June 25, 2018

Toronto Quantum Information Seminars QUINF 2006-07
held at the Fields Institute

The Toronto Quantum Information Seminar - QUINF - is held roughly every two weeks to discuss ongoing work and ideas about quantum computation, cryptography, teleportation, et cetera. We hope to bring together interested parties from a variety of different backgrounds, including math, computer science, physics, chemistry, and engineering, to share ideas as well as open questions.

Talks are held Fridays at 11 am unless otherwise indicated


Kiyoshi Tamaki


Abraham Ungar, North Dakota State University
On the Bloch Vector of Quantum Information and Computation
A qubit is a two state quantum system, completely described by the qubit density matrix $\rho(\mathbf{v})$ parametrized by the Bloch vector $\mathbf{v}$ varying in the unit ball of the Euclidean 3-space. The only well-known structure of the space of all qubit density matrices is the convex structure. Qubit density matrices give rise to the trace distance and Bures fidelity between two qubit density matrices. Much to their chagrin, Nielsen and Chuang admit:

"Unfortunately, no similarly [alluding to the trace distance and its Euclidean geometric interpretation] clear geometric interpretation is known for the [Bures] fidelity between two states of a qubit". Nielsen and Chuang [1, p. 410], 2000.

Surprisingly, Bures fidelity does have a novel rich geometric and algebraic structure, but it lies in the hyperbolic geometry of Bolyai and Lobachevsky rather than in Euclidean geometry [2].

Following [3, 4, 5] I will introduce a novel "gyrovector space" approach to the classical hyperbolic geometry of Bolyai and Lobachevsky which, unexpectedly, turns out to be fully analogous to the common vector space approach to Euclidean geometry. I will then demonstrate that

(i) Bloch vector is not a vector but, rather, a gyrovector (that is, a hyperbolic vector); and that

(ii) the space of all qubit density matrices possesses the same novel, rich, nonassociative algebraic structure that regulates (a) hyperbolic geometry and (b) Einstein's special relativity theory.

In particular, I will show that Bures fidelity has a clear hyperbolic geometric interpretation, and indicate further applications of hyperbolic geometry in quantum information and computation.

[1] Michael A. Nielsen and Isaac L. Chuang. Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.

[2] J.-L. Chen, L. Fu, A. A. Ungar, and X.-G. Zhao, "Geometric observation of Bures fidelity between two states of a qubit," Phys. Rev. A (3), vol. 65, no. 2, pp. 024303/1-3, 2002.

[3] Abraham A. Ungar. Beyond the Einstein addition law and its gyroscopic Thomas precession: The theory of gyrogroups and gyrovector spaces, volume 117 of Fundamental Theories of Physics. Kluwer Academic Publishers Group, Dordrecht, 2001.

[4] Scott Walter. Book Review: Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces, by Abraham A. Ungar. Found. Phys., 32(2):327-330, 2002.

[5] Abraham A. Ungar, Analytic Hyperbolic Geometry: Mathematical Foundations and Applications. Singapore: World Scientific, 2005.

11:00 a.m.

Lucien Hardy Perimeter Institute for Theoretical Physics
Interacting qubits in the causaloid formalism
Pairwise interacting (qu)bits can be used to perform universal (quantum) computation. The causaloid formalism was originally developed as a tentative step in the direction of constructing a theory of quantum gravity. This framework treats space and time on an equal footing. Further, it is time-symmetric. It is possible to put the theory of interacting bits (in the classical case) and of interacting qubits (in the quantum case) into this framework. It is hoped that, by placing classical and quantum theory in this framework, we can gain some insight into the nature of information processing in the two theories.

11:00 a.m.

Vadim Makarov
, Dept. of Electronics and Telecommunications, Norwegian University of Science and Technology
Practical attacks on quantum key distribution systems
Quantum cryptography allows guaranteely secure distribution of a secret key over an open optical channel. The security against eavesdropping is based on the known laws of physics and is confirmed by rigorous theoretical proofs. However, the model of legitimate users' equipment used in the proofs has so far been limited. The proofs have assumed idealized models of optical and electrooptical components in legitimate users' setups and have omitted some component imperfections. These omitted imperfections, as it has been shown, open possibilities for successful attacks.

Most quantum cryptosystems today contain two or more single photon detectors. In this talk, I will consider two non-idealities of single photon detectors, and how Eve can exploit them. The first non-ideality is a dependence of relative efficiency of '0' detector versus '1' detector on an external parameter controllable by Eve (e.g., timing of the incoming pulses). The second non-ideality is a saturation behavior of a passively-quenched avalanche photodiode, where it becomes completely blinded by a moderately strong light. I illustrate both imperfections with experimental data, show how Eve can construct successful attacks using them, and present some calculations on how strong the non-ideality should be to allow for a successful attack. I also consider countermeasures legitimate users could devise.

11:00 a.m.
Marco Lucamarini, Department of Physics, University of Camerino
Quantum cryptography with a two-way quantum channel
It is a common belief that two-way quantum channels can not represent a practical tool for quantum cryptography because of their high loss rate. I will debate this question by an explicit example of a two-way quantum cryptosystem that provides key distribution rates higher than its one-way counterpart on a small- and medium-scale distance. I will also present other potentialities and a few experimental results pertaining to this new protocol.
11:00 a.m.

Mohsen Razavi, Institute for Quantum Computing, University of Waterloo
Quantum Key Distribution over Long Distances
Quantum key distribution (QKD) is believed to be the first realizable application of quantum information science. In fact, over short distances, such QKD systems are commercially available. Over long distances, however, the scenario is much different. If we do not have access to a network of trusted nodes for key regeneration, the only known solution for long-distance QKD relies on entanglement swapping or quantum repeater systems. Such systems face their own implementation challenges, including the need for quantum memory devices and highly efficient gates and detectors. In this talk, I discuss a variety of physical requirements for quantum repeaters, compare different architectures for entanglement distribution, and address the prospect of developing these systems in the near future.


12:00 p.m.

Hans Hübl, Walter Schottky-Institut and Physik-Department E25, TU München
Related Seminar of Interest - "News on an old donor: Manipulation and detection of the spin states of phosphorus in silicon"
One of the proposed solid-state realizations of quantum computing is based on the electronic and nuclear spins of phosphorous donors in silicon. The strong Kohn-Luttinger oscillations of the donor wave function in the indirect bandgap semiconductor Si, which complicate the exchange interaction of neighboring 31P donors, can be suppressed by using strained silicon layers. Additionally, the strain will also affect the wave function at the donor atom, which can be observed directly via the hyperfine interaction between the donor electron and its nucleus in electron spin resonance. In this talk, I will present the results of detailed experimental and theoretical investigations of the hyperfine interaction by electrically detected magnetic resonance (EDMR), using the spin dependent 31P-Pb0 recombination as a spin-to-charge transfer. Furthermore, experiments studying the sensitivity limit of this detection mechanism will be summarized showing that as few as 50 P donors can already be resolved in nano-structured devices.

Beside the principal detection of phosphorus donors in silicon using EDMR, I discuss the observation of Rabi oscillations by investigating the current transient after the application of a microwave pulse which allows to read out the spin state of the electron. Pulsed EDMR experiments can be extended to Hahn echo tomography which allows to determine the T2 time of the specific spin-to-charge transfer system used.


11:00 a.m.

Prem Kumar, Northwestern University
Fiber-optic Quantum Communications
Keeping in mind the ubiquitous standard optical fiber for long-distance transmission and the widespread availability of efficient active and passive fiber devices, we have been developing telecom-band resources for practical quantum communications and information processing in wave-division-multiplexed (WDM) fiber optical networks. In this talk, I will present our recent results on telecom-band in-fiber entanglement generation, characterization, storage, and long-distance distribution for various quantum information processing applications.

Joint Quantum Optics/AMO Seminar and QUINF Seminar


11:00 a.m.
Andrei Klimov, University of Guadalajara, Mexico
Discrete Phase-Space Structure and Mutually Unbiased Basis Operators
Several construction methods for mutually unbiased bases have been proposed in the literature. Typically they involve either direct construction of the basis vectors, or sets of operators are derived where each set's (simultaneous) eigenstates are mutually unbiased with respect to every other set's. It is subsequently common to map the states onto lines in the corresponding discrete phase space. We show how to derive mutually unbiased bases from the reverse mapping. We start by considering the most general phase-space structures compatible with the concept of mutually unbiased bases, namely bundles of discrete space curves intersecting only at the origin and satisfying certain properties and develop a new method based on the analysis of geometrical structures in the finite phase-space for construction of Mutually Unbiased Bases (MUB) operators. In the case when the Hilbert space dimension is an integer power of a prime, there exist several classes of curve bundles with different properties, lines being a special case. We also consider transformations between different kinds of curves, and show that in the two-qubit case, they all correspond to local transformations, and more specifically they correspond to rotations around the Bloch-sphere principal axes. Nevertheless, in the case of more that two qubits several non isomorphic structures appear, which can be naturally classified in terms of discrete curve bundles.

The existence and a possibility of regular searching of such non isomorphic MUBs allows us to introduce a concept of complexity of tomographic scheme for state determination of multi-qubit systems.

11:00 a.m.

Ashwin Nayak, University of Waterloo, and Perimeter Institute for Theoretical Physics
Search via quantum walk
Although the original problem may not be formulated in terms of graph search, computational problems can often be recast as the problem of searching for a special kind of vertex in a graph. This turns out to be a particularly useful view to take for designing efficient algorithms---quantum particles exploring a graph may detect special (or ``marked'') vertices quadratically faster than classical particles, as illustrated by Ambainis (2004) and Szegedy (2004).

In this talk, we will see a quantum walk based algorithm that may be defined for an arbitrary ergodic Markov Chain. It combines the benefits of two previous approaches while guaranteeing the better form of run time. The algorithm is both conceptually simple and avoids several technical difficulties in the analysis of earlier approaches. It thus seems to demystify the role of quantum walks in search algorithms.

We will begin with example search problems and algorithms based on random walk, describe amplitude amplification and phase estimation (two useful building blocks for quantum algorithms), and sketch how their confluence gives our search algorithm.

This is joint work with Fr'ed'eric Magniez (CNRS--LRI), J'er'emie Roland (UC Berkeley), and Miklos Santha (CNRS--LRI).


11:00 a.m.
André Stefanov, Institut für Experimentalphysik, Universität Wien
Implementation of Simple Quantum Algorithms using Optical Cluster State
Quantum computers promise to be more efficient and powerful than their classical counterparts. In the one-way quantum computer model, a sequence of measurements processes qubits, which are initially prepared in a highly entangled cluster state. We present here an optical implementation of a 4-qubit cluster state and we show how different algorithms can be experimentally realized by performing the corresponding sequence of measurements. We demonstrate deterministic one- and two-qubit gate operations as well as Grover's quantum search algorithm. A major advantage of optical quantum computation is the very short time for one computational step achievable by using these ultra-fast switches. With present technology this feed-forward step can be performed in less than 150 nanoseconds.

We also present how cluster states can be used to realize quantum circuits simulating simple quantum games. Finally we present the experimental realization of decoherence free subspace cluster computation where each logical qubit is encoded into two physical ones, and hence protected against phase noise.

11:00 a.m.

Robert Raussendorf, Perimeter Institute for Theoretical Physics
Fault-tolerant quantum computation with high threshold in two dimensions
We present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is 0.59 percent for each source in an error model with preparation, gate, storage and measurement errors.

Joint work with Jim Harrington. See quant-ph/0610082.

11:00 a.m.
Patrick Hayden, School of Computer Science, McGill University
Quantum Information Theory: Four Lessons from the Land of Large n
What should your average quantum information scientist know about quantum Shannon theory? Over the past few years, the asymptotic theory of quantum information, known as quantum Shannon theory, has advanced tremendously. However, while many of the field's most important insights are simple to explain, they remain largely unknown to all but a small group of afficionados. In this talk, I'll present four lessons from this "land of large n", ranging from the surprising to the useful and the amusing to the painful.

If you've ever:
* assumed that correlation can be decomposed into quantum and classical parts
* wondered why so many otherwise well-adjusted people are obsessed by some mathematical problem called the "additivity conjecture"
* thought that being "more than certain" is paradoxical then this talk is for you.

11:00 a.m.

Aaron J. Pearlman
Ultrafast NbN superconducting single-photon optical detector for quantum communications
We evaluate the NbN single-photon detector (SSPD) for the purpose of integration into a fiber-based quantum communication system, namely the DARPA quantum key distribution (QKD) network. We first review free-space system measurements to characterize the SSPD in terms of counting rate and timing jitter and then demonstrate its utility in two fiber-based systems. The first utilizes fiber-coupled SSPDs placed in a cryogen-free refrigerator capable of reaching mK temperatures, and the SSPDs are evaluated in terms of system quantum efficiency (SQE) and dark counts over a broad temperature range. The second system, utilizes fiber-coupled SSPDs assembled on an insert placed in a standard helium dewar with each fiber permanently glued to a device. The SSPDs, evaluated in terms of SQE, dark counts, and timing resolution, show that the system provides relatively high fiber-detector coupling efficiency, good timing resolution, and can integrate easily into the DARPA network.

We also investigate the SSPD’s limitations by analyzing a model which takes into account the SSPD detection mechanism and device inductance to predict its response time. We then optimize the SSPD meander geometry in designing devices with high SQE and counting rate in terms of area, stripe width, fill factor, and thickness using detailed inductance simulations. We will also present a novel low inductance SSPD design and model its photoresponse.

With these designs and measurement results, we show that the SSPD outperforms its superconducting and semiconducting counterparts for quantum cryptography systems with high clock rates. Thus, the SSPD, with its combination of high QE, and low timing jitter at telecommunications wavelengths, as well as low dark counts, make it a natural choice for the DARPA network and quantum cryptography systems in general.


11:00 a.m.
Jean Christian Boileau, Institute for Quantum Computing, University of Waterloo
Obtaining the Devetak-Winter bound for Quantum Key Distribution in Terms of Entanglement Distillation
Bennett and Brassard proposed the first QKD protocol in 1984, but it was not until the work of Dominic Mayer in 1996 that it was proven to be unconditionally secure. One of the noticeable advances in the security proof technique was accomplished by Lo and Chau, followed by Shor and Preskill, when they related BB84 to entanglement distillation. Subsequently, techniques for unconditional security proofs have greatly evolved. One of the most complete security proofs for QKD protocols using single photon encoding and one-way communication has been proposed by Renner, Gisin and Kraus.

In standard entanglement distillation proofs and in the original paper by Renner, Kraus and Gisin, the quantum state prior to the raw key measurement is or could be diagonalized in the Bell-basis. Excluding pre-processing, the secret key generation rate obtained in that manner is asymptotically close to 1-H(p_{uv}) where H(p_{uv}) is the Shannon entropy of the bit and the phase error rate of the system representing the key. However, for some QKD protocols, there are other symmetrizations that give a better lower bound for secret key generation rates derived using only one-way communication.

An improved secure rate for some QKD protocols involving measurements of non-orthogonal states can be calculated by symmetrizing the state "earlier" in the protocol, as was acknowledged recently by Kraus et al. for the case of SARG04. As we show for the case of spherical code and the Singapore protocol where the QKD protocol follows some symmetries (i.e. the effective channel is dephasing), the symmetrization proposed by Renner, Gisin and Kraus can be done before a so-called filtering operation. In the absence of such symmetry, the quantum de Finetti theorem as described in Renner's thesis can be used instead to obtain a state that is close to separable. Applying the Devetak-Winter lower bound to such state, we obtain a secret key rate that can be higher than 1-H(p_{uv}) (i.e. the Devetak and Winter bound is given by I(X:B)-I(X:E), where I(X:B) or I(X:E) is the mutual information between Alice and Bob, or Alice and Eve, supposing that Alice, Bob and Eve share by a cqq state).

One of our contributions is to derive this improved bound from the perspective of entanglement distillation. To do so, it is necessary to introduce the concept of a shield, which is a system that Eve cannot access and that does not contain the key. We show that for the prepare-and-measured QKD protocol, the state of the shield can be written approximately as \sigma^ v where v describes the phase error pattern, and that the secret key generation rate is given by 1-H(p_{u})-H(p_{v})+\chi(\sigma_v, p_v), where \chi is the Holevo information. We also show that this rate is equivalent to the Devetak and Winter bound.

Joint work with J.-M. Renes.

11:00 a.m.
Thomas Coudreau, Université de Paris VII - Denis Diderot
Quantum memories with trapped ions: theoretical results and on-going experiments
The great enemy of quantum information is decoherence, through which a quantum system quickly becomes classical. Trapped ions form an ideal medium for quantum information as they can be well controlled using laser beams while being relatively well isolated from external noise sources. I will show how ensembles of cold ions can be used as quantum memories either to store the quadratures describing intense light beams (continuous variable regime) or for very long lived qubits, based on the principles of topological protection.

Joint Quantum Optics/AMO Seminar and QUINF Seminar

2:00 p.m.
Thomas Coudreau, Université de Paris VII - Denis Diderot
Quantum properties of self-phase locked Parametric Oscillators
Optical Parametric Oscillators (OPOs) consist of nonlinear (chi2) media inserted inside a cavity. When operated above the oscillation threshold, these devices generate intense, phase coherent optical beams. Triply resonant OPOs have been known for a long time to generate very large intensity quantum correlations. I will show that, when phase locking is introduced between the output beams, one can generate a record amount of entangled light with unique properties. I will also describe the principles of a novel device which can emit polarization entangled light.

Joint Quantum Optics/AMO Seminar and QUINF Seminar

11:00 a.m.


Scott Aaronson, Institute for Quantum Computing, University of Waterloo
The Learnability of Quantum States
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, I'll show that "for most practical purposes" one can learn a quantum state using a number of measurements that grows only linearly with n. Besides possible implications for experimental physics, this learning theorem has two applications to quantum computing: first, a new simulation of quantum protocols, and second, the use of trusted classical advice to verify untrusted quantum advice.


11:00 a.m.
Jim Franson, University of Maryland, Baltimore County
Entangled Photon Holes
Parametric down-conversion can be used to create pairs of photons that are entangled in energy and time. Photons entangled in this way are emitted at the same time, but with a coherent superposition of such times, which can violate Bell’s inequality and can be used in quantum key distribution, for example. We have recently introduced the idea of entangled photon holes, in which a two-photon absorbing medium absorbs pairs of photons from two laser beams at the same time, with a coherent superposition of those times. Entangled photon holes can also violate Bell’s inequality and may have some advantages in quantum communications. A recent experimental demonstration of entangled photon holes will also be discussed.

Joint Quantum Optics Condensed Matter Physics Seminar and QUINF seminar

11:00 a.m.
Carlos A. Perez, Institute for Quantum Computing, University of Waterloo
Quantum Cellular Automata and Single Spin Measurement
We propose a method for single spin measurement. Our method uses techniques from the theory of quantum cellular automata to correlate a huge amount of ancillary spins to the one to be measured. It has the distinct advantage of being very efficient, and to a certain extent fault-tolerant. Under ideal conditions, it requires the application of only $O(\sqrt[3]{N})$ external radio frequency pulses to create a system of $N$ correlated spins. It is also fairly robust against pulse errors, imperfect initial polarization of the ancilla spin system, and does not rely on entanglement. We study the scalability of our scheme through extensive numerical simulation.

This is joint work with Michele Mosca (UW), Paola Cappellaro (MIT), and David G. Cory (MIT).

11:00 a.m.
Dmitry Gavinsky, Department of Computer Science, University of Calgary
On the Role of Shared Entanglement
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known ``entanglement analogue'' for the famous theorem by Newman, saying that the number of shared random bits required for solving any communication problem can be at most logarithmic in the input length ( i.e., using more than O(log(n)) shared random bits would not reduce the complexity of an optimal solution).

We prove that the same is not true for entanglement. We establish a wide range of tight (up to a logarithmic factor) entanglement vs. communication tradeoffs for relational problems.
The "low-end" is: for any t>2, reducing shared entanglement from log^t(n) to o(log^{t-1}(n)) qubits can increase the communication required for solving a problem almost exponentially, from O(log^t(n)) to \omega(\sqrt n).
The "high-end" is: for any \eps>0, reducing shared entanglement from n^{1-\eps}\log(n) to o(n^{1-\eps}) can increase the required communication from O(n^{1-\eps}\log(n)) to \omega(n^{1-\eps/2}).
The upper bounds are demonstrated via protocols which are exact and work in the simultaneous message passing model, while the lower bounds hold for bounded-error protocols, even in the more powerful model of 1-way communication. Our protocols use shared EPR pairs while the lower bounds apply to any sort of prior entanglement.

11:00 a.m.

Gennady Berman, Theoretical Division, Los Alamos National Laboratory
Survival of quantum effects after decoherence and relaxation
I will review our results on a mathematical dynamical theory for observables for open quantum nonlinear bosonic systems for a very general class of Hamiltonians. We argue that for open quantum nonlinear systems in the “deep” quasi-classical region, important quantum effects survive even after the decoherence and relaxation processes take place. Estimates are derived which demonstrate that for a wide class of nonlinear quantum dynamical systems interacting with the environment, and which are “close” to the corresponding classical systems, quantum effects still remain important and can be observed, for example, in the frequency Fourier spectrum of the dynamical observables and in the corresponding spectral density of the noise. These preliminary estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states.

11:00 a.m.
Peter Turner, Institute for Quantum Information Science, University of Calgary
Quantal and semi-classical approaches to the degradation of quantum reference frames
There has been much recent activity in the study of quantum reference frames, from their role as resources in quantum information theory to their role in the application of superselection rules. These studies make it clear that we must carefully distinguish cases in which we take a reference frame for granted from those in which we include the physical reference frame in our dynamics. In this talk I will describe the degradation of a quantum reference frame as it is used to make repeated measurements, where the entangling of the frame and the system under study results in an increasingly mixed state for the frame which is decreasingly useful as a reference. We show that the `longevity' of the frame as a useful reference scales quadratically with the `strength' of that frame. I will also describe a recent semi-classical approach to the degradation of a directional reference frame where it is modelled as a random walk on the sphere.

11:00 a.m.
Nikolai Kiesel, Department of Physics, LMU Munich and MPQ Garching
Experimental Applications of a Linear Optical Controlled Phase Gate
I will present the experimental implementation of a probabilistic linear optical controlled phase gate. It is operating on the polarization degree of freedom of photons and is based on the second order interference at a ‘magic’ beam splitter. We characterized the gate performance with a tomographic set of measurements and, by fitting a model of the gate to the obtained data, we extracted the corresponding experimental parameters.

In a next step, the controlled phase gate served to entangle two EPR-pairs resulting in a four-photon entangled cluster state with a fidelity of 74.4 ± 1.2 %. We studied the state using entanglement witnesses, showed the violation of a bell inequality and verified its high entanglement persistency against photon loss.

Finally, we demonstrated a teleportation and an entanglement swapping experiment with a complete bell state analysis that was based on the controlled phase gate.


An International Workshop
Frontiers of Quantum Decoherence
Decoherence is a fundamental physical phenomenon which occurs in a variety of quantum systems. It has recently emerged as a priority research topic in many fields of science and technology. This Workshop is intended to bring together international experts from various disciplines, to discuss foundational issues and to explore new research horizons. Our focus will be on decoherence mechanisms in solid-state, atom/molecular and photonic systems, and on quantum algorithms for mitigating decoherence effects in quantum information processing.


11:00 a.m.
Karl-Peter Marzlin, Institute for Quantum Information Science, University of Calgary
Quantum Information with Atoms and Photons
Atomic gases and single photons are among the most promising candidates to implement quantum information technology because they can be well isolated from their environment. Despite this advantage it is challenging to design controllable interaction between these particles and to store or manipulate quantum information in a reliable way. We have explored how electromagnetically induced transparency can be used to create a large nonlinear interaction between single-photon pulses, to transfer optical states between different photon modes, and to create an unusual interaction between light fields. Furthermore, we have found new results on the physical limitations of decoherence-free states. The nature of these limitations points towards new directions in the search for decoherence-free subspaces.
11:00 a.m.
Elinor Irish, University of Rochester, Department of Physics and Astronomy
The Theory of Quantum Electromechanics
"Quantum electromechanics" combines superconducting qubits and nanofabricated mechanical devices into a system analogous to the canonical atom-cavity system of quantum optics. Many fascinating quantum-optical effects should be realizable in this solid-state system. The prospect of achieving very strong coupling even at large detuning suggests the exploration of parameter regimes in the spin-boson problem that are inaccessible in quantum optics experiments. I will talk about my work on the theory of quantum electromechanical systems, motivated in particular by the search for practical schemes to observe the quantum behavior of nanoscale mechanical resonators.