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The wide-ranging adoption of quantum technologies requires practical, high-performance advances in our ability to maintain quantum coherence while facing the challenge of state collapse under measurement. Here we use techniques from control theory and machine learning to predict the future evolution of a qubit's state; we deploy this information to suppress stochastic, semiclassical decoherence, even when access to measurements is limited. First, we implement a time-division-multiplexed approach, interleaving measurement periods with periods of unsupervised but stabilised operation during which qubits are available, for e.g. quantum information experiments. Second, we employ predictive feedback during sequential but time delayed measurements to reduce the Dick effect as encountered in passive frequency standards. Both experiments demonstrate significant improvements in qubit phase stability over "traditional" measurement-based feedback approaches by exploiting time domain correlations in the noise processes. This technique requires no additional hardware and is applicable to all two-level quantum systems where projective measurements are possible., Comment: Additional results presented. Related work available from http://www.physics.usyd.edu.au/~mbiercuk/Publications.html

Among the most popular and well studied quantum characterization, verification and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in "Pauli space." Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a gamma distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes -- consistent with existing experimental data -- highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the Filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation., Comment: Updated and expanded to include full derivation. Related papers available from http://www.physics.usyd.edu.au/~mbiercuk/Publications.html

Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent experiments in a range of technical platforms have demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions, and relativistic quantum mechanics. In all cases, the underlying hardware platforms restrict the achievable inter-particle interaction, forming a serious constraint on the ability to realize a versatile, programmable quantum simulator. In this work, we address this problem by developing novel sequences of unitary operations that engineer desired effective Hamiltonians in the time-domain. The result is a hybrid programmable analog simulator permitting a broad class of interacting spin-lattice models to be generated starting only with an arbitrary long-range native inter-particle interaction and single-qubit addressing. Specifically, our approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin-1/2 XYZ chains, but generalized to include long-range couplings. Building on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries, we show that determining the "program" of unitary pulses to implement an arbitrary spin Hamiltonian can be formulated as a linear program that runs in polynomial time and scales efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, where our approach allows for the creation of non-native ground state solutions to a computation., Comment: Related papers at http://www.physics.usyd.edu.au/~mbiercuk/Publications.html

In this manuscript we address the problem of deriving \emph{analytic} expressions for calculating universal decoherence-induced errors in qubits undergoing arbitrary, unitary, time-dependent quantum-control protocols. For a qubit undergoing unitary decoherence the evolution of a qubit state in the presence of time-varying semiclassical fields may be treated geometrically. We show that the fidelity of an arbitrary control operation may then be expressed to arbitrary order in terms of experimentally relevant spectral characteristics of the noise and the control over all Cartesian directions and accounting for noise cross-correlations. We formulate \emph{control matrices} in the time domain to capture the effects of piecewise-constant control, and convert them to generalized Fourier-domain filter functions. Such generalized filter functions may therefore be derived for complex temporally modulated control protocols, accounting for susceptibility to rotations of the qubit state vector in three dimensions. Taken together, this framework provides a computationally efficient means to calculate the effects of universal noise on arbitrary quantum control protocols without the need for time-consuming simulations of Bloch vector evolution. As a concrete example, we apply our method to treating the problem of dynamical decoupling incorporating realistic control pulses of arbitrary duration or form, including the replacement of simple $\pi$-pulses with complex dynamically corrected gates., Comment: To appear in New J. Phys. Expanded to include discussions of limits of analytic approximation, comparison of filter-function with full numerical simulation, and incorporation of explicit forms of higher-order filter functions. Related references at http://www.physics.usyd.edu.au/~mbiercuk

We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a $\sim$400 $\mu$m-diameter planar crystal of several hundred $^9$Be$^+$ ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the $^9$Be$^+$ valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing ($\sim$20 \nolinebreak$\mu$m). Center-of-mass displacements below 1 nm are detected via entanglement of spin and motional degrees of freedom., Comment: 12 pages, 7 figures (includes Supplementary Material)

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of non-commuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics., Comment: Revised and expanded to include filter function terms beyond first order in the Magnus expansion. Related manuscripts available from http://www.physics.usyd.edu.au/~mbiercuk