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.Comment: Significant modifications, including a new author. To appear in PR

Gradient Ascent Pulse Engineering with Feedback

Efficient approaches to quantum control and feedback are essential for quantum technologies, from sensing to quantum computation. Pure control tasks have been successfully solved using optimization techniques, including methods like gradient-ascent pulse engineering (GRAPE) , relying on a differentiable model of the quantum dynamics. For feedback tasks, such methods are not directly applicable, since the aim is to discover strategies conditioned on measurement outcomes. There, model-free reinforcement learning (RL) has recently proven a powerful new ansatz. What is missing is a way to combine the best of both approaches for scenarios that go beyond weak measurements. In this work, we introduce feedback-GRAPE, which borrows concepts from model-free RL to incorporate the response to strong stochastic (discrete or continuous) measurements, while still performing direct gradient ascent through the quantum dynamics. We illustrate its power on a Jaynes-Cummings model with feedback, where it yields interpretable feedback strategies for state preparation and stabilization in the presence of noise. This approach could be employed for discovering strategies in a wide range of feedback tasks, from calibration of multi-qubit devices to linear-optics quantum computation strategies, quantum-enhanced sensing with adaptive measurements, and quantum error correction

Weak Decoupling Duality and Quantum Identification

If a quantum system is subject to noise, it is possible to perform quantum error correction reversing the action of the noise if and only if no information about the system's quantum state leaks to the environment. In this article, we develop an analogous duality in the case that the environment approximately forgets the identity of the quantum state, a weaker condition satisfied by epsilon-randomizing maps and approximate unitary designs. Specifically, we show that the environment approximately forgets quantum states if and only if the original channel approximately preserves pairwise fidelities of pure inputs, an observation we call weak decoupling duality. Using this tool, we then go on to study the task of using the output of a channel to simulate restricted classes of measurements on a space of input states. The case of simulating measurements that test whether the input state is an arbitrary pure state is known as equality testing or quantum identification. An immediate consequence of weak decoupling duality is that the ability to perform quantum identification cannot be cloned. We furthermore establish that the optimal amortized rate at which quantum states can be identified through a noisy quantum channel is equal to the entanglement-assisted classical capacity of the channel, despite the fact that the task is quantum, not classical, and entanglement-assistance is not allowed. In particular, this rate is strictly positive for every non-constant quantum channel, including classical channels.Comment: 14 pages; v2 has some remarks added and inaccuracies corrected; v3 has new title, improved presentation and additional references; v4 is the final, accepted version (to appear in IEEE IT), title changed once more and numerous improvements made - the main one being that we can now show that nontrivial amortization is necessary in erasure channel

A practical scheme for error control using feedback

We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols (for example Ahn et. al, PRA, 65, 042301 (2001)), is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit-flips. We also consider implementation in a solid-state quantum computation architecture and estimate the maximal error rate which could be corrected with current technology.Comment: 12 pages, 3 figures. Minor typographic change

Continuous quantum error correction via quantum feedback control

We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control. Our protocol uses continuous measurements and Hamiltonian operations, which are weaker control tools than are typically assumed for quantum error correction. We develop a cost function appropriate for unknown quantum states and use it to optimize our state-estimate feedback. Using Monte Carlo simulations, we study our protocol for the three-qubit bit-flip code in detail and demonstrate that it can improve the fidelity of quantum states beyond what is achievable using quantum error correction when the time between quantum error correction cycles is limited.Comment: 12 pages, 6 figures, REVTeX; references fixe

Continuous quantum error correction

We describe new implementations of quantum error correction that are continuous in time, and thus described by continuous dynamical maps. We evaluate the performance of such schemes using numerical simulations, and comment on the effectiveness and applicability of continuous error correction for quantum computing.Comment: 6 pages, 3 figures. Presented at QCMC '04 (Univ. of Strathclyde, Glasgow, UK, July 25-29, 2004

Continuous quantum error correction for non-Markovian decoherence

We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.Comment: 16 pages, 4 figures, minor typos corrected, references update