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Full-Text Articles in Engineering
Quantum Algorithm For Variant Maximum Satisfiability, Abdirahman Alasow, Peter Jin, Marek Perkowski
Quantum Algorithm For Variant Maximum Satisfiability, Abdirahman Alasow, Peter Jin, Marek Perkowski
Electrical and Computer Engineering Faculty Publications and Presentations
In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a …
A Polarity-Based Approach For Optimization Of Multivalued Quantum Multiplexers With Arbitrary Single-Qubit Target Gates, Kevin Jin, Tahsin Soffat, Justin Morgan, Marek Perkowski
A Polarity-Based Approach For Optimization Of Multivalued Quantum Multiplexers With Arbitrary Single-Qubit Target Gates, Kevin Jin, Tahsin Soffat, Justin Morgan, Marek Perkowski
Electrical and Computer Engineering Faculty Publications and Presentations
Previous work has provided methods for decomposing unitary matrices to series of quantum multiplexers, but the multiplexer circuits created in this way may be highly non-minimal. This paper presents a new approach for optimizing quantum multiplexers with arbitrary single-qubit quantum target functions and ternary controls. For multivalued quantum multiplexers, we define standard forms and two types of new forms: Fixed Polarity Quantum Forms (FPQFs) and Kronecker Quantum Forms (KQFs). Drawing inspiration from the usage of butterfly diagrams, we devise a method to exhaustively construct new forms. In contrast to previous butterfly-based methods, which are used with classical Boolean functions, these …
Quantum Phase Estimation Using Multivalued Logic, Marek Perkowski, Vamsi Parasa
Quantum Phase Estimation Using Multivalued Logic, Marek Perkowski, Vamsi Parasa
Electrical and Computer Engineering Faculty Publications and Presentations
We generalize the Quantum Phase Estimation algorithm to MVL logic. We show the quantum circuits for QPE using qudits. We derive the performance requirements of the QPE to achieve high probability of success. We show how this leads to logarithmic decrease in the number of qudits and exponential decrease in error probability of the QPE algorithm as the value of the radix d increases.
Extending Classical Test To Quantum, Jacob D. Biamonte, Minki Jeong, Jae-Seung Lee, Marek Perkowski
Extending Classical Test To Quantum, Jacob D. Biamonte, Minki Jeong, Jae-Seung Lee, Marek Perkowski
Electrical and Computer Engineering Faculty Publications and Presentations
We first introduce a method called quantum path verification, where we search for a break in a quantum network. After explaining these capabilities, we address gate internal faults. We present new fault models to represent crosstalk and unwanted nearest neighbor entanglement. When witnessed, these errors are probabilistic, but there is a set of tests that has the highest probability of detecting a fault. We introduce a method of probabilistic set covering to identify this set of tests. A large part of our work consisted of writing a software package that allows us to compare various fault models and test strategies.
Synthesis Of Ternary Quantum Logic Circuits By Decomposition, Marek Perkowski
Synthesis Of Ternary Quantum Logic Circuits By Decomposition, Marek Perkowski
Electrical and Computer Engineering Faculty Publications and Presentations
Recent research in multi-valued logic for quantum computing has shown practical advantages for scaling up a quantum computer. [1,12] Multivalued quantum systems have also been used in the framework of quantum cryptography, [4] and the concept of a qudit cluster state has been proposed by generalizing the qubit cluster state. [5] An evolutionary algorithm based synthesizer for ternary quantum circuits has recently been presented, [2] as well as a synthesis method based on matrix factorization [3].In this paper, a recursive synthesis method for ternary quantum circuits based on the Cosine-Sine unitary matrix decomposition is presented.
Realizing Ternary Quantum Switching Networks Without Ancilla Bits, Marek Perkowski, Guowu Yang, Xiaoyu Song, Jinzhao Wu
Realizing Ternary Quantum Switching Networks Without Ancilla Bits, Marek Perkowski, Guowu Yang, Xiaoyu Song, Jinzhao Wu
Electrical and Computer Engineering Faculty Publications and Presentations
This paper investigates the synthesis of quantum networks built to realize ternary switching circuits in the absence of ancilla bits. The results we established are twofold. The first shows that ternary Swap, ternary NOT and ternary Toffoli gates are universal for the realization of arbitrary n × n ternary quantum switching networks without ancilla bits. The second result proves that all n×n quantum ternary networks can be generated by NOT, Controlled-NOT, Multiply-Two and Toffoli gates. Our approach is constructive.
Testing A Quantum Computer, Marek Perkowski, Jacob D. Biamonte
Testing A Quantum Computer, Marek Perkowski, Jacob D. Biamonte
Electrical and Computer Engineering Faculty Publications and Presentations
We address the problem of quantum test set generation using measurement from a single basis and the single fault model. Experimental physicists currently test quantum circuits exhaustively, meaning that each n-bit permutative circuit requires ζ x 2n tests to assure functionality, and for an m stage permutative circuit proven not to function properly the current method requires ζ x 2n x m tests as the upper bound for fault localization, where zeta varies with physical implementation. Indeed, the exhaustive methods complexity grows exponentially with the number of qubits, proportionally to the number of stages in a quantum circuit and directly …
A Hierarchical Approach To Computer-Aided Design Of Quantum Circuits, Marek Perkowski, Martin Lukac, Pawel Kerntopf, Mikhail Pivtoraiko, Michele Folgheraiter, Yong Woo Choi, Jung-Wook Kim, Dongsoo Lee, Woong Hwangbo, Hyungock Kim
A Hierarchical Approach To Computer-Aided Design Of Quantum Circuits, Marek Perkowski, Martin Lukac, Pawel Kerntopf, Mikhail Pivtoraiko, Michele Folgheraiter, Yong Woo Choi, Jung-Wook Kim, Dongsoo Lee, Woong Hwangbo, Hyungock Kim
Electrical and Computer Engineering Faculty Publications and Presentations
A new approach to synthesis of permutation class of quantum logic circuits has been proposed in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). First we synthesize a library of permutation (pseudobinary) gates using a Computer-Aided-Design approach that links evolutionary and combinatorics approaches with human experience and creativity. Next the circuit is designed using these gates and standard 1*1 and 2*2 quantum gates and finally the optimizing tautological transforms are applied to the circuit, producing a …