Quantum Control of a Single Qubit

Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyse a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two non-orthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a non-projective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realises the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.Comment: 12 pages, 7 figures, v2 includes new references and minor change

Loss-tolerant parity measurement for distant quantum bits

We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that for a probe electromagnetic field in a particular quantum state, namely a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary back-action on the probe state. This leads to a parity measurement protocol where the main effect of the transmission losses is a decrease in the measurement strength. By repeating the non-destructive (weak) parity measurement, one achieves a high-fidelity entanglement in spite of a significant transmission loss

Beating the break-even point with a discrete-variable-encoded logical qubit

Quantum error correction (QEC) aims to protect logical qubits from noises by utilizing the redundancy of a large Hilbert space, where an error, once it occurs, can be detected and corrected in real time. In most QEC codes, a logical qubit is encoded in some discrete variables, e.g., photon numbers. Such encoding schemes make the codewords orthogonal, so that the encoded quantum information can be unambiguously extracted after processing. Based on such discrete-variable encodings, repetitive QEC demonstrations have been reported on various platforms, but there the lifetime of the encoded logical qubit is still shorter than that of the best available physical qubit in the entire system, which represents a break-even point that needs to be surpassed for any QEC code to be of practical use. Here we demonstrate a QEC procedure with a logical qubit encoded in photon-number states of a microwave cavity, dispersively coupled to an ancilla superconducting qubit. By applying a pulse featuring a tailored frequency comb to the ancilla, we can repetitively extract the error syndrome with high fidelity and perform error correction with feedback control accordingly, thereby exceeding the break-even point by about 16% lifetime enhancement. Our work illustrates the potential of the hardware-efficient discrete-variable QEC codes towards a reliable quantum information processor.Comment: Main text: 8 pages, 3 figures, 1 table; Supplement: 12 pages, 8 figures, 2 table

Préparation et stabilisation de systèmes quantiques

This thesis tackles the problem of preparing and stabilizing highly non classical states of quantum systems. We consider specific models based on current experiments in cavity quantum electrodynamics, Josephson circuits and ultra-fast coherent quantum control. The problem is posed in the framework of control theory where we search for a control law which prepares or stabilizes a desired target state.Of particular interest to us are target states with no classical analog: superposition and entangled states. More generally, we propose a scheme for the stabilization of a manifold of quantum states, thus introducing some new ideas for autonomous quantum error correction in a cavity. Close collaborations with experimentalists helped us in the design of control protocols which are readily employable in the laboratory. Experimental demonstrations are currently being implemented and preliminary measurements are in good agreement with the theory introduced in this thesis.Cette thèse s'intéresse au problème de préparation et de stabilisation de systèmes quantiques. Nous considérons des modèles correspondant à des expériences actuelles en électrodynamique quantique en cavité, circuits Josephson, et de contrôle quantique cohérent par laser femtoseconde. Nous posons les problèmes dans le contexte de la théorie du contrôle et nous proposons des lois de commande qui préparent ou stabilisent des états cibles. En particulier, nous nous intéressons à des états cibles qui n'ont pas d'analogue classique: des états superpositions et intriqués. De plus, nous proposons une commande pour la stabilisation d'un sous-espace de l'espace des états, contribuant ainsi au domaine de la correction d'erreur quantique. Ces résultats ont été obtenu en étroite collaboration avec des expérimentateurs. Des mesures expérimentales préliminaires sont en bon accord avec certaines prédictions théoriques de cette thèse

Information preserving structures: A general framework for quantum zero-error information

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We also classify distinct operational criteria for preservation (e.g., "noiseless", "unitarily correctible", etc.) and introduce two new and natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational critera, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel's information-preserving structures.Comment: 29 pages, 19 examples. Contains complete proofs for all the theorems in arXiv:0705.428