|March 29, 2015|
Quantum error correction for continuously detected errors
We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. In addition, universal quantum computation is possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated. The multiple-channel case is also considered, and it is shown that for arbitrary numbers of channels n physical qubits can protect n-2 logical qubits.
Continuous-variable experiments with a nonlocal single photon
Quantum Coherent Effects in the Presence of External Control Fields
Electron coherence effects, such as the Aharonov-Bohm effect, have been the focus of much interest in condensed matter physics over the past few decades. At low temperatures, low-dimensional conductors demonstrate electron coherence even in the presence of a disordered potential. Here we present results from our initial investigations into applying quantum control methods to coherent electron systems. We examine the effects external control fields, both broadband and pulsed, have on an Aharonov-Bohm ring sample. We discuss the potential for quantum control of electron coherence through the use of both passive control and bang-bang pulses with learning control.
Creating molecular entanglement in functionalized semiconductor nanostructures
The feasibility of creating molecular entanglement in functionalized semiconductor nanostructures is computationally demonstrated. Entangled holes, localized deep in the semiconductor band gap, are generated by electron-hole pair separation after photoexcitation of surface complexes. The approach is illustrated for small arrays of catechol molecules anchored to TiO2-anatase nanowires under vacuum conditions. It is shown that molecular entanglement can persist for hundreds of picoseconds at cryogenic temperature. Moreover, it is shown that the relaxation dynamics of entangled states can be coherently controlled by a sequence of ultrashort 2-pi pulses.
Entangling capacities of noisy non-local Hamiltonians
Jean Christian Boileau, University of Waterloo
with Daniel Gottesman, Raymond Laflamme, Martin Laforest, Casey Myers, David Poulin, Rob Spekkens
Polarization-Based Quantum Key Distribution Without Shared Reference
Dan Browne, Imperial College
with Dan Browne and Terry Rudolph
Efficient linear optics quantum computation with Bell States
Tommaso Calarco, University of Innsbruck
with U. Dorner, P. Julienne, C. Williams, and P. Zoller
Exploiting quantum control for quantum computation in optical lattices:
marker atoms and molecular interactions
Hilary Carteret, Université de Montréal
with M.S. Anwar, D. Blazina, S.B. Duckett, T.K. Halstead, J.A. Jones, C.M. Kozac and R.J.K. Taylor
Preparing high purity entangled states for NMR quantum computing
Conference key-agreement and secret sharing through noisy GHZ states
Kai Chen, Dept. of Physics, University of Toronto
Coauthors: Hoi-Kwong Lo
Various protocols (BB84, Ekert91, B92) and security proofs for two-party common key-agreement have been proposed. We consider here two quantum communication protocols involving 3 parties in the noisy channel setting. The first cryptographic task is for Alice, Bob and Charlie to establish a secure conference key from noisy tripartite Greenberger-Horne-Zeilinger (GHZ) states in the presence of an eavesdropper. The second cryptographic task is for Alice to share a secret with Bob and Charlie by using noisy GHZ states. We use prepare-and-measure protocols where a preparer prepares an ensemble of GHZ states and distribute them to the three parties through some noisy channels. The three parties only need to perform quantum measurements and, subsequently, classical computations and classical communications. In other words, the three users do not need to perform quantum computation or long-term storage of quantum signals. Therefore, our protocol may be feasible with near-future technology.
Paper reference: arXiv:quant-ph/0404133
Decoherence in an Anharmonic Oscillator Coupled to a Thermal Bath
Antonio Di Lisi, Dept of Physics, University of Camerino, Italy
Coauthors: David Vitali
Closed loop techniques for decoherence control and entanglement manipulation
We give a general description of how closed loop techniques can be used in quantum optical systems for decoherence control  and for the generation and manipulation of maximally entangled states of small atomic samples . The schemes consider state of art experimental apparata (cavity QED systems or spin-polarized samples) and employ closed loops based on single photon detections.  S. Zippilli, D. Vitali, P. Tombesi, J. M. Raimond, Phys. Rev. A 67, 052101 (2003).  A. di Lisi, D. Vitali, S. de Siena, F. Illuminati, in preparation
Theoretical Methods and Experimental Implementation of Heat-Bath
Ignacio Franco, University of Toronto
Coauthors: Paul Brumer
Coherent Control of Charge Transport in Photoexcited trans-Polyacetylene
Conjugated polymers are of interest both for their broad technological applications and also because they are model systems to gain fundamental understanding of the properties of soft organic and biological matter. The photoexcited dynamics of these systems is characterized by a strong coupling between, and mutual influence of, nuclear and electronic degrees of freedom. This, in turn, gives rise to a very rich photophysics of solitons, polarons and excitons (self-localized nonlinear excitations associated with a lattice distortion) and constitutes an important distinction between "soft" materials and rigid solids based on semiconductor or crystalline metal materials.
J.D. Franson, Johns Hopkins University
Quantum Computing Using Single Photons and the Zeno Effect
Entanglement Dynamics in a Chaotic System
Entanglement-assisted Coherent Control in Bimolecular Scattering
Jiangbin Gong, Department of Chemistry and The James Franck Institute, University of Chicago
Coauthors: Paul Brumer
Intriguing quantum phase control effects that result from entangled molecular rovibrational states are considered in identical diatom-diatom scattering. Computational results on elastic and inelastic scattering of para H2 and para H2 are presented. The results are also relevant to our understanding of quantum entanglement between indistinguishable molecules.
Timothy F. Havel, MIT
Coauthors: David G. Cory, Chandrasekhar Ramanathan, Joseph Emerson, Yaakov Weinstein, Suddhasattwa Sinha
Quantum Control of Spin Systems by NMR
NMR spectroscopy is an established testbed for quantum control methods in the liquid state, and in the solid state offers a promising approach towards large-scale QIP. I will provide an overview of the current state-of-the-art in these these methods, including quantum process tomography, methods of refocussing inhomogeneous field effects, and a dressed-states approach to the interaction of dipole coupled spin systems with a radiation field.
Kaveh Khodjasteh, University of Toronto, Dept. of Physics
Coauthors: Daniel Lidar
Concatenated Dynamical Decoupling Pulse Sequences
The origins of noise and decoherence in the evolution of open quantum system are the uncontrollable interactions of the parts of the system with an environment that normally challenges production or manipulation of quantum states in experimental realizations of quantum information processing. Dynamical decoupling (DD) pulse sequences are feedback free and conceptually simple means of eliminating the unwanted terms of the interaction Hamiltonian in a system (possibly) coupled to an environment or the bath, by applying fast, strong pulses to the system in regularly paced intervals.
DD pulses, has by far been limited to simple models in which the pulses are applied in series and the removal of the undesired interactions depends on the following: (a) the width of the pulses must be small enough so that the evolution of the system during the pulse can be ignored and (b) the time between consecutive pulses has to be much smaller than the time scales of the bath. These conditions restrict the applicability of simple DD pulses, usually known as parity kicks.
In this work we use an analogy with quantum error correction codes and investigate the idea of concatenating dynamical decoupling pulses to obtain further cancellations of the error terms in the Hamiltonian. To this end we develop a series of renormalized Hamiltonians that are used to estimate the strength of the undesired interactions, after applying each layer of dynamical decoupling. The sources of these Hamiltonians will be the errors due to the pulse imperfections (including the effects of the pulse width) and the errors due to the evolution of the bath between the application of pulses. We further present a criteria in terms of the system-bath interaction Hamiltonian strength HSB, bath's internal Hamiltonian strength HB, the time between consecutive pulses \tau, and the pulse width t, for the overall usefulness of concatenating dynamical decoupling pulses against decoherence. We also compare these results with the threshold calculations in quantum error correction literature.
Robert Kosut, SC Solutions, CA
Coauthors: Ian Walmsley (Oxford University, Oxford, UK firstname.lastname@example.org) and Herschel Rabitz (Princeton University, Princeton, NJ email@example.com)
Quantum Tomography and Detection: Design via Convex Optimization
In this paper we show that a number of problems in quantum state estimation (state tomography), quantum system identification (process tomography) and quantum state and system detection can be cast as convex optimization problems. The great advantage of convex optimization is a globally optimal solution can be found efficiently and reliably, and perhaps most importantly, can be computed to within any desired accuracy using an interior-point method.
Some of the problems addressed in this paper are already known to be convex but have not fully exploited the available convex solvers or duality theory. For example, it is known that Maximum likelihood Estimation (MLE) of the quantum state (density) is a convex optimization. What we also show is that a number of other MLE problems are convex, e.g., estimating the distribution of known states and quantum process tomography in the Kraus operator sum representation (OSR) in a fixed basis. One important problem which is not convex is MLE of Hamiltonian parameters. We show, however, how duality theory can help establish bounds on the parameter estimates for this problem.
Another problem which can be solved via convex optimization is experiment design. (Experiment design here means choosing the number of experiments to be performed in a particular system configuration; a configuration being any number of combinations of sample times, hardware settings, etc. For example, in quantum state photonic tomography, we can determine the optimum number of wave plate setting to achieve a desired estimation accuracy.) In this paper we will apply the experiment design procedure invoked by the Cramer-Rao Inequality to all the MLE problems mentioned above, including MLE of Hamiltonian parameters. We will show that in all these cases the optimum experiment design problem, although integer-combinatoric, can be relaxed to a convex optimization problem whose solution provides upper and lower bounds on the unknown optimal integer solution. The MLE of the state or process can be combined with the optimal experiment design in a ``bootstrapping'' iteration to make the estimation more efficient.
Finally, we also address the problem of designing a detector which is maximally sensitive to specific quantum states. We show that the design problem can be formulated as a convex optimization problem in the matrices of the POVM (positive operator valued measure) which characterize the measurement apparatus, or with a given POVM, the matrices which characterize the OSR in a fixed basis. We specifically address maximizing the posterior probability of detection and show that this is a quasiconvex optimization problem in either the POVM or OSR matrices. Previous work in this area has only considered the joint probability of detection over POVM matrices,
In all the cases described above we show how duality theory can be used in various special cases to give insight into the nature (and possible physical implementation) of the optimal solutions. In addition we will briefly comment on the numerical properties of the convex programming methods required. At present we have some experimental results for some of the above cases.
Debbie Leung , Institute of Quantum Information
with Panos Aliferis, Andrew Childs, Michael Nielsen
A systematic derivation of measurement-based schemes for quantum
Masoud Mohseni, Department of Physics, University of Toronto
Coauthors: Daniel. A. Lidar
Universal Fault-Tolerant Quantum Computation with the Exchange Interaction
The ability of a quantum system to perform arbitrary or "universal" computation is restricted to its naturally available/controllable interactions. It has been shown that quantum systems with controllable exchange interactions can be made computationally universal by encoding the information within a subspace of the full Hilbert space: "encoded universality". However, there has not been any success on development of a general theory to make this encoded universal computation also resilient against decoherence. In this work, we introduce a class of hybrid encoded-universality stabilizer quantum error correcting codes, and demonstrate that quantum error-correction can be performed in systems with controllable exchange interactions. Specifically, we present an analytical method for leakage-correction using only unitary operations generated by exchange interactions. Furthermore, we demonstrate that any arbitrary quantum operation can be performed on these codes without accumulation or propagation of logical or leakage errors. In other words, universal fault-tolerant quantum computation is possible from the exchange interaction.
Ashwin Nayak, University of Waterloo
with Leonard Schulman (Caltech) and Umesh Vazirani (UC Berkeley)
A quantum algorithm for the Ising model
Robert Raussendorf, IQI, Caltech
Coauthors: Simon Anders, Hans Briegel (University of Innsbruck, Austria)
Fault-tolerant quantum computation using graph states
Graph states are highly entangled multi-qubit quantum states which can be created from a product state via an Ising-type (i.e. z-z-) interaction. The neighborhood relation, i.e. which qubit interacts with whom, is specified by a graph.
Graph states form algorithmic resources for quantum computation: for every quantum algorithm there exists (at least) one graph state such that this algorithm can be realized by measuring the graph state qubits in one-qubit measurements . There arises the question of whether the graph state picture of quantum computation is useful for fault- tolerance, too. In particular, can graph state constructions improve the error threshold?
As a simple illustrative example, an efficient circuit for fault- tolerant data storage (i.e. a stabilizer tester circuit) using purified bicolorable graph states  in a gate teleportation scheme  is shown. The more general problem of fault-tolerant universal quantum computation is reduced to fault-tolerantly creating two types of encoded quantum states: - +>:=X - +> and - T>:= (X+Y)/sqrt(2) - T>. Procedures to manufacture these states making use of redundant syndrome information are displayed.
 R. Raussendorf, D.E. Browne and H.J. Briegel, PRA 68, 022312 (2003).
 W. Dür, H. Aschauer and H.J. Briegel, PRL 91, 107903 (2003).
 D. Gottesman and I.L. Chuang, Nature 402, 390 (1999).
Barry C. Sanders, University of Calgary
with Rolf Horn and Karl-Peter Marzlin
Optical quantum fingerprinting
Anatoly Yu. Smirnov , D-Wave Systems Inc.
Quantum control of entanglement by phase manipulation
Vladimir S. Malinovsky
Michigan Center for Theoretical Physics & FOCUS Center, Department of Physics, University of Michigan,
Coauthors: Ignacio R. Sola, Departamento de Quimica Fisica I, Universidad Complutense, 28040 Madrid, Spain
A new method of entangled states preparation of two-qubit systems is proposed. The method combines the techniques of coherent control by manipulation of the relative phase between pulses, and adiabatic control using time-delayed pulse sequences. A two-qubits system with couplings forming a closed-loop configuration allows full preparation of entangled states by controlling the relative phase of the fields. We have shown that time-delayed sequences provide very stable mechanisms to control the dynamics in the adiabatic regime. The relative phase between the pulses is essential in preparing entanglement with specific phase relationships. We have obtained the exact relationship between the control phase and the phase of the prepared entangled state. Both counterintuitive and intuitive pulse sequences are needed to prepare entanglement with all possible phases. In the resonant scheme we have shown that the relative phase between the pulses is the most sensitive parameter that governs the entanglement in the counterintuitive sequence, while the pulse area is the most sensitive parameter that controls entanglement in the intuitive sequence. The off-resonant scheme provides the most stable mechanism to prepare specific entangled states. We believe that the present scheme provides additional flexibility for quantum control of entanglement and could facilitate experimental implementation of quantum logic gates in a few qubits systems.
All-optical processing in coherent nonlinear spectroscopy
The use of shaped ultrashort pulses has enabled achievement of coherent nonlinear vibrational spectroscopy, where both the vibrational excitation and its probing are done by the same laser pulse. Here we show that shaped pulses can not only excite and probe coherent molecular vibration but can also perform simple coherent processing and analysis of the observed spectra. This is done by inducing intereference between contributions to the total signal by quantum paths passing through different intermediate states. Due to its coherent nature, this type of optical processing results in significantly improved background rejection and in signal enhancement. Schemes allowing for single-pulse coherent multidimensional spectroscopy will also be discussed.
Unconditional Security of the Bennett 1992 quantum key-distribution protocol over a lossy and noisy channel
Kiyoshi Tamaki, Perimeter Institute for Theoretical Physics
Coauthors: Masato Koashi, Norbert Luetkenhaus, Nobuyuki Imoto
We study the unconditional security of the Bennett 1992 quantum key-distribution
protocol (B92) over a lossy and noisy channel. For the simplicity of
the analysis, we assume that Alice encodes bit values into the single
photon polarization state, and Bob's detectors discriminate between
single photon states on one hand and vacuum state or multi-photon states
on the other hand. To prove the security, we first propose an unconditionally
secure protocol that employs the entanglement distillation protocol
(EDP) based on a filtering operation and the Calderbank-Shor-Steane
(CSS) quantum error correcting codes. The bit errors and the phase errors,
which have to be estimated for the EDP based protocol, are correlated
after the filtering operation, and we can bound the phase error rate
from the observed bit error rate by an estimation method involving nonorthogonal
measurements. By showing the equivalence between this EDP based protocol
and the B92, we have proven the unconditional security of the B92.
Quantum Coherent Control of Current and Chiral Cat States
Ioannis Thanopulos, Weizmann Institute of Science
Coauthors: Petr Kral, Moshe Shapiro
We develop a robust methodology for preparation of novel quantum entangled states, by combining phase-sensitive coherent control techniques with the use of nonclassical light states. The idea is that population components of different ``semiclassical phases" in such light states guide the system to different components of the entangled states. Thus, a system of the |A> and |B> material states, driven by light in the |alpha> +|-alpha> cat state, can get in the |A>|alpha> + |B>|-alpha> entangled state. In this way, we can prepare ``current" or ``chiral" cat states, if |A> and |B> are momentum states of opposite directionality or chiral states of left-handed and right-handed symmetries, respectively.
We introduce quantum protocols for ensuring the secrecy of the individual votes of a number of voters. The votes are recorded in a distributed system using local operations yet the tally of the votes exists nonlocally. At every stage the tally remains hidden to local observers which ensures the secrecy of individual votes. The exact value of the tally during the voting can only be determined if all parties share a maximally entangled state and they cooperate. If one party, say a scrutineer, refuses to cheat in this manner, the absolute secrecy of the tally is guaranteed. At the end of the voting process the tallyman and scrutineers are given access the whole system, which allows them to determine the value the tally.
The availability of four-photon entanglement allows demonstrating probabilistic quantum logic gates, such as the controlled-not (cnot) and sign-shift gate, as well as path-entanglement of up to four photons. A cnot gate  was achieved by using polarization entangled qubits and polarizing beamsplitters. A similar configuration of the setup for the cnot-experiment leads to a sophisticated interferometer , which was required for the first experimental observation of the reduced deBroglie wavelength of a nonlocal four-photon state. One of the central elements in linear optics quantum computing is a conditional phase shift such that if one photon is present, no phase shift arises, but if two photons are present, the state achieves the phase shift of . Most recently such a gate  was realized in our group using only one beamsplitter.
 S.Gasparoni, J.-W.Pan, P.Walther, T.Rudolph, A.Zeilinger, Realization
of a Photonic CNOT Gate sufficient for Quantum Computation, accepted
for publication in Phys. Rev. Lett.
 K.Sanaka, T.Jennewein, J.-W.Pan, K.Resch, A.Zeilinger, Experimental Nonlinear Sign Shift for Linear Optics Quantum Computation, Phys. Rev. Lett. 92, 017902 (2004)
Highly efficient frequency conversion in double lambda systems without
maximal atomic coherence
The irrelevance of phase matching in obtaining efficient four-wave mixing (FWM) in various systems has recently been stressed. For example, it has been demonstrated that efficient frequency conversion can be achieved in a double lambda system within the coherence length, by establishing electromagnetically induced transparency (EIT), via maximal Raman coherence. We have re-examined this claim and found that the propagation distance for efficient conversion can also be shortened by increasing the intensity of the generating beams. We have therefore implemented an alternative scheme, based on the transverse intensity profile control of the parametrically interacting fields by means of ordinary (one-photon) or Raman self-focusing and cross-focusing. We find that in the presence of such focusing, the on-axis intensity of the generated field is much higher than in the absence of focusing, provided the two-photon coherence is not maximal. Our results clearly indicate that saturation can replace EIT for avoiding losses by absorption, and that the implementation of sufficiently intense applied fields is a sufficient condition for making phase matching irrelevant and for obtaining efficient frequency conversion within the coherence length.
Feedback Control of Open Quantum Systems with Linear Dynamics: Recent Results
Howard Wiseman, Griffith University
Coauthors: Andrew Doherty
Quantum feedback control is the control of the dynamics of a quantum system by feeding back (in real time) the results of monitoring that system. For systems with linear dynamics, the control problem is amenable to exact analysis. In these cases, the quantum system is equivalent to a stochastic system of classical phase-space variables with linear drift and constant diffusion, and with a measured current (e.g. a homodyne photocurrent) linear in the system variables. However, the classical evolution is constrained in order to represent valid quantum evolution. We quantify this in terms of a linear matrix inequality (LMI) relating the drift and diffusion (a sort of zero temperature fluctuation-dissipation theorem), and another LMI for the covariance matrix of the possible conditioned states (i.e. under all possible monitoring schemes consistent with the master equation). For manipulable systems (i.e. where the experimenter has arbitrary control over the parameters in a Hamiltonian linear in the system variables) the covariance of the conditioned state is all that is needed to calculate the effectiveness of the feedback. In this case the double optimization problem reduces to a semidefinite program, which can be solved efficiently in general. We illustrate this with an example drawn from quantum optics.
It is known that the "bang-bang" method is effective to suppress the decoherence caused by the interaction between qubit and environment. Conventionally, the degree of suppression is discussed in the limit of extremely short pulse interval. Since this condition is difficult to execute in experimental settings, we will propose a strategy where the condition for the pulse interval can be released by paying attention to the dynamical behavior of the environment. We find that the coherence can be periodically recovered by synchronizing pulse interval with the dynamical motion of the reservoir. This is because that the non-Markovian property of the system (memory effect of environment) is the physical background of the suppression of decoherence by synchronized multipulse application. We will show that we can extend this strategy to control disentanglement.