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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 …
An Extended Approach For Generating Unitary Matrices For Quantum Circuits, Zhiqiang Li, Wei Zhang, Gaoman Zhang, Juan Dai, Jiajia Hu, Marek Perkowski, Xiaoyu Song
An Extended Approach For Generating Unitary Matrices For Quantum Circuits, Zhiqiang Li, Wei Zhang, Gaoman Zhang, Juan Dai, Jiajia Hu, Marek Perkowski, Xiaoyu Song
Electrical and Computer Engineering Faculty Publications and Presentations
In this paper, we do research on generating unitary matrices for quantum circuits automatically. We consider that quantum circuits are divided into six types, and the unitary operator expressions for each type are offered. Based on this, we propose an algorithm for computing the circuit unitary matrices in detail. Then, for quantum logic circuits composed of quantum logic gates, a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement. Finally, we apply the proposed algorithm to different reversible benchmark circuits based on NCT library (including NOT gate, Controlled-NOT gate, Toffoli gate) and …
Machine-Learning Based Three-Qubit Gate For Realization Of A Toffoli Gate With Cqed-Based Transmon Systems, Sahar Daraeizadeh, Shavindra Premaratne, Xiaoyu Song, Marek A. Perkowski, Anne Y. Matsuura
Machine-Learning Based Three-Qubit Gate For Realization Of A Toffoli Gate With Cqed-Based Transmon Systems, Sahar Daraeizadeh, Shavindra Premaratne, Xiaoyu Song, Marek A. Perkowski, Anne Y. Matsuura
Electrical and Computer Engineering Faculty Publications and Presentations
We use machine learning techniques to design a 50 ns three-qubit flux-tunable controlled-controlled-phase gate with fidelity of >99.99% for nearest-neighbor coupled transmons in circuit quantum electrodynamics architectures. We explain our gate design procedure where we enforce realistic constraints, and analyze the new gate’s robustness under decoherence, distortion, and random noise. Our controlled-controlled phase gate in combination with two single-qubit gates realizes a Toffoli gate which is widely used in quantum circuits, logic synthesis, quantum error correction, and quantum games.
Minimization Of Quantum Circuits Using Quantum Operator Forms, Martin Lukac, Michitaka Kameyama, Marek Perkowski, Pawel Kerntopf
Minimization Of Quantum Circuits Using Quantum Operator Forms, Martin Lukac, Michitaka Kameyama, Marek Perkowski, Pawel Kerntopf
Electrical and Computer Engineering Faculty Publications and Presentations
In this paper we present a method for minimizing reversible quantum circuits using the Quantum Operator Form (QOF); a new representation of quantum circuit and of quantum-realized reversible circuits based on the CNOT, CV and CV† quantum gates. The proposed form is a quantum extension to the well known Reed-Muller but unlike the Reed-Muller form, the QOF allows the usage of different quantum gates. Therefore QOF permits minimization of quantum circuits by using properties of different gates than only the multi-control Toffoli gates. We introduce a set of minimization rules and a pseudo-algorithm that can be used to design circuits …
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.
Fault Testing Quantum Switching Circuits, Marek Perkowski, Jacob Biamonte
Fault Testing Quantum Switching Circuits, Marek Perkowski, Jacob Biamonte
Electrical and Computer Engineering Faculty Publications and Presentations
Test pattern generation is an electronic design automation tool that attempts to find an input (or test) sequence that, when applied to a digital circuit, enables one to distinguish between the correct circuit behavior and the faulty behavior caused by particular faults. The effectiveness of this classical method is measured by the fault coverage achieved for the fault model and the number of generated vectors, which should be directly proportional to test application time. This work address the quantum process validation problem by considering the quantum mechanical adaptation of test pattern generation methods used to test classical circuits. We found …
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.
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.
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.
A Quantum Test Algorithm, Marek Perkowski, Jacob Biamonte
A Quantum Test Algorithm, Marek Perkowski, Jacob Biamonte
Electrical and Computer Engineering Faculty Publications and Presentations
Current processes validation methods rely on diverse input states and exponential applications of state tomography. Through generalization of classical test theory exceptions to this rule are found. Instead of expanding a complete operator basis to validate a process, the objective is to utilize quantum effects making each gate realized in the process act on a complete set of characteristic states and next extract functional information. Random noise, systematic errors, initialization inaccuracies and measurement faults must also be detected. This concept is applied to the switching class comprising the search oracle. In a first approach, the test set cardinality is held …
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 …
Synthesis Of Reversible Circuits From A Subset Of Muthukrishnan-Stroud Quantum Realizable Multi-Valued Gates, Marek Perkowski, Nicholas Denler, Bruce Yen, Pawel Kerntopf
Synthesis Of Reversible Circuits From A Subset Of Muthukrishnan-Stroud Quantum Realizable Multi-Valued Gates, Marek Perkowski, Nicholas Denler, Bruce Yen, Pawel Kerntopf
Electrical and Computer Engineering Faculty Publications and Presentations
We present a new type of quantum realizable reversible cascade. Next we present a new algorithm to synthesize arbitrary single-output ternary functions using these reversible cascades. The cascades use “Generalized Multi-Valued Gates” introduced here, which extend the concept of Generalized Ternary Gates introduced previously. While there were 216 GTGs, a total of 12 ternary gates of the new type are sufficient to realize arbitrary ternary functions. (The count can be further reduced to 5 gates, three 2-qubit and two 1-qubit). Such gates are realizable in quantum ion trap devices. For some functions, the algorithm requires fewer gates than results previously …
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 …