We have reached a point in the technological development of computers where the logic gates and wires, which make up the circuits that perform all of the operations that run computers, can be etched onto integrated circuit silicon chips of less than a micron across (0.001 millimeters). Following Moore’s Law, an observation (not a physical law) by Intel co-founder, Gordon Moore, which estimates that the number of transistors on an integrated circuit chip, an approximate measure of microprocessor complexity, doubles roughly every 18 months, it is inherent that in the near future these same logic gates will soon be on the scale of single atoms. As a result, we will need quantum mechanics to describe these new “quantum computers”. The basis of quantum information is qubits which are fundamentally different than bits, the basic units of classical computational information, due to the property of quantum superposition. While bits can only be prepared in one of two physical states (ex. 0 or 1), qubits can exist in a superposition of both states. This means qubits can exist with certain probabilities of being in each individual state, 0 and 1, at the same time, because of this principle of quantum superposition n qubits can store 2^{n} values at once compared to n values in n bits.

Due to superposition and other properties of quantum mechanics, we can run quantum algorithms at a much higher efficiency than their classical analogs; although, as of now this is only true for some algorithms. One example is Peter Shor’s famous paper^{1} proving that a quantum algorithm could find prime factors of an integer in polynomial time compared with much slower sub-exponential time for a classical computer Another enhanced quantum algorithm was depicted in a recent paper concerning the reduced steps with which a quantum algorithm could solve a system of linear equations compared to a classical algorithm.^{2} Many popular encryption schemes depend on the extremely long time for computers to factor huge prime numbers and as a result, Shor’s algorithm has tremendous effects on security. Beyond practical applications, quantum computers also give an insight into the realm of testing the theory of quantum measurement and the possibility of simulating of quantum systems which classical computers fail to do. We have reached a monumental point in scientific knowledge where we can apply one of our newest discoveries in physics, quantum mechanics, to one of our newest scientific fields, computer science, to develop a computer which could have unbelievable possibilities for solving groundbreaking problems or, possibly, on the other hand, show a discrete barrier to our knowledge.

However, at this point in time we have a much greater understanding of the theory of quantum computation than the experimental understanding required for building a large scale quantum computer. This discrepancy is a result of the difficulty of extracting data and performing operations on single qubits in addition to the amount of possible error in quantum information due to deconstructive interaction of qubits with the environment. This phenomenon, known as quantum decoherence, prevents a quantum system from interfering with itself and, as a result, destroys the superposition of a quantum system and causes a loss of information. The challenge of building an instrument capable of quantum computer operations depends on roughly five requirements: 1) well-defined two level quantum states, or qubits, 2) reliable preparation of these bits in different states, 3) low decoherence, 4) accurate quantum gate operations, and 5) strong ability to make measurements of stored information.^{3}

The Wisconsin Institute for Quantum Information, a coalition of research groups within the physics department here at the University of Wisconsin-Madison, is performing research at the forefront of quantum computing. The coalition consists of three different experimental efforts working on the physical realization of quantum information processors along with a myriad of theoretical physics professors who work together with these three groups. The three branches include the McDermott group, which focuses on implementing superconducting circuits as qubits, the Eriksson group, which focuses on using semiconductors to create qubits in the form of Silicon quantum dots, and the Saffman and Walker groups, which both work on multiple approaches towards using trapped neutral atoms as qubits.

Professor Robert McDermott performed research in quantum computing as a post doctorate researcher under John Martinis at the University of California at Santa Barbara and has continued within the field here at Madison. The McDermott group focuses their research on implementing qubits with superconducting circuits, which are macroscopic circuits that display quantum mechanical behavior, usually displayed only in atoms. In a paper he wrote, while working as a post doctorate researcher under Dr. Martinis McDermott, Robert McDermott helped to open up the possibility for full characterization of quantum gates made up of multiple qubits by making measurements on coupled superconducting qubits, a step necessary for implenenting quantum algorithms.^{4}

Professor Mark Eriksson, who works closely with theorist Susan Coppersmith, leads a group that focuses on implementing silicon quantum dots, which are small semiconductor devises that are constructed by confining electrons tightly in silicon, as qubits. In 2014, Eriksson and a group of other graduate students and PhD. physicists, most of whom work here at Madison, published a paper in Nature where they demonstrated quantum operations of double quantum-dot qubits with a speed of 100 picoseconds, corresponding to over an order of magnitude faster than any other double-dot qubit previously controlled.^{5}

While the other two groups are working on solid state realizations of qubits, Saffman and Walker are looking into the possibility of using trapped neutral atoms as qubits. After all, quantum mechanics was developed because of the need for new science to explain atoms and their structure! And remarkably, Saffman and his group just recently demonstrated the largest number of individually controllable qubits, in neutral trapped atoms of Cesium, for which quantum logic gate operations have been characterized on.^{6}

The professors spearheading this research effort in the Wisconsin Institute for Quantum Information has helped to solidify the university as one of the top programs focused on quantum information devices research in the world. Their research, along with the efforts of other universities and companies across the world, are helping to bring us closer to the physical realization of a quantum computer one atom at a time.

By Noah Johnson

## References:

- Shor P. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM J Comput. 1997 October; 26 (5): 1484-1509.
- Harrow AW, Hassidim A, Lloyd S. Quantum Algorithm for Linear Systems of Equations. Phys. Rev. Lett. 2009 October 9;103 (15): 150502.
- Loss D, DiVincenzo DP. Quantum Computation with Quantum Dots. Phys. Rev. A 1998 January; 57 (1):120-6
- McDermott R, Simmonds RW, Steffen M, Cooper KB, Cicak K, Osborn KD, Oh S, Pappas DP, Martinis JM. Simultaneous State Measurement of Coupled Josephson Phase Qubits. Science. 2005 February 25: 307;1299-1302
- Kim D, Shi Z, Simmons CB, Ward DR, Prance JR, Seng Koh T, King Gamble J, Savage DE, Lagally MG, Friesen M, Coppersmith SN, Eriksson MA. Quantum Control and Process Tomography of a Semiconductor Quantum Dot Hybrid Qubit. Nature. 2014 July 3: 511;70-4
- Xia T, Lichtman M, Maller K, Carr AW, Piotrowicz MJ, Isenhower L, Saffman M. Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits. Phys. Rev. Lett. 2015 March 13;114:100503