In the century since Einstein postulated light's quantum nature—an event celebrated last year, along with SPIE's 50th birthday—the quantum revolution has progressed from formalizing the mathematical theory of the electron and photon, to a second wave that uses quantum phenomena for new information-processing technologies. These applications are found in fields as diverse as communications, cryptography, computing, and even imaging.

Since photons are the de facto information-encoding entity, this means photonic information processing often amounts to quantum information processing, which can be carried out on chips fabricated with very large scale integration (VLSI) techniques, such as the array of single-photon detectors shown in Figure 1, for significant cost reduction. Our experience with VLSI has taught us the importance of having good rules^{B1} that abstract away the underlying physics and allow engineers to design chips. This inspired us to consider an analogous set of quantum design rules (QDRs) for VLSI photonics.^{2,3}

**Figure 1.** This device includes a 32 × 32 array of CMOS single-photon detectors.

Understanding the quantum rules

To establish correct engineering guidelines, we first need to understand the quantum rules that photons obey. We adopt the quantum path integral (QPI) formalism^{4} to avoid traps that arise from treating the photon as either a classical particle or a classical wave. Under this formalism, a photon propagating in free space is represented by an infinite set of QPI amplitudes *φ*_{i} between source s and detector *d*.

The probability for detecting a physical photon is determined by summing over all of these paths, and then taking the squared modulus of the result. Some eight quantum rules^{2,3} of this type will correctly calculate probabilities in VLSI information-processing devices. For example, in Figure 2, which shows a scattering event ε, path *φ*_{1} would be computed as the product of the two legs, *φ*_{1a} and *φ*_{1b}, an example of the ‘AND-ing’ rule. We have shown elsewhere that flawed claims can result when these rules are ignored.^{2}

**Figure 2.** Shown is one of infinitely many paths φ a photon can take going from source s to detector d. Path φ_{1} includes an interaction with matter, an event denoted by ε, and two legs, φ_{1a} and φ_{1b}.

Entanglement, loops, and ghosts

We have extended QPI formalism to *entanglement*.^{2,3} The most common method for producing entangled ‘biphotons’ pumps a nonlinear crystal, such as beta-barium borate (BBO), with UV photons to create photon pairs whose total momenta and energy equal that of each pump photon. An entangled pair acts like the two-segment QPI amplitude shown in Figure 2. Figure 3 depicts the BBO crystal as the scattering event ε in Figure 2, and detectors *D*_{1} and *D*_{2} as the source and detector, respectively. One biphoton (*signal*) propagates from ε to detector *D*_{2} in the expected way, but the *idler* photon propagates backward from *D*_{1} to ε. The coincidence counter (CC) forms a closed circuit of paths.

Figure 3. The entangled biphoton may be viewed as a quantum path integral amplitude with idler and signal segments, i and s, created by event ε. D_{1}, D_{2}: Detectors. CC: Coincidence counter.

Figure 3, as adapted in Figure 4, also explains how quantum ghost imaging^{5,6} works. Detector *D*_{1} acts like a source for the idler photon passing through a focusing lens to the BBO crystal, which propagates the signal photon to the detector array *D*_{2}. The ghost image appears only in the coincidence counts, focused in accordance with the thin lens equation.

**Figure 4.** This quantum ghost imaging device is topologically equivalent to the closed-circuit arrangement of

Figure 3 with an interposing thin lens. d

_{o}, d

_{i}: Object and image distances.

Toward QDRs

With the photon rules in hand, we can discern some engineering-level QDRs. (i) Photons don't interact with photons, but only the material comprising the device. (ii) The minutest change to the material comprising a quantum information device can completely alter its operation. (iii) The distinction between amplitudes and intensities made in Fourier optics becomes redundant: only quantum amplitudes lead to probabilities. (iv) The thin lens equation *d*_{1}^{-1} + *d*_{o}^{-1} = *f*^{-1} still holds for quantum-ghost imaging devices.^{5} More experiments are needed to enumerate other QDRs, and that is a major thrust of our current research conducted in the Quantum Architecture Group at the Swiss Federal Institute of Technology Lausanne (EPFL; Figure 5).

**Figure 5.** The Quantum Architecture Group at the Swiss Federal Institute of Technology Lausanne uses this laser system to create entangled biphotons.

Authors

Neil Gunther

Performance Dynamics

Castro Valley, CA

Neil Gunther is an internationally recognized consultant who founded Performance Dynamics in 1994. He holds an MSc in applied mathematics and a PhD in theoretical physics. He presented at the SPIE Quantum Communications and Quantum Imaging conferences in 2005 and 2006.

Edoardo Charbon, Dmitri Boiko

Faculté Informatique et Communications, EPFL

Lausanne, Switzerland

Edoardo Charbon holds a diploma from the Swiss Federal Institute of Technology Zurich (ETH Zurich), an MS from the University of California, San Diego, and a PhD in electrical engineering and computer sciences from the University of California, Berkeley. He is on the faculty of EPFL and founded its Quantum Architecture Group. He is a member of the technical committees for VLSI-SOC and ESSCIRC.

Dmitri Boiko received MSc and PhD degrees from the Moscow Institute of Physics and Technology while developing the first solid-state chip-laser gyro. He is a scientific consultant to EPFL's Quantum Architecture Group.

Giordano Beretta

Digital Printing and Imaging Laboratory, Hewlett-Packard Corp.

Palo Alto, CA

Giordano Beretta works in HP's Digital Printing and Imaging Laboratory. He obtained a diploma in mathematics and a PhD in computer science from ETH Zurich, and holds a dozen patents related to color imaging technology. Beretta is a SPIE Fellow.