Density-matrix simulation of small surface codes under current and projected experimental noise

We present a full density-matrix simulation of the quantum memory and computing performance of the distance-3 logical qubit Surface-17, following a recently proposed quantum circuit and using experimental error parameters for transmon qubits in a planar circuit QED architecture. We use this simulation to optimize components of the QEC scheme (e.g., trading off stabilizer measurement infidelity for reduced cycle time) and to investigate the benefits of feedback harnessing the fundamental asymmetry of relaxation-dominated error in the constituent transmons. A lower-order approximate calculation extends these predictions to the distance-$5$ Surface-49. These results clearly indicate error rates below the fault-tolerance threshold of surface code, and the potential for Surface-17 to perform beyond the break-even point of quantum memory. At state-of-the-art qubit relaxation times and readout speeds, Surface-49 could surpass the break-even point of computation.Comment: 10 pages + 8 pages appendix, 12 figure

Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester models, for which we find that the double-row transfer matrices satisfy functional equations with an su(2) structure.Comment: 48 pages, LaTeX, requires about 79000 words of TeX memory. Submitted to J. Stat. Phy

A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

Integrated Silicon Photonics for High-Speed Quantum Key Distribution

Integrated photonics offers great potential for quantum communication devices in terms of complexity, robustness and scalability. Silicon photonics in particular is a leading platform for quantum photonic technologies, with further benefits of miniaturisation, cost-effective device manufacture and compatibility with CMOS microelectronics. However, effective techniques for high-speed modulation of quantum states in standard silicon photonic platforms have been limited. Here we overcome this limitation and demonstrate high-speed low-error quantum key distribution modulation with silicon photonic devices combining slow thermo-optic DC biases and fast (10~GHz bandwidth) carrier-depletion modulation. The ability to scale up these integrated circuits and incorporate microelectronics opens the way to new and advanced integrated quantum communication technologies and larger adoption of quantum-secured communications

Calculating energy derivatives for quantum chemistry on a quantum computer

Modeling chemical reactions and complicated molecular systems has been proposed as the `killer application' of a future quantum computer. Accurate calculations of derivatives of molecular eigenenergies are essential towards this end, allowing for geometry optimization, transition state searches, predictions of the response to an applied electric or magnetic field, and molecular dynamics simulations. In this work, we survey methods to calculate energy derivatives, and present two new methods: one based on quantum phase estimation, the other on a low-order response approximation. We calculate asymptotic error bounds and approximate computational scalings for the methods presented. Implementing these methods, we perform the world's first geometry optimization on an experimental quantum processor, estimating the equilibrium bond length of the dihydrogen molecule to within 0.014 Angstrom of the full configuration interaction value. Within the same experiment, we estimate the polarizability of the H2 molecule, finding agreement at the equilibrium bond length to within 0.06 a.u. (2% relative error).Comment: 19 pages, 1 page supplemental, 7 figures. v2 - tidied up and added example to appendice

Single-Walled Carbon Nanotubes as Shadow Masks for Nanogap Fabrication

We describe a technique for fabricating nanometer-scale gaps in Pt wires on insulating substrates, using individual single-walled carbon nanotubes as shadow masks during metal deposition. More than 80% of the devices display current-voltage dependencies characteristic of direct electron tunneling. Fits to the current-voltage data yield gap widths in the 0.8-2.3 nm range for these devices, dimensions that are well suited for single-molecule transport measurements

Violation of the Leggett-Garg inequality with weak measurements of photons

By weakly measuring the polarization of a photon between two strong polarization measurements, we experimentally investigate the correlation between the appearance of anomalous values in quantum weak measurements, and the violation of realism and non-intrusiveness of measurements. A quantitative formulation of the latter concept is expressed in terms of a Leggett-Garg inequality for the outcomes of subsequent measurements of an individual quantum system. We experimentally violate the Leggett-Garg inequality for several measurement strengths. Furthermore, we experimentally demonstrate that there is a one-to-one correlation between achieving strange weak values and violating the Leggett-Garg inequality.Comment: 5 pages, 4 figure