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Minimax rational approximation of the Fermi-Dirac distribution

Journal of Chemical Physics

Moussa, Jonathan E.

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(-1)) poles to achieve an error tolerance at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

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TYPE Journal Article YEAR 2016
ScopusOSTIDOI

Transversal Clifford gates on folded surface codes

Physical Review A

Moussa, Jonathan E.

Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. The specific application of these codes to universal quantum computation based on qubit fusion is also discussed.

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TYPE Journal Article YEAR 2016
ScopusOSTIDOI

Quantum circuits for qubit fusion

Quantum Information and Computation

Moussa, Jonathan E.

We consider four-dimensional qudits as qubit pairs and their qudit Pauli operators as qubit Clifford operators. This introduces a nesting, C21 ⊂ C42 ⊂ C23, where Cmn is the nth level of the m-dimensional qudit Clifford hierarchy. If we can convert between logical qubits and qudits, then qudit Clifford operators are qubit non-Clifford operators. Conversion is achieved by qubit fusion and qudit fission using stabilizer circuits that consume a resource state. This resource is a fused qubit stabilizer state with a fault- tolerant state preparation using stabilizer circuits.

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TYPE Journal Article YEAR 2016
ScopusOSTI

Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis

Parekh, Ojas D.; Wendt, Jeremy D.; Shulenburger, Luke N.; Landahl, Andrew J.; Moussa, Jonathan E.; Aidun, John B.

We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking efforts, in particular those involving adiabatic quantum computation and the Adiabatic Quantum Optimizers produced by D-Wave Systems, Inc. We find that the performance of D-Wave's Adiabatic Quantum Optimizers scales roughly on par with classical approaches for some hard combinatorial optimization problems; however, architectural limitations of D-Wave devices present a significant hurdle in evaluating real-world applications. In addition to identifying and isolating such limitations, we develop algorithmic tools for circumventing these limitations on future D-Wave devices, assuming they continue to grow and mature at an exponential rate for the next several years.

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TYPE SAND Report YEAR 2015
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39 Results
39 Results