Universal logic with encoded spin qubits in silicon.

Quantum computation features known examples of hardware acceleration for certain problems, but is challenging to realize because of its susceptibility to small errors from noise or imperfect control. The principles of fault tolerance may enable computational acceleration with imperfect hardware, but they place strict requirements on the character and correlation of errors1. For many qubit technologies2-21, some challenges to achieving fault tolerance can be traced to correlated errors arising from the need to control qubits by injecting microwave energy matching qubit resonances. Here we demonstrate an alternative approach to quantum computation that uses energy-degenerate encoded qubit states controlled by nearest-neighbour contact interactions that partially swap the spin states of electrons with those of their neighbours. Calibrated sequences of such partial swaps, implemented using only voltage pulses, allow universal quantum control while bypassing microwave-associated correlated error sources1,22-28. We use an array of six 28Si/SiGe quantum dots, built using a platform that is capable of extending in two dimensions following processes used in conventional microelectronics29. We quantify the operational fidelity of universal control of two encoded qubits using interleaved randomized benchmarking30, finding a fidelity of 96.3% ± 0.7% for encoded controlled NOT operations and 99.3% ± 0.5% for encoded SWAP. The quantum coherence offered by enriched silicon5-9,16,18,20,22,27,29,31-37, the all-electrical and low-crosstalk-control of partial swap operations1,22-28 and the configurable insensitivity of our encoding to certain error sources28,33,34,38 all combine to offer a strong pathway towards scalable fault tolerance and computational advantage.

Quantifying error and leakage in an encoded Si/SiGe triple-dot qubit.

Quantum computation requires qubits that satisfy often-conflicting criteria, which include long-lasting coherence and scalable control1. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits. Although such encoded qubits may be particularly susceptible to leakage out of their computational subspace, they can be insensitive to certain noise processes2,3 and can also allow logical control with a single type of entangling interaction4 while maintaining favourable features of the underlying physical system. Here we demonstrate high-fidelity operation of an exchange-only qubit encoded in a subsystem of three coupled electron spins5 confined in gated, isotopically enhanced silicon quantum dots6. This encoding requires neither high-frequency electric nor magnetic fields for control, and instead relies exclusively on the exchange interaction4,5, which is highly local and can be modulated with a large on-off ratio using only fast voltage pulses. It is also compatible with very low and gradient-free magnetic field environments, which simplifies integration with superconducting materials. We developed and employed a modified blind randomized benchmarking protocol that determines both computational and leakage errors7,8, and found that unitary operations have an average total error of 0.35%, with half of that, 0.17%, coming from leakage driven by interactions with substrate nuclear spins. The combination of this proven performance with complete control via gate voltages makes the exchange-only qubit especially attractive for use in many-qubit systems.

Breaking Lorentz Reciprocity with Frequency Conversion and Delay.

We introduce a method for breaking Lorentz reciprocity based upon the noncommutation of frequency conversion and delay. The method requires no magnetic materials or resonant physics, allowing for the design of scalable and broadband nonreciprocal circuits. With this approach, two types of gyrators-universal building blocks for linear, nonreciprocal circuits-are constructed. Using one of these gyrators, we create a circulator with >15 dB of isolation across the 5-9 GHz band. Our designs may be readily extended to any platform with suitable frequency conversion elements, including semiconducting devices for telecommunication or an on-chip superconducting implementation for quantum information processing.

Superconducting microwave multivibrator produced by coherent feedback.

We investigate a nonlinear coherent feedback circuit constructed from preexisting superconducting microwave devices. The network exhibits emergent bistable and astable states, and we demonstrate its operation as a latch and the frequency locking of its oscillations. While the network is tedious to model by hand, our observations agree quite well with the semiclassical dynamical model produced by a new software package (N. Tezak et al., arXiv:1111.3081v1 [Phil. Trans. R. Soc. A (to be published)]) that systematically interpreted an idealized schematic of the system as a quantum optic feedback network.

Remnants of semiclassical bistability in the few-photon regime of cavity QED.

Broadband homodyne detection of the light transmitted by a Fabry-Perot cavity containing a strongly-coupled (133)Cs atom is used to probe the dynamic optical response in a regime where semiclassical theory predicts bistability but strong quantum corrections should apply. While quantum fluctuations destabilize true equilibrium bistability, our observations confirm the existence of metastable states with finite lifetimes and a hysteretic response is apparent when the optical drive is modulated on comparable timescales. Our experiment elucidates remnant semiclassical behavior in the attojoule (~10 photon) regime of single-atom cavity QED, of potential significance for ultra-low power photonic signal processing.

The dressed atom as binary phase modulator: towards attojoule/edge optical phase-shift keying.

We use a single 133Cs atom strongly coupled to an optical resonator to induce random binary phase modulation of a near infra-red, ∼ 500 pW laser beam, with each modulation edge caused by the dissipation of a single photon (≈ 0.23 aJ) by the atom. While our ability to deterministically induce phase edges with an additional optical control beam is limited thus far, theoretical analysis of an analogous, solid-state system indicates that efficient external control should be achievable in demonstrated nanophotonic systems.

Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction.

We propose an approach to quantum error correction based on coding and continuous syndrome readout via scattering of coherent probe fields, in which the usual steps of measurement and discrete restoration are replaced by direct physical processing of the probe beams and coherent feedback to the register qubits. Our approach is well matched to physical implementations that feature solid-state qubits embedded in planar electromagnetic circuits, providing an autonomous and "on-chip" quantum memory design requiring no external clocking or control logic.

Van der Waals enhancement of optical atom potentials via resonant coupling to surface polaritons.

Contemporary experiments in cavity quantum electrodynamics (cavity QED) with gas-phase neutral atoms rely increasingly on laser cooling and optical, magneto-optical or magnetostatic trapping methods to provide atomic localization with sub-micron uncertainty. Difficult to achieve in free space, this goal is further frustrated by atom-surface interactions if the desired atomic placement approaches within several hundred nanometers of a solid surface, as can be the case in setups incorporating monolithic dielectric optical resonators such as microspheres, microtoroids, microdisks or photonic crystal defect cavities. Typically in such scenarios, the smallest atom-surface separation at which the van der Waals interaction can be neglected is taken to be the optimal localization point for associated trapping schemes, but this sort of conservative strategy generally compromises the achievable cavity QED coupling strength. Here we suggest a new approach to the design of optical dipole traps for atom confinement near surfaces that exploits strong surface interactions, rather than avoiding them, and present the results of a numerical study based on (39)K atoms and indium tin oxide (ITO). Our theoretical framework points to the possibility of utilizing nanopatterning methods to engineer novel modifications of atom-surface interactions.