# SCIENTIFIC PROGRAMS AND ACTIVITIES

May  4, 2016

## Quantum Information and Quantum Control Conference July 19- 23, 2004

### Abstracts

Robert Alicki, University of Gdansk
Is quantum error correction feasible?
It is rather generally accepted that without, at least in principle, effective quantum error correction schemes quantum computers cannot overpower classical ones and provide merely another very interesting example of hybrid digital-analog computing machines which do not violate Church-Turing thesis. The main aim of this talk is to discuss critically the existing schemes of error correction schemes and the threshold results for the fault-tolerant quantum computation. The recent progress in formulating and proving no-go theorem for mantaining unknown quantum state in the presence of noise and its relevance for the quantum error correction schemes will be presented also.

Thomas Baumert, Universitaet Kassel
Quantum control in intense phase shaped laser fields
Joint work with M. Wollenhaupt, A. Assion, A. Präkelt, D. Liese, C. Sarpe. The ability to selectively steer quantum systems from an initial state |i> to any desired final state |f> with the help of suitably shaped light fields opens up undreamed-of prospects for applications in physics, chemistry, biology and engineering ranging from quantum computation to the control of complex chemical reactions. It turns out that the manipulation of the interferences of matter waves is the key ingredient of quantum control. In the weak field regime, i.e. when perturbation theory is operative, a couple of methods have been devised and are well understood [1] [2]. In addition, strong field control schemes such as the rapid adiabatic passage (RAP) and the stimulated Raman adiabatic passage (STIRAP) with all their extensions have been demonstrated to achieve population transfer with 100 % efficiency and remarkable robustness (see also [1] [2]). A theoretical method to obtain laser pulses which effectively excite a preselected target state is provided by the optimal control theory (OCT) [3]. The experimentalist's analogue to OCT, the so-called optimal control experiments (OCE) makes use of the combination of pulse shaping techniques with adaptive feedback learning loops (see [4] for theory and [5] [6] for selected experimental realizations). This technique allows to optimize virtually any conceivable observable with enormous success. However, especially in strong field cases the underlying physical mechanism cannot be inferred from the electrical fields obtained by this procedure.
Our approach is based on the investigation of specific control objectives studied on simple well defined model systems using well characterized femtosecond laser pulses in order to elucidate possible physical mechanisms of quantum control especially in strong fields. To that end we combine time resolved photoelectron spectroscopy, femtosecond pump-probe and pulse shaping techniques together with atomic / molecular beam techniques.
In a first experiment we demonstrate that the coherence properties of femtosecond laser pulses can be transferred to electron wave packets in the continuum. The coherence properties of the electron wave packet are studied in an interference experiment where we use a sequence of two time delayed laser pulses to ionize potassium atoms [7].
In a second experiment on potassium atoms we investigate strong field quantum control with shaped femtosecond laser pulses where the manipulation of the quantum mechanical phase with intense phase modulated pulses leaves a fingerprint in the measured photoelectron spectra [8]. Pulse sequences, chirped pulses and sinusoidally phase modulated pulses as well as "closed loop" adaptive pulse shaping are employed to elucidate a robust physical mechanism of adaptive strong field control based on the selective population of dressed states.

[1] S. A. Rice and M. Zhao, Optical control of molecular dynamics (Wiley, New York, 2000).
[2] M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes (John Wiley & Sons, Hoboken, New Jersey, ed. 1, 2003).
[3] A. Peirce, M. Dahleh, H. Rabitz, Phys.Rev.A 37, 4950-4964 (1988).
[4] R. S. Judson and H. Rabitz, Phys.Rev.Lett. 68, 1500-1503 (1992).
[5] A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, G. Gerber, Science 282, 919-923 (1998).
[6] T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, Ch. Horn, D. Liese, T. Baumert, Phys.Rev.Lett. 92, 208301-1-208301-4 (2004).
[7] M. Wollenhaupt, A. Assion, D. Liese, C. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, G. Gerber, Phys.Rev.Lett. 89, 173001-1-173001-4 (2002).
[8] M. Wollenhaupt, A. Assion, O. Bazhan, Ch. Horn, C. Sarpe-Tudoran, M. Winter, T. Baumert, Phys.Rev.A 68, 015401-1-015401-4 (2003).

Charles H. Bennett, IBM
Back Communication and Forward Capacities of Quantum Channels
Long ago Shannon showed that classical back communication cannot increase a classical channel's forward capacity. For quantum channels the situation is more complicated. It is known that classical back communication can increase quantum capacity, but no example was known where it increased a quantum channel's classical capacity. Granting a widely held additivity conjecture, we have found channels where this occurs. These channels may be thought of as having a "data" input and output, as well as a control input that partly influences, and a control output that partly reveals, which of a set of unitary evolutions the data undergoes en route from input to output. The channel is designed so that the data's evolution can be exactly inferred by a classically coordinated processing of the control output, and a reference system entangled with the control input, but not from either of these resources alone. The same family of channels can be used to demonstrate various other capacity inequalities. Joint work with Igor Devetak, Peter Shor, and John Smolin. quant-ph/0406086.

Gilles Brassard, Université de Montréal
A Quarter of Century of Quantum Cryptography
For ages, mathematicians have searched for a system that would allow two people to exchange messages in absolute secrecy. Around the middle of last century, Shannon proved that this dream is possible if and only if the legitimate participants share a random secret key as long as the message they wish to transmit. But Shannon's theorem did not take account of the quantum world in which we live. When information is appropriately encoded as quantum states, any attempt from an eavesdropper to access it yields partial information at best and entails a probability of spoiling it irreversibly. This unavoidable disturbance can be detected by the legitimate users. This phenomenon can be exploited to implement a cryptographic system that is unconditionally secure even against an eavesdropper with unlimited computing power and technology, with no need for a long shared secret key. Sophisticated prototypes have been built in several countries, over tens of kilometres of ordinary optical fibre as well as line-of-sight optical paths. Satellite-based implementations are being contemplated.

In this talk, I shall provide a historical perspective on quantum cryptography, which goes back 35, 25 or 20 years in the past, depending on where you start counting. I shall also discuss the present and the future of the field.

No prior knowledge of quantum cryptography will be assumed.

Philip H. Bucksbaum, FOCUS Center and Department of Physics, University of Michigan
Control Analysis based on Learning Feedback Experiments
Feedback learning algorithms are widely used to control ultrafast optical pulse shapes. A new problem in the study of quantum control of many-body systems is how to use the solutions found by these algorithms to learn about the system quantum dynamics. We are developing techniques to analyze the principal controls that are discovered by a genetic learning algorithm during its search. I will discuss how this technique can be used to reveal the number and character of the degrees of freedom responsible for control, and may aid in the construction of an effective Hamiltonian for the dynamics.

Richard Cleve, University of Calgary
Consequences and Limits of Nonlocal Strategies
We investigate connections between (a) the nonlocal effects that can occur when entangled quantum information is shared between two parties and (b) certain
notions of "proof systems" that arise in computational complexity theory. One way to think about Bell inequalities is to imagine that two "provers" are trying
to convince a "verifier" that a certain mathematical object exists. In a classical two-prover interactive proof system, the verifier becomes convinced
only when the object exists. If prior entanglement between the provers is introduced into the model then such systems can become invalid, and the
expressive power of the underlying model can, in some respects, become weaker.

This is joint work with Peter Hoyer, Ben Toner, and John Watrous.

David DiVincenzo, IBM Research
Control and decoherence in Josephson junction qubits
Josephson junction qubits are unique in that they are specified entirely as electrical circuits. I will review the general theoretical procedure for turning the description of the circuit into a Hamiltonian. This Hamiltonian can be separated into a system part, an environment part, and a coupling part. I will review what controls are available in the system part, how we estimate the decoherence from the coupling and bath parts, and how this theory has been applied to a variety of flux-based Josephson qubits in the laboratory.

Mark Dykman, Michigan State University
Localizing excitations in a quantum computer with perpetually coupled qubits
Joint work with L. Santos and M. Shapiro. Strong many-excitation localization is studied in a chain of perpetually coupled qubits, which describes many proposed models of a quantum computer. In these models, the transition frequencies of the qubits can be individually controlled. We propose a sequence of the qubit transition frequencies, that eliminates resonant excitation transfer between both nearest and remote neighbors. It leads to strong on-site single-excitation localization. It also leads to a large lifetime of strongly localized many-excitation states. This lifetime exceeds the reciprocal frequency of inter-qubit excitation hopping by six orders of magnitude for a comparatively narrow bandwidth of the qubit transition frequencies. The proposed frequency sequence is robust with respect to small errors. This makes quantum computing with time-independent qubit coupling viable.

Mark Eriksson, University of Wisconsin
Silicon/Silicon-Germanium for Quantum Computation
Silicon/Silicon-Germanium quantum wells have many properties that make them interesting candidates for spin-based quantum computation. I will review recent progress in achieving low noise quantum dots and Coulomb blockade in strained silicon/silicon-germanium quantum wells. I will also discuss recent advances in top-gating silicon quantum dots. An important spin decoherence mechanism in quantum wells in any material is the fluctuating effective magnetic field that arises due to scattering and the Rashba effect. I will provide an overview of this effect and discuss recent measurements on six different quantum wells revealing a wide range in Rashba parameters. Finally, silicon differs from many other quantum well materials in that its conduction band has a six-fold valley degeneracy in its bulk state. This six-fold degeneracy is lifted by both strain and confinement in silicon quantum wells. I will present a simple and direct spectroscopic measurement of the key splitting, the valley splitting, over a wide magnetic field range.

Daniel Gottesman, Perimeter Institute
High Fidelity to Low Weight
In order to establish a property in cryptography, generally we have to do some test, and rarely is this test completely reliable. As a trivial example, we might wish to test that a state is |0>, but we do so on a large ensemble of such states, and only sample a small fraction of them. Even if the state passes the test, we cannot be sure that all the states are |0>; indeed, an adversary could include a small number of |1> states with a fairly small chance of being caught. In general, the state that passes the test will thus not be an all-|0> state, but rather a state with high fidelity to the subspace of low-weight states, which are mostly |0>, but with a few |1>s. In quantum cryptography, we could in general have an entangled state with this property. I will discuss a lemma about such "high fidelity to low weight" states, bounding their distribution in a complementary basis. I have so far used this lemma twice in security proofs, and I will describe the more recent such application, to quantum key distribution with imperfect apparatus.

Ronnie Kosloff, The Hebrew University of Jerusalem
Quantum molecular computing: Optimal control theory for unitary transformations
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The general quantum compiler is the inverse problem of finding the field that generates a specific unitary transformation. We study this problem within the context of a quantum model composed of a large Hilbert space where only a small fraction serves to store quantum information. Specifically we study the inversion of a Fourier transform using as registers the vibrational levels of the $X^1\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\Sigma^+_u$ electronic state induce the transitions. Using optimal control theory light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. The implementation of the $Q$ qubit Fourier transform in the Na$_2$ molecule was carried out for up to 5 qubits.
The classical computation effort for implementing the quantum compiler was found to scale exponentially with the number of levels. This estimate was based on Krotov's method for optimal control theory solving the inversion required to obtain the algorithm with a given fidelity. The resources required are related to the number of controlled interference pathways $K$ used to construct the evolution. For low intensity $K$ scales linearly with the product of light-field bandwidth and pulse duration. But $K$ increases exponentially with the pulse intensity. This means that only a moderate increase in intensity is required with increase
in the number of qubits. The possibility of teaching the molecule to compute via an experimentally implemented feedback algorithm is explored.\\
Jose P. Palao and Ronnie Kosloff,
Phys. Rev. Lett., {\bf 89},\hspace{0.25em}188501 (2002).\\
Jose P. Palao and Ronnie Kosloff,
Phys. Rev. A, {\bf 68},\hspace{0.25em}062308 (2003).

Manny Knill, NIST
Postselected Quantum Computation
Postselected quantum computation is quantum computation that succeeds and gives the correct answer with probability 0<p<1. For each instance of the computation, whether it succeeded is known. Postselected quantum computation can be implemented fault-tolerantly with high depolarizing error probabilities per gate (well above 1%). The techniques that achieve this can be modified for fault-tolerant conditional preparation of states that can be used in standard fault-tolerant quantum computation. Heuristics and direct simulation indicate that with these techniques, it is possible, at least in principle, to realize scalable quantum computers with depolarizing error probabilities per gate well above 1%.

Gershon Kurizki, The Weizmann Institute of Science
A Unified Approach to Dynamical Control of Decoherence
Joint work with A.Kofman , S.Pellegrin and D. Petrosyan. We present our progress towards the development of a comprehensive strategy for the prevention or suppression of decoherence and decay in entangled multipartite systems coupled to arbitrary reservoirs or sources of fluctuations. This strategy employs dynamical perturbations of the system by coherent electromagnetic fields . The perturbations are tailored to the spectra of the couplings between the system
and its environment , based on a universal master equation developed by us for arbitrarily driven multidimensional systems undergoing non Markovian relaxation. Dynamically induced cooperative multipartite effects are used to suppress the decoherence more effectively , but strictly individual relaxation of the different particles to their respective environments can be dynamically suppressed as well. Surprisingly , nonadiabatic periodic modulation of the energy levels may outperform adiabatic manipulations in suppressing decoherence and maintaining high fidelity of quantum logic.

Raymond Laflamme, University of Waterloo
Experimental quantum error correction
In the past few years, there has been a flurry of activity in the area of experimental quantum information processing. Many technologies have demonstrated control of a few qubits by characterising noise and implementing various protocols and algorithms. One of the main obstacle for scaling up is the fragility of quantum information. Fortunately quantum error correction has been discovered. I will give a brief review of the importance of quantum error correction and of various experiments which have implemented some of its elements. I will discuss NMR experiments which have implemented two qubit error detecting code and quantum error correcting codes correcting for phase and full one bit error. I will also describe the encoding of information in a noiseless subsystems which protects against collective rotation. Then I will show how these noiseless subsystems can be useful to protect states used for quantum cryptography. I will also discuss quantum error correction using ion traps and photonic technologies. I will put an emphasis on what are we and what can we learn by implementing the protocols. I will conclude by pointing the task that lies ahead to implement robust quantum information processing.

Daniel Lidar, University of Toronto
Hybrid quantum error prevention, reduction, and correction methods
Various methods have been designed to overcome decoherence and noise in quantum information processing tasks. Well-known examples are quantum error correcting codes, dynamical decoupling, and decoherence-free subspaces/subsystems. Each method has its limited set of advantages and realm of applicability. It is advantageous to consider a combination of these various methods in order to optimize their performance and compatibility with experimental constraints. This talk will survey our recent progress along these lines. It appears that hybrid methods are particularly well-suited to spin-based solid-state quantum computing proposals, as well as to trapped ions. Time permitting, these applications will be discussed as well.

Norbert Lütkenhaus, University of Erlangen
Quantum Correlations in Quantum Cryptography
Joint work with M. Curty (Erlangen), M. Lewenstein (Hannover). In basic quantum communication protocols one party creates quantum states and uses a quantum channel to transmit it to another party that performs immediately some measurement on it. This means, we effectively create correlated (classical) data between distant parties. In order to use the power of quantum mechanics, these correlation must show effects of quantum mechanics.

In the specific example of quantum key distribution one uses the correlations to distill a secret key in (classical) public discussion protocols e.g. via sifting, error correction and privacy amplification. We give a necessary condition for the success of any public discussion protocol: the observed correlations should allow to prove the presence of an internal, virtual state of entanglement in the distribution. This poses a first test whether any presented real quantum key distribution is indeed useful for the desired purpose. Moreover, a gap between the parameter regime of proven security of given realistic schemes and the regime of proven presence of vitual entanglement furthers the search for the optimal public discussion protocol.

Ari Mizel, Penn State University
Teleportation in ground state quantum computation
Ground state quantum computation is an alternative to the usual time-dependent approach to quantum computation. This alternative (which possesses some
noteworthy similarities to existing digital computer architectures) presents its own challenges and advantages. We review ground state computation and show how it can be improved using teleportation methods.

Herschel Rabitz, Princeton University
The Landscape for Controlling Quantum Phenomena

Controlling quantum phenomena includes applications ranging from steering about a dynamic observable through the creation a particular unitary transformation for quantum information science applications. Regardless of the application, the desired objective is a functional of the input control field. In the case of quantum state preparation, mounting simulations and laboratory evidence suggest that attaining good yields is surprisingly easy even in cases where hundreds of control variables are being searched over. The reason for this behavior is shown to lie in a kinematic analysis of controlled quantum phenomena. The control landscape is defined as the desired output as a functional of the control field, or alternatively, as a function of a complete set of discrete variables. The control landscapes are shown to have particularly simple structure for the cases of state or unitary transformation preparation. The topology of the landscapes will be discussed in relation to the ease of finding effective controls and robustness to control fluctuations.

Stuart A. Rice, The University of Chicago
Variations on Adiabatic Passage in Optical Control of Molecular Processes
A number of variations on adiabatic passage for the realization of efficient and selective population transfer in both the gas and liquid phases will be discussed. The advantageous use of decaying quantum states and/or the influence of continuous measurements during the population transfer will be stressed.

Aephraim M. Steinberg, University of Toronto
Shedding a Bit of Information on Light: Measurement and Manipulation of Quantum States
Over the past decade, a revolution has begun in the way we think about physics, putting information at the centre of quantum mechanics. In this talk, I will describe some recent experiments with nonclassical states of photons and of trapped atoms, showing how information can be stored in quantum systems and how it can be extracted. In particular, quantum state and process tomography will be used to show how quantum devices can be characterized, a necessary step for quantum computation and error correction. The problem of unambiguous discrimination between non-orthogonal quantum states will also be presented, showing that non-unitary transformations can enable us to achieve things which would be impossible with only unitary operations. We will also demonstrate the application of such operations to the generation of novel 3-photon entangled states, previously experimentally unattainable. If time permitted, some more controversial topics such as "interaction-free" measurement, "weak" measurement, and Hardy's "retrodiction" paradox would also be touched upon.