We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of donors in silicon, using the ability to set the donor nuclear spins in arbitrary states. The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the two nuclei are prepared in opposite spin states. This can be exploited to switch SWAP operations on and off with modest tuning of the electron exchange interaction. Furthermore, the hyperfine detuning enables high-fidelity conditional rotation gates based on selective resonant excitation. The latter requires no dynamic tuning of the exchange interaction at all and offers a very attractive scheme to implement two-qubit logic gates under realistic experimental conditions.

When a measurement has limited strength, only partial information, regarding the initial state, is extracted, and, correspondingly, there is a probability to reverse its effect on the system and retrieve the original state. Recently, a clear and direct quantitative description of this complementary relationship, in terms of a tradeoff relation, was developed by Y. K. Cheong and S. W. Lee. [Phys. Rev. Lett. 109, 150402 (2012)]. Here, this tradeoff relation is experimentally verified using polarization-encoded single photons from a quantum dot. Measurement operators representing a complete range, from not affecting the system to a projection to a single polarization state, are realized. In addition, for each measurement operator, an optimal reversal operator is also implemented. The upper bound of the tradeoff relation is mapped to experimental parameters representing the measurement strength. Our results complement the theoretical work and provide a hands-on characterization of general quantum measurements.

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have built a series of architecturally scalable QA processors consisting of networks of manufactured interacting spins (qubits). Here, we use qubit tunneling spectroscopy to measure the energy eigenspectrum of two- and eight-qubit systems within one such processor, demonstrating quantum coherence in these systems. We present experimental evidence that, during a critical portion of QA, the qubits become entangled and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that QA is a viable technology for large-scale quantum computing.

The electronic circulator and its close relative the gyrator are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative nonreciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an Ohmically contacted four-terminal Hall bar, explaining why this approach leads to unacceptably high device loss. We find that capacitive coupling to such a Hall conductor has much greater promise for achieving good circulator and gyrator functionality. We formulate a classical Ohm-Hall analysis for calculating the properties of such a device, and show how this classical theory simplifies remarkably in the limiting case of the Hall angle approaching 90°. In this limit, we find that either a four-terminal or a three-terminal capacitive device can give excellent circulator behavior, with device dimensions far smaller than the ac wavelength. An experiment is proposed to achieve GHz-band gyration in millimeter (and smaller) scale structures employing either semiconductor heterostructure or graphene Hall conductors. An inductively coupled scheme for realizing a Hall gyrator is also analyzed.

Recently, a programmable quantum annealing machine has been built that minimizes the cost function of hard optimization problems by, in principle, adiabatically quenching quantum fluctuations. Tests performed by different research teams have shown that, indeed, the machine seems to exploit quantum effects. However, experiments on a class of random-bond instances have not yet demonstrated an advantage over classical optimization algorithms on traditional computer hardware. Here, we present evidence as to why this might be the case. These engineered quantum annealing machines effectively operate coupled to a decohering thermal bath. Therefore, we study the finite-temperature critical behavior of the standard benchmark problem used to assess the computational capabilities of these complex machines. We simulate both random-bond Ising models and spin glasses with bimodal and Gaussian disorder on the D-Wave Chimera topology. Our results show that while the worst-case complexity of finding a ground state of an Ising spin glass on the Chimera graph is not polynomial, the finite-temperature phase space is likely rather simple because spin glasses on Chimera have only a zero-temperature transition. This means that benchmarking optimization methods using spin glasses on the Chimera graph might not be the best benchmark problems to test quantum speedup. We propose alternative benchmarks by embedding potentially harder problems on the Chimera topology. Finally, we also study the (reentrant) disorder-temperature phase diagram of the random-bond Ising model on the Chimera graph and show that a finite-temperature ferromagnetic phase is stable up to 19.85(15)% antiferromagnetic bonds. Beyond this threshold, the system only displays a zero-temperature spin-glass phase. Our results therefore show that a careful design of the hardware architecture and benchmark problems is key when building quantum annealing machines.

The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However, the question of how to obtain and process information about what errors have occurred in order to negate their effects has not yet been considered. This is in stark contrast with quantum computation proposals for Abelian anyons, for which decoding algorithms have been tailor-made for many topological error-correcting codes and error models. Here, we address this issue by considering the properties of non-Abelian error correction, in general. We also choose a specific anyon model and error model to probe the problem in more detail. The anyon model is the charge submodel of $D(S_3)$. This shares many properties with important models such as the Fibonacci anyons, making our method more generally applicable. The error model is a straightforward generalization of those used in the case of Abelian anyons for initial benchmarking of error correction methods. It is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin. This is remarkably comparable with the thresholds for Abelian models.

We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution or, more generally, any unital trace-preserving evolution. This approach inherits randomized benchmarking’s robustness to preparation, measurement, and gate imperfections, thereby avoiding systematic errors caused by these imperfections. We also extend these techniques to efficiently estimate the average fidelity of a quantum map to unitary maps outside of the Clifford group. The unitaries we consider correspond to large circuits commonly used as building blocks to achieve scalable, universal, and fault-tolerant quantum computation. Hence, we can efficiently verify all such subcomponents of a circuit-based universal quantum computer. In addition, we rigorously bound the time and sampling complexities of randomized benchmarking procedures, proving that the required nonlinear estimation problem can be solved efficiently.

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green’s observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional $p+ip$ superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the ${\mathbb{Z}}_3$ Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-$2e$ Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane’s construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a $p+ip$ superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.

The application of postselection to a weak quantum measurement leads to the phenomenon of weak values. Expressed in units of the measurement strength, the displacement of a quantum coherent measuring device is ordinarily bounded by the eigenspectrum of the measured observable. Postselection can enable an interference effect that moves the average displacement far outside this range, bringing practical benefits in certain situations. Employing the Fisher-information metric, we argue that the amplified displacement offers no fundamental metrological advantage, due to the necessarily reduced probability of success. Our understanding of metrological advantage is the possibility of a lower uncertainty in the estimate of an unknown parameter with a large number of trials. We analyze a situation in which the detector is pixelated with a finite resolution and in which the detector is afflicted by random displacements: imperfections that degrade the fundamental limits of parameter estimation. Surprisingly, weak-value amplification is no more robust to them than a technique making no use of the amplification effect brought about by a final, postselected measurement.

The technical merits of weak-value-amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them). Using the Fisher-information metric, we demonstrate that weak-value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time-correlated noise model and find that a Fisher-information analysis indicates that the standard method can have much larger information about the detected parameter than the postselected technique. However, the estimator needed to gather the information is technically difficult to implement, showing that the inefficient (but practical) signal-to-noise estimation of the parameter is usually superior. We also describe other technical advantages unique to imaginary weak-value-amplification techniques, focusing on beam-deflection measurements. In this case, we discuss combined noise types (such as detector transverse jitter, angular beam jitter before the interferometer, and turbulence) for which the interferometric weak-value technique gives higher Fisher information over conventional methods. We go on to calculate the Fisher information of the recently proposed photon-recycling scheme for beam-deflection measurements and show it further boosts the Fisher information by the inverse postselection probability relative to the standard measurement case.

The locking effect is a phenomenon that is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. The Fawzi-Hayden-Sen locking protocol harnesses this effect in a cryptographic context, whereby one party can encode $n$ bits into $n$ qubits while using only a constant-size secret key. The encoded message is then secure against any measurement that an eavesdropper could perform in an attempt to recover the message, but the protocol does not necessarily meet the composability requirements needed in quantum key distribution applications. In any case, the locking effect represents an extreme violation of Shannon’s classical theorem, which states that information-theoretic security holds in the classical case if and only if the secret key is the same size as the message. Given this intriguing phenomenon, it is of practical interest to study the effect in the presence of noise, which can occur in the systems of both the legitimate receiver and the eavesdropper. This paper formally defines the locking capacity of a quantum channel as the maximum amount of locked information that can be reliably transmitted to a legitimate receiver by exploiting many independent uses of a quantum channel and an amount of secret key sublinear in the number of channel uses. We provide general operational bounds on the locking capacity in terms of other well-known capacities from quantum Shannon theory. We also study the important case of bosonic channels, finding limitations on these channels’ locking capacity when coherent-state encodings are employed and particular locking protocols for these channels that might be physically implementable.

The future progress of semi-device-independent quantum information science depends crucially on our ability to bound the strength of the nonlocal correlations achievable with finite-dimensional quantum resources. In this work, we characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations. In the bipartite case, we find that the first level of the hierarchy returns nontrivial bounds in all cases considered, allowing us to study nonlocality scenarios with four measurement settings on one side and twelve on the other in a normal desktop. In the tripartite case, we apply the hierarchy to derive a Bell-type inequality that can only be violated when each of the three parties has local dimension greater than 2, hence certifying three-dimensional tripartite entanglement in a device-independent way. Finally, we show how the new method can be trivially modified to detect nonseparable measurements in two-qubit scenarios.

Highly nonclassical quantum states of light, characterized by Wigner functions with negative values, have been all-optically created so far only in a heralded fashion. In this case, the desired output emerges rarely and randomly from a quantum-state generator. An important example is the heralded production of high-purity single-photon states, typically based on some nonlinear optical interaction. In contrast, on-demand single-photon sources are also reported, exploiting the quantized level structure of matter systems. These sources, however, lead to highly impure output states, composed mostly of vacuum. While such impure states may still exhibit certain single-photon-like features such as antibunching, they are not nonclassical enough for advanced quantum-information processing. On the other hand, the intrinsic randomness of pure, heralded states can be circumvented by first storing and then releasing them on demand. Here, we propose such a controlled release, and we experimentally demonstrate it for heralded single photons. We employ two optical cavities, where the photons are both created and stored inside one cavity and finally released through a dynamical tuning of the other cavity. We demonstrate storage times of up to 300 ns while keeping the single-photon purity around $50\%$ after storage. Our experiment is the first demonstration of a negative Wigner function at the output of an on-demand photon source or a quantum memory. In principle, our storage system is compatible with all kinds of nonclassical states, including those known to be essential for many advanced quantum-information protocols.

We propose a mechanism of coherent coupling between distant spin qubits interacting dipolarly with a ferromagnet. We derive an effective two-spin interaction Hamiltonian and find a regime where the dynamics is coherent. Finally, we present a sequence for the implementation of the entangling controlled-not gate and estimate the corresponding operation time to be a few tens of nanoseconds. A particularly promising application of our proposal is to atomistic spin qubits such as silicon-based qubits and nitrogen-vacancy centers in diamond to which existing coupling schemes do not apply.

We discuss how a lattice Schwinger model can be realized in a linear ion trap, allowing a detailed study of the physics of Abelian lattice gauge theories related to one-dimensional quantum electrodynamics. Relying on the rich quantum-simulation toolbox available in state-of-the-art trapped-ion experiments, we show how one can engineer an effectively gauge-invariant dynamics by imposing energetic constraints, provided by strong Ising-like interactions. Applying exact diagonalization to ground-state and time-dependent properties, we study the underlying microscopic model and discuss undesired interaction terms and other imperfections. As our analysis shows, the proposed scheme allows for the observation in realistic setups of spontaneous parity- and charge-symmetry breaking, as well as false-vacuum decay. Besides an implementation aimed at larger ion chains, we also discuss a minimal setting, consisting of only four ions in a simpler experimental setup, which enables us to probe basic physical phenomena related to the full many-body problem. The proposal opens a new route for analog quantum simulation of high-energy and condensed-matter models where gauge symmetries play a prominent role.

Adiabatic quantum computation (AQC) has been lauded for its inherent robustness to control imperfections and relaxation effects. A considerable body of previous work, however, has shown AQC to be acutely sensitive to noise that causes excitations from the adiabatically evolving ground state. In this paper, we develop techniques to mitigate such noise, and then we point out and analyze some obstacles to further progress. First, we examine two known techniques that leverage quantum error-detecting codes to suppress noise and show that they are intimately related and may be analyzed within the same formalism. Next, we analyze the effectiveness of such error-suppression techniques in AQC, identify critical constraints on their performance, and conclude that large-scale, fault-tolerant AQC will require error correction, not merely suppression. Finally, we study the consequences of encoding AQC in quantum stabilizer codes and discover that generic AQC problem Hamiltonians rapidly convert physical errors into uncorrectable logical errors. We present several techniques to remedy this problem, but all of them require unphysical resources, suggesting that the adiabatic model of quantum computation may be fundamentally incompatible with stabilizer quantum error correction.

Multipartite entanglement of large numbers of physically distinct linear resonators is of both fundamental and applied interest, but there have been no feasible proposals to date for achieving it. At the same time, the Bose-Hubbard model with attractive interactions (ABH) is theoretically known to have a phase transition from the superfluid phase to a highly entangled nonlocal superposition, but observation of this phase transition has remained out of experimental reach. In this theoretical work, we jointly address these two problems by (1) proposing an experimentally accessible quantum simulation of the ABH phase transition in an array of tunably coupled superconducting circuit microwave resonators and (2) incorporating the simulation into a highly scalable protocol that takes as input any microwave-resonator state with negligible occupation of number states $|0⟩$ and $|1⟩$ and nonlocally superposes it across the whole array of resonators. The large-scale multipartite entanglement produced by the protocol is of the $W$ type, which is well known for its robustness. The protocol utilizes the ABH phase transition to generate the multipartite entanglement of all of the resonators in parallel, and is therefore deterministic and permits an increase in resonator number without any increase in protocol complexity; the number of resonators is limited instead by system characteristics such as resonator-frequency disorder and inter-resonator coupling strength. Only one local and two global controls are required for the protocol. We numerically demonstrate the protocol with realistic system parameters and estimate that current experimental capabilities can realize the protocol with high fidelity for greater than 40 resonators. Because superconducting-circuit microwave resonators are capable of interfacing with other devices and platforms such as mechanical resonators and (potentially) optical fields, this proposal provides a route toward large-scale $W$-type entanglement in those systems as well.

Device-independent quantum key distribution (DIQKD) is a formalism that supersedes traditional quantum key distribution, as its security does not rely on any detailed modeling of the internal working of the devices. This strong form of security is only possible using devices producing correlations that violate a Bell inequality. Full security proofs of DIQKD have recently been reported, but they tolerate zero or small amounts of noise and are restricted to protocols based on specific Bell inequalities. Here, we provide a security proof of DIQKD that is both more efficient and noise resistant, and also more general, as it applies to protocols based on arbitrary Bell inequalities and can be adapted to cover supraquantum eavesdroppers limited by the no-signaling principle only. It is formulated, however, in the bounded-quantum-storage model, where an upper bound on the adversary’s quantum memory is a priori known. This condition is not a limitation at present, since the best existing quantum memories have very short coherence times.

Device-independent quantum key distribution (DIQKD) in its current design requires a violation of a Bell’s inequality between two parties, Alice and Bob, who are connected by a quantum channel. However, in reality, quantum channels are lossy and current DIQKD protocols are thus vulnerable to attacks exploiting the detection loophole of the Bell test. Here, we propose a novel approach to DIQKD that overcomes this limitation. In particular, we propose a protocol where the Bell test is performed entirely on two casually independent devices situated in Alice’s laboratory. As a result, the detection loophole caused by the losses in the channel is avoided.