Qubit Noise Spectroscopy for Non-Gaussian Dephasing Environments.

We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. By engineering a multidimensional frequency comb via repetition of suitably designed pulse sequences, the desired high-order spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieving spectral reconstruction over an extended bandwidth, overcoming the limitations of existing schemes. Non-Gaussian spectroscopy is demonstrated for a classical noise model describing quadratic dephasing at an optimal point, as well as a quantum spin-boson model out of equilibrium. In both cases, we obtain spectral reconstructions that accurately predict the qubit dynamics in the non-Gaussian regime.

General transfer-function approach to noise filtering in open-loop quantum control.

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-function set suffices to characterize the error suppression capabilities of the control protocol in both the time and the frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.

Optimally combining dynamical decoupling and quantum error correction.

Quantum control and fault-tolerant quantum computing (FTQC) are two of the cornerstones on which the hope of realizing a large-scale quantum computer is pinned, yet only preliminary steps have been taken towards formalizing the interplay between them. Here we explore this interplay using the powerful strategy of dynamical decoupling (DD), and show how it can be seamlessly and optimally integrated with FTQC. To this end we show how to find the optimal decoupling generator set (DGS) for various subspaces relevant to FTQC, and how to simultaneously decouple them. We focus on stabilizer codes, which represent the largest contribution to the size of the DGS, showing that the intuitive choice comprising the stabilizers and logical operators of the code is in fact optimal, i.e., minimizes a natural cost function associated with the length of DD sequences. Our work brings hybrid DD-FTQC schemes, and their potentially considerable advantages, closer to realization.

Zeno effect for quantum computation and control.

It is well known that the quantum Zeno effect can protect specific quantum states from decoherence by using projective measurements. Here we combine the theory of weak measurements with stabilizer quantum error correction and detection codes. We derive rigorous performance bounds which demonstrate that the Zeno effect can be used to protect appropriately encoded arbitrary states to arbitrary accuracy while at the same time allowing for universal quantum computation or quantum control.

Fault tolerance with noisy and slow measurements and preparation.

It is not so well known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite their potential advantages in terms of the relaxation of accuracy, speed, and addressing requirements, they have usually been overlooked since they are expected to yield a very bad threshold. We show that this is not the case. We design fault-tolerant circuits for the 9-qubit Bacon-Shor code and find an error threshold for unitary gates and preparation of p((p,g)thresh)=3.76×10(-5) (30% of the best known result for the same code using measurement) while admitting up to 1/3 error rates for measurements and allocating no constraints on measurement speed. We further show that demanding gate error rates sufficiently below the threshold pushes the preparation threshold up to p((p)thresh)=1/3.

Perfect mirror transport protocol with higher dimensional quantum chains.

A globally controlled scheme for quantum transport is proposed. The scheme works on a 1D chain of nearest neighbor coupled systems of qudits (finite dimension), or qunats (continuous variable), taking any arbitrary initial quantum state of the chain and producing a final quantum state, which is perfectly spatially mirrored about the midpoint of the chain. As a particular novel application, the method can be used to transport continuous variable quantum states. A physical realization is proposed where it is shown how the quantum states of the microwave fields held in a chain of driven superconducting coplanar waveguides can experience quantum mirror transport when coupled by switchable Cooper pair boxes.