II Cambridge-MIT Q.Info workshop - abstracts
A. Talks
E. Farhi (MIT)Quantum Adiabatic Evolution versus Simulated Annealing"
abstract tba
N. Boulant (MIT)
Probing and controlling decoherence
Quantum process tomography is the characterization of an unknown quantum evolution, which may include decoherence and relaxation in addition to unitary dynamics. The most general description of such a process is as a Kraus operator sum. Because the observables are quadratic in the matrix elements of the Kraus operators, however, it is more convenient to first determine the "supermatrix" of the overall superoperator, regarded as a linear transformation on the space of "columnized" density matrices. This can be done by linear least squares fits to the results of quantum state tomography over a set of input density matrices which spans all possibilities.
In this talk, I will present the basic ideas of quantum process tomography and illustrate them with some nuclear magnetic resonance data on a two-qubit system. With additional numerical methods, the reconstruction of the generator of the superoperator allows to determine the Lindblad operators that cause decoherence. Following these results, I will briefly discuss some quantum error correction schemes such as decoherence free subspaces and noiseless subsystems to counteract some instances of noise processes.
S. Shahriar (Northwestern/MIT)
Constraints on Qubit Operations Due to
the Bloch-Siegert Oscillation
In
many situation where a quantum bit (qubit) is represented by two non-degenerate
states
of a massive particle, it is necessary to apply an electromagnetic field
at a frequency
matching
the energy difference between these states, in order to produce an arbitrary
rotation
of
the qubit. Such operation are
at the heart of quantum computing, and are also necessary in
some
cases for quantum communication via teleportation. In
order to minimize the decoherence
rate
of such a qubit, one often chooses to use low energy spin transition, which
can be mediated
by
either a direct application of a radio-frequency field, or an optically-off-resonant
Raman
transition
[1]. In general, one is interested
in performing these transitions as fast as possible.
As
such, it is desirable to use a strong Rabi frequency. The
ratio of the Rabi frequency to the
qubit
transition frequency, is therefore not necessarily very small. Under
this condition, one can
not
ignore the effect of the so-called counter-rotating term in the Hamiltonian
that describes the
interaction. One
well-known consequence of this is that the effective transition frequency
is shifted
from
the free-particle value by an amount known as the Bloch-Siegert shift [2,
3]. Recently, we
have
shown that there is another effect associated with it: namely the Bloch-Siegert
oscillation.
Here,
we consider the potentially deleterious effect of this oscillation on the
qubit rotation.
Specifically, we show that the degree of excitation (e.g., the amplitude of the excited state) depends not only on the product of the Rabi-frequency and the duration of the excitation, but also on the phase of the field at the time the interaction starts. The scale of this effect is proportional to the ratio of the Rabi-frequency and the transition frequency. For example, if the ratio is 0.2, the phase-dependent part of the qubit state amplitudes can be as large as 0.1. Thus, in order to ensure deterministic evolution of the qubit, one has to keep track of the phase of the excitation field at the location of the qubit. Alternatively, one has to limit the strength of the Rabi frequency to a level dictated by the precision required of the particualr qubit operation involved. We note that this effect is present for both direct radio-frequency excitation, as well as for indirect Raman excitation. We discuss a method of tracking this phase for qubits based on Zeeman sub-level transitions in an Alkali atom.
1.
?Long Distance, Unconditional Teleportation of Atomic States via Complete
Bell State
Measurements,?
S. Lloyd, M.S. Shahriar, J.H. Shapiro, and P.R. Hemmer, Phys. Rev.
Lett.87,
167903 (2001).
2.
?Determination of the Phase of an Electromagnetic Field via Incoherent
Detection of
Fluorescence,?
M.S. Shahriar, P. Pradhan, and J.
Morzinsky, submitted to Phys. Rev.
Letts.(available
on LANL server).
3. ?Bloch-Siegert oscillation for detection and quantum teleportation of the phase of an oscillating field,? M.S. Shahriar proceedings of the Conference on Quantum Optics 8, Rochester, NY, July 2001.
D. Williams (Cambridge / Hitachi)
Silicon-based Structures for Quantum Information
Processing
There are several projects in quantum information processing currently in progress at the Hitachi Cambridge Laboratory, in collaboration with the Microelectronics Research Centre of Cambridge University and the Materials Science Department of Oxford University. These are aimed at practical implementations of quantum information processing, and are largely, but not exclusively, based on the existing expertise within the laboratories in single-electronics and coherent charge transport. This paper will describe experiments performed on devices made using processes compatible with silicon technology.
Nanometer scale devices are being used to investigate the possibility of making solid-state qubits based on charge and spin states in multiple quantum dots. Single and multiple quantum dots with typical diameters of 30nm are fabricated in silicon:germanium on insulator, using electron-beam lithography, in an arrangement which allows near-independent control of dot energies and barrier strengths. Transport measurements have shown good noise characteristics, and the ability to control the interaction between adjacent dots, as well as the occupancies of the individual dots. These structures are being integrated with single-electron electrometers to make full qubits.
T. Orlando (MIT)
Superconducting Qubits for Quantum Computation
We are investigating a quantum circuit of a superconducting loop interrupted by three Josephson junctions and fabricated in Nb. The two states of the qubit have oppositely directed persistent currents of about a microamp and correspond to the center-of-mass motion of millions of Cooper pairs.
The goal of the present research is to use superconducting quantum circuits to model the measurement process, understand the sources of decoherence, and to develop scalable algorithms. A particularly promising feature of using superconducting technology is the potential of developing high-speed, on-chip control circuitry with SFQ electronics. The picosecond time scales of SFQ electronics means that the superconducting qubits can be controlled rapidly on the time scale that the qubits remain phase-coherent. Recent experiments on our qubit as well as in other superconducting systems will be reviewed.
This work at MIT is in collaboration with the University of Rochester, Harvard, and the Technical University of Delft and is supported in part by ARDA through a DoD and AFOSR DURINT grant and through an ARO grant.
C. Barnes (Cambridge)
A review of quantum processor work in the
Cavendish Laboratory
C. Ramanathan (MIT)
Exploring large spin systems with solid
state NMR
In the approach to designing and implementing a scalable quantum computer, it is essential that we develop the ability to accurately perform desired unitary transformations in a large Hilbert space, as well as understand the sensitivity to decoherence of states in this space. In this talk we describe the creation of spin states containing multiple quantum coherences using solid state nuclear magnetic resonance techniques, and show how the properties of these states can be inferred by encoding them in different basis representations. We also explore the sensitivity of these states to noise and decoherence. These multiple quantum coherences correspond to off-diagonal terms in the density matrix in the Zeeman basis, with higher order coherences located farther off the diagonal.
The nuclear spins in a dielectric solid such as calcium fluoride have very long spin-lattice relaxation times, ranging from minutes to days depending on the concentration of paramagnetic impurities present in the crystal. It is therefore possible to investigate the dynamical behaviour of these spins under the action of their mutual dipolar couplings and applied radiofrequency perturbations, while they are essentially isolated from their environment. Average Hamiltonian Theory provides a framework within which we can design experiments in which the internal Hamiltonian of the spins is modulated by radiofrequency pulses so that the spins appear to evolve under a suitably designed effective Hamiltonian. This methodology has been used extensively in the design of NMR experiments.
Such studies provide us with an experimental paradigm within which we can begin to understand the dynamics of spins in a large Hilbert space under the action of a many-body Hamiltonian.
S. Lloyd (MIT)
The computational capacity of the universe
All physical systems register and process information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The universe is a physical system. This paper quantifies the amount of information that the universe can register and the number of elementary operations that it can have performed over its history. The universe can have performed 10^{120} ops on 10^{90} bits (10^{120} bits including gravitational degrees of freedom).
M. Christandl (Cambridge/ETH)
The Quantum Analog of Intrinsic Information
We consider a cryptographic scenario with three parties Alice, Bob and Eve, each given a random variable with joint probability distribution P(X,Y,Z). The goal of Alice and Bob is to achieve a common secret key by public discussion from which Eve has virtually no knowledge. A measure for the correlation of Alice and Bob with respect to Eve is the so-called 'Intrinsic Information'. Based on work from Gisin and Wolf, who suggest an analogy between intrinsic information and entanglement, we introduce an 'information-theoretic' entanglement measure for bipartite mixed states and construct thereby a quantum analog to Intrinsic Information. We show some properties of the proposed measure and give an upper bound as well as suggestions for further research.
A. Kent (Cambridge / HP labs)
Quantum Theory and the Collapse Locality
Loophole
Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no non-local correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise theory of state vector reduction.
Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes.
Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it obvious that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments -- the {\it collapse locality loophole} -- which exists because of the possible time lag between a particle entering a measuring device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by $\approx 0.1$ light seconds.
A. Skeen / Y. Suhov (Cambridge)
The von Neumann entropy as the dimensional
information rate of quantum
Gibbs sources"
The notion of a quantum source as per the book by Nielsen and Chuang is
generalised slightly and using this definition and the spectral
decomposition
for the density matrix corresponding to this quantum source, we define
a 1-1
encoding map between the eigenbasis of the density matrix and the
space
of finite binary strings. We then consider the problem of compressing
these
classical strings in such a way that asymptotically (i.e. as the dimension
of the
Hilbert space we are considering increases to 
),
the information rate
of this compression achieves the optimal von Neumann entropy rate. In
the
case of 2 particular classes of quantum sources, we are able to fulfil
the
criterion of asymptotic optimality by using a version of the classical
Lempel-Ziv
algorithm to compress these binary strings
Let r(1), r(2), ... be a sequence of density matrices in Hilbert spaces H(1) Ì H(2) Ì ¼. Let f(n)1, f(n)2... be orthonormal eigen-vectors for r(n), with eigen-values k(n)1, k(n)2, ... :
|
|
|
Let K* = È1 £ s < ¥{0,1}s be the space of all finite binary sequences k = (k1,k2,¼) and set l(k) = s if k Î {0,1}s. We are also interested in constructing a sequence of maps fn:S(n)®K* achieving the rate h:
|
In the talks by Skeen and Suhov and Datta and Suhov we will give examples of quantum information sources for which these goals can be achieved.
N. Datta / Y. Suhov (Cambridge)
Data
compression limit for an information source of
interacting qubits
A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each other. We establish the limit for the compression of information from such a source and show that asymptotically it is given by the von Neuman entropy rate. Our result can be viewed as a quantum analog of Shannon's noiseless coding theorem for a class of non - i.i.d. quantum information sources.
G. Milburn (Cambridge/Queensland)
High precision measurements with entangled
coherent states
I will discuss the possibility of using entangled states of harmonic oscillators for sensitive force detection beyond the standard quantum limit. In particular I will discuss the advantages of using entangled coherent states.
L. Maccone (MIT)
Entanglement and dynamical evolution
Entanglement is a fundamental resource to achieve the maximum allowed speed in the dynamical evolution of a system. In general, energy entangled states evolve to an orthogonal state faster than their unentangled counterparts.
This is work done in collaboration with Vittorio Giovannetti and Seth Lloyd.
C. Doran (Cambridge)
Entanglement and the multiparticle spacetime
algebra
When two or more subsystems of a quantum system interact with each other they can become entangled. An important issue in QIP is finding useful methods of describing this entanglement. Most solutions to this problem work at the level of the density matrix. Here we describe a method which applies directly to the wavefunction. The result is a generalisation of the Schmidt decomposition appropriate for arbitrary particle numbers. The decomposition employs a novel representation of a multiparticle state within a Clifford (geometric) algebra of configuration space.
Y. Shi (Cambridge)
From multi-partite entanglement to entanglement
in many-particle systems
I talk about some ideas and results on multi-partite entanglement and on entanglement in many-body systems. We consider all possible entanglements in a muti-partite system, and show that all GHZ-like states is not a reversible entanglement generating set under LOCC. We clarify the issues concerning entanglement in identical-particle systems and in statistical ensembles. Discussions are made on the nature of entanglement in some important condensed matter systems. It is shown that diminishing of entanglement underlies long-range orders.
B. Posters
T. M. Stace, C.H.W. Barnes and G. J. Milburn
Erasing which-path information from a two-photon
source using an optical cavity
We investigate the possibility of erasing the which-path information contained in the frequencies of photons produced by biexcitons confined in asymmetric quantum dots. We consider a biexciton with non-degenerate intermediate excitonic states in an optical cavity with cavity modes very close to the non-degenerate emission frequenegimes.
We first investigate a BEC of exciton polaritons in an isolated microcavity. We take into account the fermionic structure of polaritons treating the excitons as two-level systems coupled to a single mode in a microcavity. We examine the existence of the condensate as the temperature and excitation density is changed.
We then study the intermediate regime between an ordinary lasing and a BEC of exciton polaritons in microcavities. To do this, we introduce decoherence and dissipation processes into the model. Using the analogy to superconductivity we notice that some of these processes are pair-breaking analogous to the magnetic impurities in superconductors. Using the Green functions techniques similar to Abrikosov and Gor'kov theory of gapless superconductivity we study different regimes as the decoherence parameter is increased.
In the limit of very large decoherence we obtain a conventional laser. In the opposite regime we can examine the stability of the BEC of polaritons. The crossover between these regimes is discussed and an indication of how ordinary lasing could be distinguished from polariton condensation is given.
P.A. Cain, D. Dovinos, D.A.
Williams, M. Wagner, J.M. Bonar,
D.G. Hasko and H. Ahmed.
Coupled Quantum Dots by Trench Isolation
in SiGe
We have observed the splitting of Coulomb oscillation peaks in coupled Si0.9Ge0.1 double quantum dots at 4.2 K. The quantum dots are formed by trench isolation, which means that the dots can be made much smaller than the more usual surface gated approach, with a diameter of 50 nm or less, increasing the charging energy and therefore the operating temperature of the device compared to previous approaches. A simulation of the results using parameters calculated from the lithographic dimensions of the device shows that a good fit to the experimental data can be achieved with a realistic interdot capacitance value. Also, we have observed photon-assisted tunnelling in a SiGe quantum dot structure at a dilution refrigerator temperature of 20mK. A simulation using a continuous black-body spectrum at 4.2K gives good agreement with the measurements.
A Ferguson and D Williams
Charging effects in a SiGe double quantum
dot
We present electrical transport measurements on a nanofabricated lateral SiGe double quantum dot. In a similar way to the 2DEG systems, we use gates to alter the chemical potential on each dot. As these potentials are swept a hexagonal charging diagram is traced out. This indicates that the dots are strongly tunnel coupled, and that it is possible to add single electrons to each island in turn. A additional feature of this charging diagram is asymmetry of the conductance oscillations which indicate that inelastic processes are occurring.
William M. Kaminsky, Seth Lloyd, and Terry
P. Orlando (MIT)
A Superconducting Architecture for Adiabatic
Quantum Computation of NP-Hard Problems
We propose an architecture for an adiabatic quantum computer using superconducting persistent-current qubits that can treat NP-hard problems without requiring local coherent operations. Instead, computation can be performed entirely by adiabatically varying a magnetic field applied to all the qubits simultaneously. Local (incoherent) operations are needed only for: (a) switching on or off certain pairwise, nearest-neighbor inductive couplings in order to set the problem to be solved and (b) measuring some subset of the qubits in order to obtain the answer to the problem. Assuming the qubits are operated in a regime in which their characteristic time scales are much quicker than those of their environment, this approach--like all adiabatic ground-state computational schemes--should be robust against dephasing and relaxation.
For comments or queries please contact Daniel Jonathan at D.Jonathan@damtp.cam.ac.uk