Mehdi Saeedi (Research Overview--- July 2012)

University of Southern California
Department of EE-Systems, EEB-200
3740 McClintock Ave.
Los Angeles CA 90089
msaeedi AT


Reversible Circuits


Reversible circuits have attracted interest as components of quantum algorithms. While unitary transformations can be difficult to work with in general, many prominent quantum algorithms contain large blocks with reversible circuits --- multiple-control Toffoli and Fredkin gates --- that do not invoke the full power of quantum computation. Examples include in modular arithmetic operations and circuits for quantum error-correction which contain large sections of reversible circuits to implement GF(2)-linear transformations. My contributions in the field include:


Arbitrary Quantum Circuits


Any quantum computation involves evolution of an initial quantum state under a series of elementary unitary transformations. Any unitary transformation can be exactly realized if the set of single-qubit operations plus CNOT are applied as the elementary gates. Additionally, for years, quantum circuit community has been convinced that the addition of auxiliary qubits is instrumental in constructing a smaller quantum circuit. My contributions in this field include:


Arithmetic Quantum Circuits


Reversible circuits for modular multiplication $Cx\%M$ with $x<M$ arise as components of modular exponentiation in Shor's quantum number-factoring algorithm. However, existing generic constructions focus on asymptotic gate count and circuit depth rather than actual values, producing fairly large circuits not optimized for specific $C$ and $M$ values. We develop such optimizations in a bottom-up fashion, starting with most convenient $C$ values. My contribution in this field include:


Quantum Architectures


Among the different technological constraints of quantum architectures, limited interaction distance between gate qubits is one of the most common ones. Although arbitrary-distance interaction is possible with moving qubits, restrictions exist in some quantum technologies. To consider quantum architectures with linear nearest-neighbor interactions, we developed a synthesis flow. My contribution in this field include: