The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a $d$-sparse Hamiltonian $\widehat{H}$ for time-interval $t$ with error $\epsilon$ is $\mathcal{O}[td\parallel \widehat{H}{\parallel }_{\max }+\log (1/\epsilon )/\log \log (1/\epsilon )]$, which matches lower bounds in all parameters. This connection is made through general three-step “quantum signal processing” methodology, comprised of (i) transducing eigenvalues of $\widehat{H}$ into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

We derive a general exact formula for the mean first passage time (MFPT) from a fixed point inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet-Neumann boundary value problem is conformally mapped onto the unit disk, solved exactly, and mapped back. The resulting formula for the MFPT is valid for an arbitrary space-dependent diffusion coefficient, while the leading logarithmic term is explicit, simple, and remarkably universal. In contrast to earlier works, we show that the natural small parameter of the problem is the harmonic measure of the escape region, not its perimeter. The conventional scaling of the MFPT with the area of the domain is altered when diffusing particles are released near the escape region. These findings change the current view of escape problems and related chemical or biochemical kinetics in complex, multiscale, porous or fractal domains, while the fundamental relation to the harmonic measure opens new ways of computing and interpreting MFPTs.

Quantum measurements on a two-level system can have more than two independent outcomes, and in this case, the measurement cannot be projective. Measurements of this general type are essential to an operational approach to quantum theory, but so far, the nonprojective character of a measurement can only be verified experimentally by already assuming a specific quantum model of parts of the experimental setup. Here, we overcome this restriction by using a device-independent approach. In an experiment on pairs of polarization-entangled photonic qubits we violate by more than 8 standard deviations a Bell-like correlation inequality that is valid for all sets of two-outcome measurements in any dimension. We combine this with a device-independent verification that the system is best described by two qubits, which therefore constitutes the first device-independent certification of a nonprojective quantum measurement.

To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be reduced in different ways. Coherent errors are generally easier to reduce at the hardware level, e.g., by improving calibration, whereas some sources of incoherent errors, e.g., $T_2^{*}$ processes, can be reduced by engineering robust pulses. In this work, we illustrate how purity benchmarking and randomized benchmarking can be used together to distinguish between coherent and incoherent errors and to quantify the reduction in both of them due to using optimal control pulses and accounting for the transfer function in an electron spin resonance system. We also prove that purity benchmarking provides bounds on the optimal fidelity and diamond norm that can be achieved by correcting the coherent errors through improving calibration.

We provide an analytic solution to the problem of system-bath dynamics under the effect of high-frequency driving that has applications in a large class of settings, such as driven-dissipative many-body systems. Our method relies on discrete symmetries of the system-bath Hamiltonian and provides the time evolution operator of the full system, including bath degrees of freedom, without weak-coupling or Markovian assumptions. An interpretation of the solution in terms of the stroboscopic evolution of a family of observables under the influence of an effective static Hamiltonian is proposed, which constitutes a flexible simulation procedure of nontrivial Hamiltonians. We instantiate the result with the study of the spin-boson model with time-dependent tunneling amplitude. We analyze the class of Hamiltonians that may be stroboscopically accessed for this example and illustrate the dynamics of system and bath degrees of freedom.

Detector-device-independent quantum key distribution (DDI-QKD) held the promise of being robust to detector side channels, a major security loophole in quantum key distribution (QKD) implementations. In contrast to what has been claimed, however, we demonstrate that the security of DDI-QKD is not based on postselected entanglement, and we introduce various eavesdropping strategies that show that DDI-QKD is in fact insecure against detector side-channel attacks as well as against other attacks that exploit devices’ imperfections of the receiver. Our attacks are valid even when the QKD apparatuses are built by the legitimate users of the system themselves, and thus, free of malicious modifications, which is a key assumption in DDI-QKD.

We extend covert communication to the quantum regime by showing that covert quantum communication is possible over optical channels with noise arising either from the environment or from the sender’s lab. In particular, we show that sequences of qubits can be transmitted covertly by using both a single photon and a coherent state encoding. We study the possibility of performing covert quantum key distribution (QKD) and show that positive key rates and covertness can be achieved simultaneously. Covert communication requires a secret key between the sender and receiver, which raises the problem of how this key can be regenerated covertly. We show that covert QKD consumes more secret bits than it can generate and propose instead a hybrid protocol for covert key regeneration that uses pseudorandom number generators (PRNGs) together with covert QKD to regenerate secret keys. The security of the new key is guaranteed by QKD while the security of the covert communication is at least as strong as the security of the PRNG.

We obtain a low optical inhomogeneous linewidth of 25 MHz in the stoichiometric rare-earth crystal ${\mathrm{EuCl}}_3·6{\mathrm{H}}_2\mathrm{O}$ by isotopically purifying the crystal in ${}^{35}\mathrm{Cl}$. With this linewidth, an important limit for stoichiometric rare-earth crystals is surpassed: the hyperfine structure of ${}^{153}\mathrm{Eu}$ is spectrally resolved, allowing the whole population of ${{}^{153}\mathrm{Eu}}^{3+}$ ions to be prepared in the same hyperfine state using hole-burning techniques. This material also has a very high optical density, and can have long coherence times when deuterated. This combination of properties offers new prospects for quantum information applications. We consider two of these: quantum memories and quantum many-body studies. We detail the improvements in the performance of current memory protocols possible in these high optical depth crystals, and describe how certain memory protocols, such as off-resonant Raman memories, can be implemented for the first time in a solid-state system. We explain how the strong excitation-induced interactions observed in this material resemble those seen in Rydberg systems, and describe how these interactions can lead to quantum many-body states that could be observed using standard optical spectroscopy techniques.

Multiplexed quantum memories capable of storing and processing entangled photons are essential for the development of quantum networks. In this context, we demonstrate and certify the simultaneous storage and retrieval of two entangled photons inside a solid-state quantum memory and measure a temporal multimode capacity of ten modes. This is achieved by producing two polarization-entangled pairs from parametric down-conversion and mapping one photon of each pair onto a rare-earth-ion-doped (REID) crystal using the atomic frequency comb (AFC) protocol. We develop a concept of indirect entanglement witnesses, which can be used as Schmidt number witnesses, and we use it to experimentally certify the presence of more than one entangled pair retrieved from the quantum memory. Our work puts forward REID-AFC as a platform compatible with temporal multiplexing of several entangled photon pairs along with a new entanglement certification method, useful for the characterization of multiplexed quantum memories.

We propose an architecture for an analog quantum simulator of electromagnetism in $2+1$ dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1) representation of the quantum link model formulation of compact $U(1)$ lattice gauge theory. We show how to engineer Gauss’ law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from ’t Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.

We introduce a cryptographically motivated quantifier of entanglement in bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The GIE is defined as the optimized mutual information of a Gaussian distribution of outcomes of measurements on parts of a system, conditioned on the outcomes of a measurement on a purifying subsystem. We show that GIE vanishes only on separable states and exhibits monotonicity under Gaussian local trace-preserving operations and classical communication. In the two-mode case, we compute GIE for all pure states as well as for several important classes of symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE is equal to Gaussian Rényi-2 entanglement. As GIE is operationally associated with the secret-key agreement protocol and can be computed for several important classes of states, it offers a compromise between computable and physically meaningful entanglement quantifiers.

Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement results. After entanglement swapping the two independent multipartite entangled states are merged into a large entangled state in which all unmeasured quantum modes are entangled. The entanglement swapping between a tripartite GHZ state and an Einstein-Podolsky-Rosen entangled state is also demonstrated and the dependence of the resultant entanglement on transmission loss is investigated. The presented experiment provides a feasible technical reference for constructing more complicated quantum networks.

We propose a scalable architecture for a quantum network based on a simple on-chip photonic circuit that performs loss-tolerant two-qubit measurements. The circuit consists of two quantum emitters positioned in the arms of an on-chip Mach-Zehnder interferometer composed of waveguides with chiral-light–matter interfaces. The efficient chiral-light–matter interaction allows the emitters to perform high-fidelity intranode two-qubit parity measurements within a single chip and to emit photons to generate internode entanglement, without any need for reconfiguration. We show that, by connecting multiple circuits of this kind into a quantum network, it is possible to perform universal quantum computation with heralded two-qubit gate fidelities $\mathcal{F}\sim 0.998$ achievable in state-of-the-art quantum dot systems.