Experimental quantum verification in the presence of temporally correlated noise

Growth in the complexity and capabilities of quantum information hardware mandates access to practical techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). We study these using an analytic toolkit based on a formalism mapping noise to errors for arbitrary sequences of unitary operations. This analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped $^{171}$Yb$^{+}$ ion as a qubit and inject engineered noise ($\propto \sigma^z$) to probe protocol performance. Experiments on RB validate predictions that the distribution of measured fidelities over sequences is described by a gamma distribution varying between approximately Gaussian for rapidly varying noise, and a broad, highly skewed distribution for the slowly varying case. Similarly we find a strong gate set dependence of GST in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated $\sigma^z$ errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated $\sigma^x$ or $\sigma^y$ errors or rapidly varying noise processes, highlighting the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.Comment: Expanded and updated analysis of GST, including detailed examination of the role of gauge optimization in GST. Full GST data sets and supplementary information available on request from the authors. Related results available from http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm

Aharonov-Bohm interference as a probe of Majorana fermions

Majorana fermions act as their own antiparticle, and they have long been thought to be confined to the realm of pure theory. However, interest in them has recently resurfaced, as it was realized through the work of Kitaev that some experimentally accessible condensed matter systems can host these exotic excitations as bound states on the boundaries of 1D chains, and that their topological and non-abelian nature holds promise for quantum computation. Unambiguously detecting the experimental signatures of Majorana bound states has turned out to be challenging, as many other phenomena lead to similar experimental behaviour. Here, we computationally study a ring comprised of two Kitaev model chains with tunnel coupling between them, where an applied magnetic field allows for Aharonov-Bohm interference in transport through the resulting ring structure. We use a non-equilibrium Green's function technique to analyse the transport properties of the ring in both the presence and absence of Majorana zero modes. This computational model suggests another signature for the presence of these topologically protected bound states can be found in the magnetic field dependence of devices with loop geometries.Comment: 9 pages, 9 figure

Pulse-induced acoustoelectric vibrations in surface-gated GaAs-based quantum devices

We present the results of a numerical investigation which show the excitation of acoustoelectric modes of vibration in GaAs-based heterostructures due to sharp nano-second electric-field pulses applied across surface gates. In particular, we show that the pulses applied in quantum information processing applications are capable of exciting acoustoelectric modes of vibration including surface acoustic modes which propagate for distances greater than conventional device dimensions. We show that the pulse-induced acoustoelectric vibrations are capable of inducing significant undesired perturbations to the evolution of quantum systems.Comment: To be published in Phys. Rev.

Approximate method for treating dispersion in one-way quantum channels

Coupling the output of a source quantum system into a target quantum system is easily treated by cascaded systems theory if the intervening quantum channel is dispersionless. However, dispersion may be important in some transfer protocols, especially in solid-state systems. In this paper we show how to generalize cascaded systems theory to treat such dispersion, provided it is not too strong. We show that the technique also works for fermionic systems with a low flux, and can be extended to treat fermionic systems with large flux. To test our theory, we calculate the effect of dispersion on the fidelity of a simple protocol of quantum state transfer. We find good agreement with an approximate analytical theory that had been previously developed for this example

Mesoscopic one-way channels for quantum state transfer via the Quantum Hall Effect

We show that the one-way channel formalism of quantum optics has a physical realisation in electronic systems. In particular, we show that magnetic edge states form unidirectional quantum channels capable of coherently transporting electronic quantum information. Using the equivalence between one-way photonic channels and magnetic edge states, we adapt a proposal for quantum state transfer to mesoscopic systems using edge states as a quantum channel, and show that it is feasible with reasonable experimental parameters. We discuss how this protocol may be used to transfer information encoded in number, charge or spin states of quantum dots, so it may prove useful for transferring quantum information between parts of a solid-state quantum computer.Comment: 4 pages, 3 figure

Parity measurement of one- and two-electron double well systems

We outline a scheme to accomplish measurements of a solid state double well system (DWS) with both one and two electrons in non-localised bases. We show that, for a single particle, measuring the local charge distribution at the midpoint of a DWS using an SET as a sensitive electrometer amounts to performing a projective measurement in the parity (symmetric/antisymmetric) eigenbasis. For two-electrons in a DWS, a similar configuration of SET results in close-to-projective measurement in the singlet/triplet basis. We analyse the sensitivity of the scheme to asymmetry in the SET position for some experimentally relevant parameter, and show that it is realisable in experiment.Comment: 18 Pages, to appear in PR

Dynamical steady states in driven quantum systems

We derive dynamical equations for a driven, dissipative quantum system in which the environment-induced relaxation rate is comparable to the Rabi frequency, avoiding assumptions on the frequency dependence of the environmental coupling. When the environmental coupling varies significantly on the scale of the Rabi frequency, secular or rotating wave approximations break down. We avoid these approximations, yielding dynamical steady states which account for the interaction between driven quantum dots and their phonon environment. The theory, which is motivated by recent experimental observations, qualitatively and quantitatively describes the transition from asymmetric unsaturated resonances at weak driving to population inversion at strong driving

The Effect of Stochastic Noise on Quantum State Transfer

We consider the effect of classical stochastic noise on control laser pulses used in a scheme for transferring quantum information between atoms, or quantum dots, in separate optical cavities via an optical connection between cavities. We develop a master equation for the dynamics of the system subject to stochastic errors in the laser pulses, and use this to evaluate the sensitivity of the transfer process to stochastic pulse shape errors for a number of different pulse shapes. We show that under certain conditions, the sensitivity of the transfer to the noise depends on the pulse shape, and develop a method for determining a pulse shape that is minimally sensitive to specific errors.Comment: 10 pages, 9 figures, to appear in Physical Review