Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.

One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc., in order to accelerate the process of discovery. It is important to ask the following question: Can this simulation be achieved using near-future quantum processors, of modest size and under imperfect control, or must it await the more distant era of large-scale fault-tolerant quantum computing? Here, we propose a variational method involving closely integrated classical and quantum coprocessors. We presume that all operations in the quantum coprocessor are prone to error. The impact of such errors is minimized by boosting them artificially and then extrapolating to the zero-error case. In comparison to a more conventional optimized Trotterization technique, we find that our protocol is efficient and appears to be fundamentally more robust against error accumulation.

The divacancies in SiC are a family of paramagnetic defects that show promise for quantum communication technologies due to their long-lived electron spin coherence and their optical addressability at near-telecom wavelengths. Nonetheless, a high-fidelity spin-photon interface, which is a crucial prerequisite for such technologies, has not yet been demonstrated. Here, we demonstrate that such an interface exists in isolated divacancies in epitaxial films of 3C-SiC and 4H-SiC. Our data show that divacancies in 4H-SiC have minimal undesirable spin mixing, and that the optical linewidths in our current sample are already similar to those of recent remote entanglement demonstrations in other systems. Moreover, we find that 3C-SiC divacancies have a millisecond Hahn-echo spin coherence time, which is among the longest measured in a naturally isotopic solid. The presence of defects with these properties in a commercial semiconductor that can be heteroepitaxially grown as a thin film on Si shows promise for future quantum networks based on SiC defects.

Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite states continues to be a great challenge both from the theoretical and the experimental point of view. Most of the known methods either have computational costs that scale inefficiently with the number of particles or require more information on the state than what is attainable in everyday experiments. We introduce a new technique for entanglement detection that provides several important advantages in these respects. First, it scales efficiently with the number of particles, thus allowing for application to systems composed by up to few tens of particles. Second, it needs only the knowledge of a subset of all possible measurements on the state, therefore being apt for experimental implementation. Moreover, since it is based on the detection of nonlocality, our method is device independent. We report several examples of its implementation for well-known multipartite states, showing that the introduced technique has a promising range of applications.

Trapped Rydberg ions are a promising new system for quantum information processing. They have the potential to join the precise quantum operations of trapped ions and the strong, long-range interactions between Rydberg atoms. Combining the two systems is not at all straightforward. Rydberg atoms are severely affected by electric fields which may cause Stark shifts and field ionization, while electric fields are used to trap ions. Thus, a thorough understanding of the physical properties of Rydberg ions due to the trapping electric fields is essential for future applications. Here, we report the observation of two fundamental trap effects. First, we investigate the interaction of the Rydberg electron with the trapping electric quadrupole fields which leads to Floquet sidebands in the excitation spectra. Second, we report on the modified trapping potential in the Rydberg state compared to the ground state that results from the strong polarizability of the Rydberg ion. By controlling both effects we observe resonance lines close to their natural linewidth demonstrating an unprecedented level of control of this novel quantum platform.

The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes, and even by braiding engineered Majorana modes using twist defects. Here, we present a unified framework to describe these methods, which can be used to better compare different schemes and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyze ways in which different schemes can be combined and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code, without loss of distance, using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.

Quantum correlations between long-lived quantum memories and telecom photons that can propagate with low loss in optical fibers are an essential resource for the realization of large-scale quantum information networks. Significant progress has been realized in this direction with atomic and solid-state systems. Here, we demonstrate quantum correlations between a telecom photon and a multimode on-demand solid state quantum memory. This is achieved by mapping a correlated single photon onto a spin collective excitation in a ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal for a controllable time. The stored single photons are generated by cavity-enhanced spontaneous parametric down-conversion and heralded by their partner photons at telecom wavelength. These results represent the first demonstration of a multimode on-demand solid state quantum memory for external quantum states of light. They provide an important resource for quantum repeaters and pave the way for the implementation of quantum information networks with distant solid state quantum nodes.

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale of the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Furthermore, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.

Almheiri, Dong, and Harlow [J. High Energy Phys. 04 (2015) 163.] proposed a highly illuminating connection between the $\mathrm{AdS}/\mathrm{CFT}$ holographic correspondence and operator algebra quantum error correction (OAQEC). Here, we explore this connection further. We derive some general results about OAQEC, as well as results that apply specifically to quantum codes that admit a holographic interpretation. We introduce a new quantity called price, which characterizes the support of a protected logical system, and find constraints on the price and the distance for logical subalgebras of quantum codes. We show that holographic codes defined on bulk manifolds with asymptotically negative curvature exhibit uberholography, meaning that a bulk logical algebra can be supported on a boundary region with a fractal structure. We argue that, for holographic codes defined on bulk manifolds with asymptotically flat or positive curvature, the boundary physics must be highly nonlocal, an observation with potential implications for black holes and for quantum gravity in AdS space at distance scales that are small compared to the AdS curvature radius.

We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two layers of unitary matrices which act on blocks of $\ell$ contiguous sites. We argue that this yields an exponential reduction in computational time and memory requirement as compared to all previous approaches for finding a representation of the complete eigenspectrum of large many-body localized systems with a given accuracy. Concretely, we optimize the unitaries by minimizing the magnitude of the commutator of the approximate integrals of motion and the Hamiltonian, which can be done in a local fashion. This further reduces the computational complexity of the tensor networks arising in the minimization process compared to previous work. We test the accuracy of our method by comparing the approximate energy spectrum to exact diagonalization results for the random-field Heisenberg model on 16 sites. We find that the technique is highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the predicted dynamical phase transition. To demonstrate the power of our technique, we study a system of 72 sites, and we are able to see clear signatures of the phase transition. Our work opens a new avenue to study properties of the many-body localization transition in large systems.

Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.

We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programing. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translationally invariant (TI) case, we provide an exponentially faster computation of the classical bound and analytically closed expressions of the quantum value for appropriate observables and Hamiltonians. The power and generality of our method is illustrated through four representative examples: a tight TI inequality for eight parties, a quasi-TI uniparametric inequality for any even number of parties, ground states of spin-glass systems, and a nonintegrable interacting $XXZ$-like Hamiltonian. Our work opens the possibility for the use of low-energy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.

Communication over proven-secure quantum channels is potentially one of the most wide-ranging applications of currently developed quantum technologies. It is generally envisioned that in future quantum networks, separated nodes containing stationary solid-state or atomic qubits are connected via the exchange of optical photons over large distances. In this work, we explore an intriguing alternative for quantum communication via all-microwave networks. To make this possible, we describe a general protocol for sending quantum states through thermal channels, even when the number of thermal photons in the channel is much larger than 1. The protocol can be implemented with state-of-the-art superconducting circuits and enables the transfer of quantum states over distances of about 100 m via microwave transmission lines cooled to only $T=4\mathrm{K}$. This opens up new possibilities for quantum communication within and across buildings and, consequently, for the implementation of intracity quantum networks based on microwave technology only.

We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL) in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

The creation of composite quantum gates that implement quantum response functions $\widehat{U}(\theta )$ dependent on some parameter of interest $\theta$ is often more of an art than a science. Through inspired design, a sequence of $L$ primitive gates also depending on $\theta$ can engineer a highly nontrivial $\widehat{U}(\theta )$ that enables myriad precision metrology, spectroscopy, and control techniques. However, discovering new, useful examples of $\widehat{U}(\theta )$ requires great intuition to perceive the possibilities, and often brute force to find optimal implementations. We present a systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $\theta$ act on a single spin. We fully characterize the realizable family of $\widehat{U}(\theta )$, provide an efficient algorithm that decomposes a choice of $\widehat{U}(\theta )$ into its shortest sequence of gates, and show how to efficiently choose an achievable $\widehat{U}(\theta )$ that, for fixed $L$, is an optimal approximation to objective functions on its quadratures. A strong connection is forged with classical discrete-time signal processing, allowing us to swiftly construct, as examples, compensated gates with optimal bandwidth that implement arbitrary single-spin rotations with subwavelength spatial selectivity.

Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Rényi $q$ entropy, generalized Kullback-Leibler and Jensen-Shannon divergences, the latter allowing us to define a natural distance measure between complex networks. First, we show that by minimizing the Kullback-Leibler divergence between an observed network and a parametric network model, inference of model parameter(s) by means of maximum-likelihood estimation can be achieved and model selection can be performed with appropriate information criteria. Second, we show that the information-theoretic metric quantifies the distance between pairs of networks and we can use it, for instance, to cluster the layers of a multilayer system. By applying this framework to networks corresponding to sites of the human microbiome, we perform hierarchical cluster analysis and recover with high accuracy existing community-based associations. Our results imply that spectral-based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory.

The emerging field of quantum acoustics explores interactions between acoustic waves and artificial atoms and their applications in quantum information processing. In this experimental study, we demonstrate the coupling between a surface acoustic wave (SAW) and an electron spin in diamond by taking advantage of the strong strain coupling of the excited states of a nitrogen vacancy center while avoiding the short lifetime of these states. The SAW-spin coupling takes place through a $\mathrm{\Lambda }$-type three-level system where two ground spin states couple to a common excited state through a phonon-assisted as well as a direct dipole optical transition. Both coherent population trapping and optically driven spin transitions have been realized. The coherent population trapping demonstrates the coupling between a SAW and an electron spin coherence through a dark state. The optically driven spin transitions, which resemble the sideband transitions in a trapped-ion system, can enable the quantum control of both spin and mechanical degrees of freedom and potentially a trapped-ion-like solid-state system for applications in quantum computing. These results establish an experimental platform for spin-based quantum acoustics, bridging the gap between spintronics and quantum acoustics.

We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities. Using nearly quantum-noise-limited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment. The quantum trajectories of transmon qubits naturally split into low and high entanglement classes. The distribution of concurrence is found at any given time, and we explore the dynamics of entanglement creation in the state space. The distribution exhibits a sharp cutoff in the high concurrence limit, defining a maximal concurrence boundary. The most-likely paths of the qubits’ trajectories are also investigated, resulting in three probable paths, gradually projecting the system to two even subspaces and an odd subspace, conforming to a “half-parity” measurement. We also investigate the most-likely time for the individual trajectories to reach their most entangled state, and we find that there are two solutions for the local maximum, corresponding to the low and high entanglement routes. The theoretical predictions show excellent agreement with the experimental entangled-qubit trajectory data.

We study how useful random states are for quantum metrology, i.e., whether they surpass the classical limits imposed on precision in the canonical phase sensing scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to superclassical scaling of precision even when allowing for local unitary optimization. Conversely, we show that random pure states from the symmetric subspace typically achieve the optimal Heisenberg scaling without the need for local unitary optimization. Surprisingly, the Heisenberg scaling is observed for random isospectral states of arbitrarily low purity and preserved under loss of a fixed number of particles. Moreover, we prove that for pure states, a standard photon-counting interferometric measurement suffices to typically achieve resolution following the Heisenberg scaling for all values of the phase at the same time. Finally, we demonstrate that metrologically useful states can be prepared with short random optical circuits generated from three types of beam splitters and a single nonlinear (Kerr-like) transformation.

Diamond is a proven solid-state platform for spin-based quantum technology. The nitrogen-vacancy center in diamond has been used to realize small-scale quantum information processing and quantum sensing under ambient conditions. A major barrier in the development of large-scale quantum information processing in diamond is the connection of nitrogen-vacancy spin registers by a quantum bus at room temperature. Given that diamond is expected to be an ideal spin transport material, the coherent transport of spin directly between the spin registers offers a potential solution. Yet, there has been no demonstration of spin transport in diamond due to difficulties in achieving spin injection and detection via conventional methods. Here, we exploit detailed knowledge of the paramagnetic defects in diamond to identify novel mechanisms to photoionize, transport, and capture spin-polarized electrons in diamond at room temperature. Having identified these mechanisms, we explore how they may be combined to realize an on-chip spin quantum bus.