scholarly journals Quantum computing formulation of some classical Hadamard matrix searching methods and its implementation on a quantum computer

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Andriyan Bayu Suksmono ◽  
Yuichiro Minato

AbstractFinding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order is a hard problem that can be solved by a quantum computer. Due to the limitation on the number of qubits and connections in current quantum processors, only low order H-matrix search of orders 2 and 4 were implementable by previous method. In this paper, we show that by adopting classical searching techniques of the H-matrices, we can formulate new quantum computing methods for finding higher order ones. We present some results of finding H-matrices of order up to more than one hundred and a prototypical experiment of the classical-quantum resource balancing method that yields a 92-order H-matrix previously found by Jet Propulsion Laboratory researchers in 1961 using a mainframe computer. Since the exactness of the solutions can be verified by an orthogonality test performed in polynomial time; which is untypical for optimization of hard problems, the proposed method can potentially be used for demonstrating practical quantum supremacy in the near future.

Author(s):  
Lee Spector ◽  
Jon Klein

AbstractWe demonstrate the use of genetic programming in the automatic invention of quantum computing circuits that solve problems of potential theoretical and practical significance. We outline a developmental genetic programming scheme for such applications; in this scheme the evolved programs, when executed, build quantum circuits and the resulting quantum circuits are then tested for “fitness” using a quantum computer simulator. Using the PushGP genetic programming system and the QGAME quantum computer simulator we demonstrate the invention of a new, better than classical quantum circuit for the two-oracle AND/OR problem.


2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Andriyan Bayu Suksmono ◽  
Yuichiro Minato

Abstract Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix problem and address its implementation limitation on existing quantum annealing machine (QAM) that allows up to quadratic terms, whereas the problem naturally introduces higher order ones. For an M-order H-matrix, such a limitation increases the number of variables from M2 to (M3 + M2 − M)/2, which makes the formulation of the Hamiltonian too exhaustive to do by hand. We use symbolic computing techniques to manage this problem. Three related cases are discussed: (1) finding N < M orthogonal binary vectors, (2) finding M-orthogonal binary vectors, which is equivalent to finding a H-matrix, and (3) finding N-deleted vectors of an M-order H-matrix. Solutions of the problems by a 2-body simulated annealing software and by an actual quantum annealing hardware are also discussed.


Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 79 ◽  
Author(s):  
John Preskill

Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.


Author(s):  
Palash Dutta Banik ◽  
Asoke Nath

Quantum Computing is relatively new and it's kind of a special type of computing that uses the laws of quantum physics. In classical computing, we have some limitations and we can overcome those with the help of Quantum Computing as it uses qubits, but we need to keep those qubits at low temperature. Quantum Computing uses the probabilistic nature of electrons. The power of a quantum computer increases exponentially with the number of qubits linked tougher. Quantum computers are very difficult to make but there are a huge number of calculations that can be done easily with the use of a quantum computer. Quantum computers are way better and faster than classical computers. So, we can say that quantum computers rather than quantum computing will be used in the near future to replace classical computing.


2020 ◽  
Vol 20 (9&10) ◽  
pp. 747-765
Author(s):  
F. Orts ◽  
G. Ortega ◽  
E.M. E.M. Garzon

Despite the great interest that the scientific community has in quantum computing, the scarcity and high cost of resources prevent to advance in this field. Specifically, qubits are very expensive to build, causing the few available quantum computers are tremendously limited in their number of qubits and delaying their progress. This work presents new reversible circuits that optimize the necessary resources for the conversion of a sign binary number into two's complement of N digits. The benefits of our work are two: on the one hand, the proposed two's complement converters are fault tolerant circuits and also are more efficient in terms of resources (essentially, quantum cost, number of qubits, and T-count) than the described in the literature. On the other hand, valuable information about available converters and, what is more, quantum adders, is summarized in tables for interested researchers. The converters have been measured using robust metrics and have been compared with the state-of-the-art circuits. The code to build them in a real quantum computer is given.


2014 ◽  
Vol 1078 ◽  
pp. 413-416
Author(s):  
Hai Yan Liu

The ultimate goal of quantum calculation is to build high performance practical quantum computers. With quantum mechanics model of computer information coding and computational principle, it is proved in theory to be able to simulate the classical computer is currently completely, and with more classical computer, quantum computation is one of the most popular fields in physics research in recent ten years, has formed a set of quantum physics, mathematics. This paper to electronic spin doped fullerene quantum aided calculation scheme, we through the comprehensive use of logic based network and based on the overall control of the two kinds of quantum computing model, solve the addressing problem of nuclear spin, avoids the technical difficulties of pre-existing. We expect the final realization of the quantum computer will depend on the integrated use of in a variety of quantum computing model and physical realization system, and our primary work shows this feature..


2020 ◽  
pp. 1-5
Author(s):  
Bahman Zohuri ◽  
◽  
Farhang Mossavar Rahmani ◽  

Companies such as Intel as a pioneer in chip design for computing are pushing the edge of computing from its present Classical Computing generation to the next generation of Quantum Computing. Along the side of Intel corporation, companies such as IBM, Microsoft, and Google are also playing in this domain. The race is on to build the world’s first meaningful quantum computer—one that can deliver the technology’s long-promised ability to help scientists do things like develop miraculous new materials, encrypt data with near-perfect security and accurately predict how Earth’s climate will change. Such a machine is likely more than a decade away, but IBM, Microsoft, Google, Intel, and other tech heavyweights breathlessly tout each tiny, incremental step along the way. Most of these milestones involve packing more quantum bits, or qubits—the basic unit of information in a quantum computer—onto a processor chip ever. But the path to quantum computing involves far more than wrangling subatomic particles. Such computing capabilities are opening a new area into dealing with the massive sheer volume of structured and unstructured data in the form of Big Data, is an excellent augmentation to Artificial Intelligence (AI) and would allow it to thrive to its next generation of Super Artificial Intelligence (SAI) in the near-term time frame.


2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Joe O’Gorman ◽  
Naomi H Nickerson ◽  
Philipp Ross ◽  
John JL Morton ◽  
Simon C Benjamin

Abstract Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.


2005 ◽  
Vol 5 (2) ◽  
pp. 102-112
Author(s):  
C.M. Dawson ◽  
H.L. Haselgrove ◽  
A.P. Hines ◽  
D. Mortimer ◽  
M.A. Nielsen ◽  
...  

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP/P/\#P and BQP/PP.


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