Creation of entangled states in coupled quantum dots via adiabatic rapid passage

Quantum state preparation through external control is fundamental to established methods in quantum information processing and in studies of dynamics. In this respect, excitons in semiconductor quantum dots (QDs) are of particular interest since their coupling to light allows them to be driven into a specified state using the coherent interaction with a tuned optical field such as an external laser pulse. We propose a protocol, based on adiabatic rapid passage, for the creation of entangled states in an ensemble of pairwise coupled two-level systems, such as an ensemble of QD molecules. We show by quantitative analysis using realistic parameters for semiconductor QDs that this method is feasible where other approaches are unavailable. Furthermore, this scheme can be generically transferred to some other physical systems including circuit QED, nuclear and electron spins in solid-state environments, and photonic coupled cavities.Comment: 10 pages, 2 figures. Added reference, minor changes. Discussion, results and conclusions unchange

Amplitude-mode dynamics of polariton condensates

We study the stability of collective amplitude excitations in non-equilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wavevectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical parametric oscillators and the atomic Bose supernova.Comment: 4 pages, 2 figure

Finite momentum condensation in a pumped microcavity

We calculate the absorption spectra of a semiconductor microcavity into which a non-equilibrium exciton population has been pumped. We predict strong peaks in the spectrum corresponding to collective modes analogous to the Cooper modes in superconductors and fermionic atomic gases. These modes can become unstable, leading to the formation of off-equilibrium quantum condensates. We calculate a phase diagram for condensation, and show that the dominant instabilities can be at a finite momentum. Thus we predict the formation of inhomogeneous condensates, similar to Fulde-Ferrel-Larkin-Ovchinnikov states.Comment: 7 pages, 4 figures, updated to accepted versio

New class of quantum error-correcting codes for a bosonic mode

We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the timestep between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to 'cat codes' based on superpositions of the coherent states, but offer several advantages such as smaller mean number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up- and down-conversion.Comment: Published versio

Affine Constellations Without Mutually Unbiased Counterparts

It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those of mutually unbiased constellations, mostly in dimension six. The observed discrepancies make a deeper relation between the two existence problems unlikely.Comment: 8 page

Performance and structure of single-mode bosonic codes

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce new codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat/binomial/GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multi-qubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a new multi-qudit code.Comment: 34 pages, 11 figures, 4 tables. v3: published version. See related talk at https://absuploads.aps.org/presentation.cfm?pid=1351

Implementing and characterizing precise multi-qubit measurements

There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction and simulation often make a more exacting demand: the ability to perform non-destructive measurements of specific correlations within that system. We realize such measurements by employing a protocol adapted from [S. Nigg and S. M. Girvin, Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time selection of arbitrary register-wide Pauli operators. Our implementation consists of a simple circuit quantum electrodynamics (cQED) module of four highly-coherent 3D transmon qubits, collectively coupled to a high-Q superconducting microwave cavity. As a demonstration, we enact all seven nontrivial subset-parity measurements on our three-qubit register. For each we fully characterize the realized measurement by analyzing the detector (observable operators) via quantum detector tomography and by analyzing the quantum back-action via conditioned process tomography. No single quantity completely encapsulates the performance of a measurement, and standard figures of merit have not yet emerged. Accordingly, we consider several new fidelity measures for both the detector and the complete measurement process. We measure all of these quantities and report high fidelities, indicating that we are measuring the desired quantities precisely and that the measurements are highly non-demolition. We further show that both results are improved significantly by an additional error-heralding measurement. The analyses presented here form a useful basis for the future characterization and validation of quantum measurements, anticipating the demands of emerging quantum technologies.Comment: 10 pages, 5 figures, plus supplemen

Model estimates of metazoans' contributions to the biological carbon pump

Funding: This work was supported by the Centre for Ocean Life, a VKR Centre of Excellence funded by the Villum Foundation, and by the Gordon and Betty Moore Foundation (grant no. 5479). André W. Visser was funded in part through the Horizon 2020 project ECOTIP (grant no. 869383). Andrew S. Brierley and Roland Proud were funded in part through the EU BG3 project “SUMMER” and BG8 project “Mission Atlantic”. Collated echo-sounder data obtained from the British Oceanographic Data Centre (BODC) included observations made during the Atlantic Meridional Transect. The Atlantic Meridional Transect (AMT) is funded by the UK Natural Environment Research Council through its National Capability Long-term Single Centre Science Programme, Climate Linked Atlantic Sector Science (grant number NE/R015953/1).The daily vertical migrations of fish and other metazoans actively transport organic carbon from the ocean surface to depth, contributing to the biological carbon pump. We use an oxygen-constrained, game-theoretic food-web model to simulate diel vertical migrations and estimate near-global (global ocean minus coastal areas and high latitudes) carbon fluxes and sequestration by fish and zooplankton due to respiration, fecal pellets, and deadfalls. Our model provides estimates of the carbon export and sequestration potential for a range of pelagic functional groups, despite uncertain biomass estimates of some functional groups. While the export production of metazoans and fish is modest (∼20 % of global total), we estimate that their contribution to carbon sequestered by the biological pump (∼800 PgC) is conservatively more than 50 % of the estimated global total (∼1300 PgC) and that they have a significantly longer sequestration timescale (∼250 years) than previously reported for other components of the biological pump. Fish and multicellular zooplankton contribute about equally to this sequestered carbon pool. This essential ecosystem service could be at risk from both unregulated fishing on the high seas and ocean deoxygenation due to climate change.Publisher PDFPeer reviewe