driven domain and explore how deep it can penetrate the disordered region by probing its dynamics. Furthermore, we perform an ensemble average over 50 realizations of disorder, which clearly shows the proximity effect. Our work opens a new avenue to build quantum simulators of driven-disordered systems with applications in condensed matter physics and material science.

Crystals arise as the result of the breaking of a spatial translation symmetry. Similarly, translation symmetries can also be broken in time so that discrete time crystals appear. Here, we introduce a method to describe, characterize, and explore the physical phenomena related to this phase of matter using tools from graph theory. The analysis of the graphs allows to visualizing time-crystalline order and to analyze features of the quantum system. For example, we explore in detail the melting process of a minimal model of a period-2 discrete time crystal and describe it in terms of the evolution of the associated graph structure. We show that during the melting process, the network evolution exhibits an emergent preferential attachment mechanism, directly associated with the existence of scale-free networks. Thus, our strategy allows us to propose a previously unexplored far-reaching application of time crystals as a quantum simulator of complex quantum networks., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

Distributed quantum information processing is based on the transmission of quantum data over lossy channels between quantum processing nodes. These nodes may be separated by a few microns or on planetary scale distances, but transmission losses due to absorption and/or scattering in the channel are the major source of error for most distributed quantum information tasks. Of course, quantum error correction (QEC) and detection techniques can be used to mitigate such effects, but error detection approaches have severe performance limitations due to the signaling constraints between nodes, and so error correction approaches are preferable-assuming one has sufficient high quality local operations. Typically, performance comparisons between loss-mitigating codes assume one encoded qubit per photon. However, single photons can carry more than one qubit of information and so our focus in this Letter is to explore whether loss-based QEC codes utilizing quantum multiplexed photons are viable and advantageous, especially as photon loss results in more than one qubit of information being lost. We show that quantum multiplexing enables significant resource reduction, in terms of the number of single-photon sources, while at the same time maintaining (or even lowering) the number of 2-qubit gates required. Further, our multiplexing approach requires only conventional optical gates already necessary for the implementation of these codes.

Entanglement witnesses are operators that are crucial for confirming the generation of specific quantum systems, such as multipartite and high-dimensional states. For this reason, many witnesses have been theoretically derived which commonly focus on establishing tight bounds and exhibit mathematical compactness as well as symmetry properties similar to that of the quantum state. However, for increasingly complex quantum systems, established witnesses have lacked experimental achievability, as it has become progressively more challenging to design the corresponding experiments. Here, we present a universal approach to derive entanglement witnesses that are capable of detecting the presence of any targeted complex pure quantum system and that can be customized towards experimental restrictions or accessible measurement settings. Using this technique, we derive experimentally optimized witnesses that are able to detect multipartite d-level cluster states, and that require only two measurement settings. We present explicit examples for customizing the witness operators given different realistic experimental restrictions, including witnesses for high-dimensional entanglement that use only two-dimensional projection measurements. Our work enables us to confirm the presence of probed quantum states using methods that are compatible with practical experimental realizations in different quantum platforms.

Randomness is important for many information processing applications, including numerical modelling and cryptography 1,2 . Device-independent quantum random-number generation (DIQRNG) 3,4 based on the loophole-free violation of a Bell inequality produces genuine, unpredictable randomness without requiring any assumptions about the inner workings of the devices, and is therefore an ultimate goal in the field of quantum information science 5-7 . Previously reported experimental demonstrations of DIQRNG 8,9 were not provably secure against the most general adversaries or did not close the 'locality' loophole of the Bell test. Here we present DIQRNG that is secure against quantum and classical adversaries 10-12 . We use state-of-the-art quantum optical technology to create, modulate and detect entangled photon pairs, achieving an efficiency of more than 78 per cent from creation to detection at a distance of about 200 metres that greatly exceeds the threshold for closing the 'detection' loophole of the Bell test. By independently and randomly choosing the base settings for measuring the entangled photon pairs and by ensuring space-like separation between the measurement events, we also satisfy the no-signalling condition and close the 'locality' loophole of the Bell test, thus enabling the realization of the loophole-free violation of a Bell inequality. This, along with a high-voltage, high-repetition-rate Pockels cell modulation set-up, allows us to accumulate sufficient data in the experimental time to extract genuine quantum randomness that is secure against the most general adversaries. By applying a large (137.90 gigabits × 62.469 megabits) Toeplitz-matrix hashing technique, we obtain 6.2469 × 10 7 quantum-certified random bits in 96 hours with a total failure probability (of producing a random number that is not guaranteed to be perfectly secure) of less than 10 -5 . Our demonstration is a crucial step towards transforming DIQRNG from a concept to a key aspect of practical applications that require high levels of security and thus genuine randomness 7 . Our work may also help to improve our understanding of the origin of randomness from a fundamental perspective.

Inspired by the recent remarkable progress in the experimental test of local realism, we report here such a test that achieves an efficiency greater than (78%)^{2} for entangled photon pairs separated by 183 m. Further utilizing the randomness in cosmic photons from pairs of stars on the opposite sides of the sky for the measurement setting choices, we not only close the locality and detection loopholes simultaneously, but also test the null hypothesis against local hidden variable mechanisms for events that took place 11 years ago (13 orders of magnitude longer than previous experiments). After considering the bias in measurement setting choices, we obtain an upper bound on the p value of 7.87×10^{-4}, which clearly indicates the rejection with high confidence of potential local hidden variable models. One may further push the time constraint on local hidden variable mechanisms deep into the cosmic history by taking advantage of the randomness in photon emissions from quasars with large aperture telescopes.

Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields scales inversely with the square root of the measurement time T. On the other hand, by using quantum resources, we can reduce this scaling of the uncertainty with time to 1/T. However, as quantum states are susceptible to dephasing, it has not been clear whether we can achieve sensitivities with a scaling of 1/T for a measurement time longer than the coherence time. Here, we propose a scheme that estimates the amplitude of globally applied fields with the uncertainty of 1/T for an arbitrary time scale under the effect of dephasing. We use one-way quantum-computing-based teleportation between qubits to prevent any increase in the correlation between the quantum state and its local environment from building up and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our method has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensor.

This corrects the article DOI: 10.1038/ncomms4524.

The engineering of quantum systems and their environments has led to our ability now to design composite or complex systems with the properties one desires. In fact, this allows us to couple two or more distinct systems to the same environment where potentially unusual behavior and dynamics can be exhibited. In this Letter we investigate the relaxation of two giant spins or collective spin ensembles individually coupled to the same reservoir. We find that, depending on the configuration of the two individual spin ensembles, the steady state of the composite system does not necessarily reach the ground state of the individual systems, unlike what one would expect for independent environments. Further, when the size of one individual spin ensemble is much larger than the second, collective relaxation can drive the second system to an excited steady state even when it starts in the ground state; that is, the second spin ensemble relaxes towards a negative-temperature steady state.

Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last 50 years. Recently, the ability to engineer quantum metamaterials through hybridization has allowed us to explore these nonlinear effects in systems with no natural analog. We investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogen-vacancy centers. One of the exciting properties of this spin system is its long spin lifetime, which is many orders of magnitude longer than other relevant time scales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds-a time scale much longer than observed so far for this effect. Our results provide a foundation for future quantum technologies based on nonlinear phenomena.

Quantum information systems are expected to exhibit superiority compared with their classical counterparts. This superiority arises from the quantum coherences present in these quantum systems, which are obviously absent in classical ones. To exploit such quantum coherences, it is essential to control the phase information in the quantum state. The phase is analogue in nature, rather than binary. This makes quantum information technology fundamentally different from our classical digital information technology. In this paper, we analyse error sources and illustrate how these errors must be managed for the system to achieve the required fidelity and a quantum superiority.This article is part of the themed issue 'Quantum technology for the 21st century'., (© 2017 The Author(s).)

The hybridization of distinct quantum systems is now seen as an effective way to engineer the properties of an entire system leading to applications in quantum metamaterials, quantum simulation, and quantum metrology. Recent improvements in both fabrication techniques and qubit design have allowed the community to consider coupling large ensembles of artificial atoms, such as superconducting qubits, to a resonator. Here, we demonstrate the coherent coupling between a microwave resonator and a macroscopic ensemble composed of several thousand superconducting flux qubits, where we observe a large dispersive frequency shift in the spectrum of 250 MHz. We achieve the large dispersive shift with a collective enhancement of the coupling strength between the resonator and qubits. These results represent the largest number of coupled superconducting qubits realized so far.

Macroscopic realism is the name for a class of modifications to quantum theory that allow macroscopic objects to be described in a measurement-independent manner, while largely preserving a fully quantum mechanical description of the microscopic world. Objective collapse theories are examples which aim to solve the quantum measurement problem through modified dynamical laws. Whether such theories describe nature, however, is not known. Here we describe and implement an experimental protocol capable of constraining theories of this class, that is more noise tolerant and conceptually transparent than the original Leggett-Garg test. We implement the protocol in a superconducting flux qubit, and rule out (by ∼84 s.d.) those theories which would deny coherent superpositions of 170 nA currents over a ∼10 ns timescale. Further, we address the 'clumsiness loophole' by determining classical disturbance with control experiments. Our results constitute strong evidence for the superposition of states of nontrivial macroscopic distinctness.

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size.

Optically detected magnetic resonance (ODMR) is a way to characterize the ensemble of NV - centers. Recently, a remarkably sharp dip was observed in the ODMR with a high-density ensemble of NV centers. The model (Zhu et al 2014 Nat. Commun. 5 3424) indicated that such a dip was due to the spin-1 properties of the NV - centers. Here, we present many more details of the analysis to show how this model can be applied to investigate the properties of the NV - centers. By using our model, we have reproduced the ODMR with and without applied external magnetic fields. Additionally, we investigate how the ODMR is affected by the typical parameters of the ensemble NV - centers such as strain distributions, inhomogeneous magnetic fields, and homogeneous broadening width. Our model provides a way to characterize the NV - center from the ODMR, which would be crucial to realize diamond-based quantum information processing.

In this article we present a simple repeater scheme based on the negatively-charged nitrogen vacancy centre in diamond. Each repeater node is built from modules comprising an optical cavity containing a single NV(-), with one nuclear spin from (15)N as quantum memory. The module uses only deterministic processes and interactions to achieve high fidelity operations (>99%), and modules are connected by optical fiber. In the repeater node architecture, the processes between modules by photons can be in principle deterministic, however current limitations on optical components lead the processes to be probabilistic but heralded. Our resource-modest repeater architecture contains two modules at each node, and the repeater nodes are then connected by entangled photon pairs. We discuss the performance of such a quantum repeater network with modest resources and then incorporate more resource-intense strategies step by step. Our architecture should allow large-scale quantum information networks with existing or near future technology.

Recent field demonstrations of quantum key distribution (QKD) networks hold promise for unconditionally secure communication. However, owing to loss in optical fibres, the length of point-to-point links is limited to a hundred kilometers, restricting the QKD networks to intracity. A natural way to expand the QKD network in a secure manner is to connect it to another one in a different city with quantum repeaters. But, this solution is overengineered unless such a backbone connection is intercontinental. Here we present a QKD protocol that could supersede even quantum repeaters for connecting QKD networks in different cities below 800 km distant. Nonetheless, in contrast to quantum repeaters, this protocol uses only a single intermediate node with optical devices, requiring neither quantum memories nor quantum error correction. Our all-photonic 'intercity' QKD protocol bridges large gaps between the conventional intracity QKD networks and the future intercontinental quantum repeaters, conceptually and technologically.

Recently, there have been significant developments in entanglement-based quantum metrology. However, entanglement is fragile against experimental imperfections, and quantum sensing to beat the standard quantum limit in scaling has not yet been achieved in realistic systems. Here, we show that it is possible to overcome such restrictions so that one can sense a magnetic field with an accuracy beyond the standard quantum limit even under the effect of decoherence, by using a realistic entangled state that can be easily created even with current technology. Our scheme could pave the way for the realizations of practical entanglement-based magnetic field sensors.

A hybrid system that combines the advantages of a superconductor flux qubit and an electron spin ensemble in diamond is one of the promising devices to realize quantum information processing. Exploring the properties of the superconductor diamond system is essential for the efficient use of this device. When we perform spectroscopy of this system, significant power broadening is observed. However, previous models to describe this system are known to be applicable only when the power broadening is negligible. Here, we construct a new approach to analyze this system with strong driving, and succeed in reproducing the spectrum with the power broadening. Our results provide an efficient way to analyze this hybrid system.

In this Letter, we propose a counterintuitive use of a hybrid system where the coherence time of a quantum system can be significantly improved by coupling it with a system of a shorter coherence time. Coupling a two-level system with a single nitrogen-vacancy (NV^{-}) center, a dark state of the NV^{-} center naturally forms after the hybridization. We show that this dark state becomes robust against noise due to the coupling even when the coherence time of the two-level system is much shorter than that of the NV^{-} center. Our proposal opens a new way to use a quantum hybrid system for the realization of robust quantum information processing.

We demonstrate the generation and demultiplexing of quantum correlated photons on a monolithic photonic chip composed of silicon and silica-based waveguides. Photon pairs generated in a nonlinear silicon waveguide are successfully separated into two optical channels of an arrayed-waveguide grating fabricated on a silica-based waveguide platform.

The hybridization of distinct quantum systems has opened new avenues to exploit the best properties of these individual systems. Superconducting circuits and electron spin ensembles are one such example. Strong coupling and the coherent transfer and storage of quantum information has been achieved with nitrogen vacancy centres in diamond. Recently, we have observed a remarkably sharp resonance (~1 MHz) at 2.878 GHz in the spectrum of flux qubit negatively charged nitrogen vacancy diamond hybrid quantum system under zero external magnetic field. This width is much narrower than that of both the flux qubit and spin ensemble. Here we show that this resonance is evidence of a collective dark state in the ensemble, which is coherently driven by the superposition of clockwise and counter-clockwise macroscopic persistent supercurrents flowing in the flux qubit. The collective dark state is a unique physical system and could provide a long-lived quantum memory.

We have built a hybrid system composed of a superconducting flux qubit (the processor) and an ensemble of nitrogen-vacancy centers in diamond (the memory) that can be directly coupled to one another, and demonstrated how information can be transferred from the flux qubit to the memory, stored, and subsequently retrieved. We have established the coherence properties of the memory and succeeded in creating an entangled state between the processor and memory, demonstrating how the entangled state's coherence is preserved. Our results are a significant step towards using an electron spin ensemble as a quantum memory for superconducting qubits.