May 26, 2016 | Research News

by By Dirk Englund, Jamieson Career Development Assistant Professor of Electrical Engineering and Computer Science, Research Laboratory of Electronics

From an engineering perspective, quantum mechanics seems like a nightmare at first sight. It’s impossible to predict how a system will behave or even to measure it without changing it. But it turns out that quantum mechanics also opens up entirely new applications that would be impossible in a classical world. Over the past decades, an improved mastery of quantum phenomena has given rise to new fields of “quantum technologies.”

There are two concepts underpinning these technologies (Figure 1). The first is the superposition principle: a system can exist in all possible states at the same time. For example, whereas in a classical world a coin with sides labeled “0” and “1” can only be in one state at once, a “quantum coin” can be in both states simultaneously (though it is “collapsed” to one possible outcome when measured). Two quantum coins can be in four states (superpositions of 00, 01, 10, and 11) simultaneously, three coins in eight states, etc. The size of the superposition grows exponentially with the number of particles. Recording the amplitudes of an arbitrary superposition of just 60 quantum coins would require more than a million terabytes on a classical computer.

**Figure 1: **Quantum technologies make use of two central aspects of quantum mechanics: (1) The superposition principle — a system can be in all possible states at the same time; and (2) The No-Cloning Theorem — unknown states cannot be copied. Also shown are key quantum technologies being developed today: Quantum simulation and computing; quantum measurement; and quantum communications.

**Realizing Feynman’s Dream: Quantum Simulation and Computing**

This exponential increase in complexity makes even small systems of interacting particles impossible to model. We have the equations, but we cannot solve them. But there is a possible solution: we could try to simulate a hard quantum problem by mapping it onto a controllable quantum system in the laboratory. This is the concept of a “quantum simulator,” proposed originally in 1981 by Richard Feynman[1].

It’s now possible to construct quantum systems with enough (individually controllable) quantum particles, such as trapped atoms, that they are virtually impossible to be modeled classically. In coming decades, such quantum simulators could solve important many-body quantum problems — e.g., to model high-temperature superconductivity or perform ab-initio design of materials or pharmaceuticals.

A more general version of a quantum simulator is a quantum computer, which has additional requirements beyond the simulator. A general-purpose quantum computer could not only simulate any classical computer efficiently, it could also perform quantum simulations and run other algorithms more efficiently than known classical-computer algorithms (including database searches, machine learning tasks, and prime number factorization).

**Quantum Measurement**

The second unusual idea about quantum mechanics is the so-called “No-Cloning Theorem”: it is impossible to copy an unknown quantum state. Measuring any quantity comes down to reading a probe, such as a magnetometer, which is ultimately a quantum system. Measuring the quantum probe projects it into one of several possible final states, a process that has inherent uncertainty and noise. One may hope to skirt this projection noise by repeatedly measuring clones of the state, but that would violate the no-cloning theorem. Quantum mechanics places hard limits on how precisely we can measure, and we may long for a simpler classical-physics world that allows perfect measurements. But, quantum technologies are being developed that at least allow us to measure close to the physical limits. Indeed, the field of quantum metrology has produced the most precise measurement instruments devised by humankind. Atomic clocks developed by the National Institute of Standards and Technology are so precise that they wouldn’t lose a second over the age of the universe. Other types of sensors are improving navigation equipment and magnetic resonance imaging.

**Quantum Communication**

The No-Cloning Theorem also paves the way for secure communications. If two parties, Alice and Bob, send quantum states of light (photons) between them, then an eavesdropper, Eve, cannot measure these photons without also perturbing them. Alice and Bob, being paranoid cryptographers, ascribe all perturbances to Eve. If the perturbations are sparse enough, then Alice and Bob can upper-bound how much information Eve may have gleaned and erase it by classical privacy amplification codes. They end up with a cryptographic key of shared random bits, which allows for perfect encryption if used just once. This is an example of quantum key distribution (QKD). Unlike classical crypto-protocols, which rely on assumptions about the computational capabilities of an eavesdropper, QKD is secured by the laws of physics.

**A Quantum Internet of Things**

Today’s Internet is so powerful because it combines computing, sensing, and communication. A “quantum network” — a network of stationary quantum memories (a memory for a quantum state) connected via photons — could do the same for quantum technologies, combining quantum computers/simulators, quantum communications, and quantum probes/measurements. It could combine these disparate quantum technologies as a kind of “quantum Internet of Things.” A quantum network architecture is one way to build a “modular” quantum computer combining many well-controlled quantum memories. Alternatively, the memories could also be distributed between cities, connected via fiber-optic cables. The primary function of such a quantum network would be to distribute entanglement across distributed network users. Suppose Alice in Atlanta and Bob in Boston each have one quantum coin of an entangled pair. Measuring these qubits would result in random, but correlated, outcomes, which Alice and Bob could use as cryptographic key. Entangled states in a quantum network could also be used as resource for teleporting unknown quantum states. These states could encode local measurements that are optimally measured together at one location; this could be useful, for example, for long-baseline astronomical telescopes[3]. Figure 2 lists several other applications that would be possible on a quantum network.

**Figure 2:** The quantum internet (left panel) will likely combine different network topologies, including the tree and mesh topologies shown here. It will link different types of quantum memory nodes, such as neutral atoms, trapped ions, and diamond color centers. By distributing entanglement to different users, such as Alice (with her Barium ion memories) and Bob (with his diamond spin memory), these users could, for example, teleport Alice’s quantum probe |\Ψ> to Bob. Other proposed network applications are listed on the right.

**Building the Quantum Internet**

So, how do we build the quantum internet? Many types of stationary qubit architectures are being investigated, including trapped atoms and atom-like defects in solids. Semiconductor quantum memories are particularly attractive for scaling and deployment, if Moore’s Law for integrated ciruits is any guide. In particular, color centers in diamond have emerged as a leading contender for scalable and reliable qubits. Foremost is the nitrogen vacancy (NV) center in diamond, which consists of a nitrogen atom substituting for a carbon atom in the diamond lattice, adjacent to a lattice vacancy (Figure 3). The NV has the desired properties of a quantum network memory: long spin coherence times in excess of one second, efficient two-qubit gates, and quantum error correction including non-destructive measurements and real-time feedback. In 2015, two NV centers were entangled over more than a kilometer[4], demonstrating an important step towards distributed quantum networks. But, challenges remain: we need to find ways to entangle qubits much faster (sub-millisecond), control tens to hundreds of NVs simultaneously, perform full error correction, and develop scalable fabrication and assembly processes.

At MIT, we are working on these problems at the intersection of physics and electrical engineering. A major goal is to develop a scalable “quantum memory node.” Figure 2 lists several other applications that would be possible on a quantum network. This node requires high-quality NV quantum memories that couple efficiently to photons. We’ve recently taken the first steps in this direction, including efficient NV-photon interfaces in diamond optical cavities[5], techniques for scalable assembly of NV quantum memories on PICs[6], and ways to implant NV centers in diamond with nanometer scale precision[7]. Figure 3 shows an envisioned photonic integrated circuit (PIC) for controlling eight quantum memories, each consisting of several NV electron and nuclear spins. Multiple spins are needed to overcome qubit errors using quantum error correction by redundant encoding. Using our spin-photon interfaces, it should soon be possible to entangle electron spins and photons rapidly. Photons are routed on the PIC and measured jointly in a way that can entangle the respective on-chip quantum registers of on-chip quantum registers, or they are sent out into the larger quantum network for entanglement with remote quantum memories (up to a few tens of kilometers). Our work at MIT, together with collaborators at Harvard and Lincoln Laboratory focuses on these quantum nodes, the photonic circuits, sensors, other quantum network components, as well as the system architecture.

**Figure 3: **Top: A proposed quantum node consisting of eight diamond quantum memories, each consisting of three NV centers. Each NV has one electron spin memory coupled to multiple nuclear spins. Multiple spins are needed for error correction. The PIC routs NV photoemission for on-chip detection (and heralded entanglement) or into the network. Bottom: Installed dark fiber links in the Boston area. QKD is generating key between MIT and Lincoln Laboratory. NV-quantum memories are coming online at MIT and Harvard (Mikhail Lukin, Marko Loncar, and Hongkun Park groups).

Many experimental and theoretical challenges still must be overcome to identify these challenges and find solutions, there’s no better way than to actually build a prototype network. This is what we’ve started over the past years. Figure 3 (bottom panel) shows a testbed network linking MIT to Harvard University in Cambridge (6 km by buried fiber) and to MIT Lincoln Laboratory in Lexington, MA (43 km by optical fiber). The fiber optic links are “dark” — there’s no regular optical traffic over them — which reduces spurious photons in our spectrum. The links are designed for light near 1.55 µm wavelength, where fiber attenuation is minimized. Because most quantum memories couple to photons at shorter wavelengths, wavelength conversion techniques are required. This step is technically challenging, but has the upside of forcing all disparate types of quantum registers to interface at a common wavelength — an important step towards standardization of quantum networks. As of 2016, this network supports QKD with a secure key rate exceeding 1 Mbit/sec between Lincoln Laboratory and MIT’s main campus (not bad compared to some cable companies!). The next big step is to bring the quantum memories online.

Other teams around the globe are also beginning to build early stage quantum networks. Over the next years, it will become increasingly feasible to efficiently link qubits and to distribute entanglement across larger and larger networks, and we’ve just seen the first glimpses of what such networks could enable. In retrospect, engineers and scientists of the early days of quantum mechanics didn’t need to be so gloomy. The aspects of quantum mechanics that seemed so upsetting at first sight actually turned out to be pretty amazing.

**References**

[1] R. P. Feynman, Int. J. Theor. Phys. 21, 467 (n.d.).

[2] H. J. Kimble, Nature 453, 1023 (2008).

[3] D. Gottesman, T. Jennewein, S. Croke, and L. Boyle, in International Conference on Quantum Information (OSA, Washington, D.C., n.d.), p. PDPB1.

[4] B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Nature 526, 682 (2015).

[5] L. Li, T. Schröder, E. H. Chen, M. Walsh, I. Bayn, J. Goldstein, O. Gaathon, M. E. Trusheim, M. Lu, J. Mower, M. Cotlet, M. L. Markham, D. J. Twitchen, and D. Englund, Nat. Commun. 6, 6173 (2015).

[6] S. L. Mouradian, T. Schröder, C. B. Poitras, L. Li, J. Goldstein, E. H. Chen, M. Walsh, J. Cardenas, M. L. Markham, D. J. Twitchen, M. Lipson, and D. Englund, Phys. Rev. X 5, 031009 (2015).

[7] I. Bayn, E. H. Chen, M. E. Trusheim, L. Li, T. Schröder, O. Gaathon, M. Lu, A. Stein, M. Liu, K. Kisslinger, H. Clevenson, and D. Englund, Nano Lett. 6, (2015).

[8] D. Gottesman, Quantum Inf. Comput. 14, 1338 (2014).

[9] N. H. Nickerson, J. F. Fitzsimons, and S. C. Benjamin, Phys. Rev. X 4, 041041 (2014).