Duality Quantum Research Articles

Towards Conceptualization Of A Prototype For Quantum Database: A Complete Ecosystem

This study proposes a conceptualization of a prototype And a possibility to converge classical database and fully quantum database. This study mostly identifies the gap between this classical and quantum database and proposes a prototype that can be implemented in future products. It is a way that can be used in future industrial product development on hybrid quantum computers. The existing concept used to consider oracle as a black box in this study opens up the possibility for the quantum industry to develop the QASAM module so that we can create a fully quantum database instead of using a classical database as BlackBox.As the Toffoli gate is basically an effective NAND gate it is possible to run any algorithm theoretically in quantum computers. So we will propose a logical design for memory management for the quantum database, security enhancement model, Quantum Recovery Manager & automatic storage management model, and more for the quantum database which will ensure the quantum advantages. In this study, we will also explain the Quantum Vector Database as well as the possibility of improvement in duality quantum computing. It opens up a new scope, possibilities, and research areas in a new approach for quantum databases and duality quantum computing.

Quantitative analysis method for extraordinary optical transmission of thin microcavity by the catastrophic theory

Extraordinary optical transmission (EOT) can be regarded as a phase transition process based on the variation of the aperture of the thin microcavity by the published results. Considering that the catastrophe theory could describe quantitatively any phase transition process, a novel method is proposed to analyze the EOT transition quantitatively based on a cusp catastrophic model with dimensionless analysis. The quantitative relationship of transmitted energy spectral density is fully obtained, which is also related to the aperture radius and incident electromagnetic frequency. Furthermore, from this method, a quantum transition factor is derived strictly to describe the EOT transition process, which can be divided into wave region, wave-particle duality region and quantum region with the factor increasing from 0 to 1, and Bethe's aperture theory stating that transmission is proportional to is only one of our special cases in the wave region. Finally, the influence of the aperture and the frequency of incident wave on the EOT transmittance is analysed, and the catastrophic model is verified by previous experiments. The novel method of transition analysis provides a new insight into the EOT.

Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation

When faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that differs from the two approaches. By using the duality quantum algorithm, we construct a quantum-solving algorithm for solving the first-order wave equation, which represents a typical class of partial differential equations. Numerical results of the quantum circuit have high precision consistency with the theoretical d'Alembert solution. Then the routine is applied to the wave equation with either a dissipation or dispersion term. As shown by complexity analysis for all these cases of the wave equation, our algorithm has a quadratic acceleration for each iteration compared to the classical algorithm.

Fixed-point oblivious quantum amplitude-amplification algorithm

The quantum amplitude amplification algorithms based on Grover’s rotation operator need to perform phase flips for both the initial state and the target state. When the initial state is oblivious, the phase flips will be intractable, and we need to adopt oblivious amplitude amplification algorithm to handle. Without knowing exactly how many target items there are, oblivious amplitude amplification also suffers the “soufflé problem”, in which iterating too little “undercooks” the state and too much “overcooks” the state, both resulting in a mostly non-target final state. In this work, we present a fixed-point oblivious quantum amplitude-amplification (FOQA) algorithm by introducing damping based on methods proposed by A. Mizel. Moreover, we construct the quantum circuit to implement our algorithm under the framework of duality quantum computing. Our algorithm can avoid the “soufflé problem”, meanwhile keep the square speedup of quantum search, serving as a subroutine to improve the performance of quantum algorithms containing oblivious amplitude amplification procedure.

Quantum simulation of τ-anti-pseudo-Hermitian two-level systems

Different from the Hermitian case, non-Hermitian (NH) systems have novel properties and strongly relate to open and dissipative quantum systems. In this work, we investigate how to simulate τ-anti-pseudo-Hermitian systems in a Hermitian quantum device using linear combinations of unitaries and duality quantum algorithm. Specifying the τ to time-reversal (T) and parity-time-reversal (PT) operators, we construct the two NH two-level systems, design quantum circuits including three qubits, and decide the quantum gates explicitly in detail. We also calculate the success probabilities of the simulation. Experimental implementation can be expected in small quantum simulator.

Quantum Simulation of Pseudo-Hermitian-φ-Symmetric Two-Level Systems.

Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian--symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices.

Quantum simulation of PT-arbitrary-phase–symmetric systems

Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT–symmetric systems and their featured properties have started to be investigated. In this work, we develop the PT and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT-φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT symmetry, unifying the PT and anti-PT symmetries and having intermediate properties between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH system in two dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.

Universal quantum simulation of single-qubit nonunitary operators using duality quantum algorithm

Quantum information processing enhances human’s power to simulate nature in quantum level and solve complex problem efficiently. During the process, a series of operators is performed to evolve the system or undertake a computing task. In recent year, research interest in non-Hermitian quantum systems, dissipative-quantum systems and new quantum algorithms has greatly increased, which nonunitary operators take an important role in. In this work, we utilize the linear combination of unitaries technique for nonunitary dynamics on a single qubit to give explicit decompositions of the necessary unitaries, and simulate arbitrary time-dependent single-qubit nonunitary operator F(t) using duality quantum algorithm. We find that the successful probability is not only decided by F(t) and the initial state, but also is inversely proportional to the dimensions of the used ancillary Hilbert subspace. In a general case, the simulation can be achieved in both eight- and six-dimensional Hilbert spaces. In phase matching conditions, F(t) can be simulated by only two qubits. We illustrate our method by simulating typical non-Hermitian systems and single-qubit measurements. Our method can be extended to high-dimensional case, such as Abrams–Lloyd’s two-qubit gate. By discussing the practicability, we expect applications and experimental implementations in the near future.

Solving Sudoku game using a hybrid classical-quantum algorithm

Sudoku is a fun combinatorial game, based on the Latin square, which has wide applications as being an efficient design in controlling multiple sources of variable nuisance simultaneously. Quantum Sudoku solver uses basics of quantum mechanics such as superposition and entanglement. Using the concept of duality quantum computing, we propose an algorithm which solves a Sudoku puzzle with a space complexity [] (where N = 4). Our proposed algorithm has a primary aim to provide a theoretical framework for an application of duality quantum computing.

Brief Review: Simulation of Novel Systems Using Duality Quantum Algorithm

In this article, we review the recent works of quantum simulation of novel systems briefly, the parity-time-reversal-symmetric (PT-symmetric) quantum system and the Yang-Baxter-equation (YBE) system, using duality quantum algorithm. Duality quantum algorithm studies the linear combinations of unitary operators, making it possible to simulate non-unitary evolutions of novel quantum systems. A PT-symmetric quantum system is a typical non-Hermitian system of which the evolution is not unitary and cannot be simulated directly by a conventional quantum computer. A recent work by C. Zheng has established a theory to simulate a general PT-symmetric two level system by duality quantum computing. The other typical example is the YBE quantum systems, of which the evolutions can be both unitary and non-unitary. C. Zheng and S. J. Wei described a theory that the two hand sides of the YBE can be simulated efficiently by the duality quantum algorithm in their recent research. Perspectives of future applications are expected at last. Copyright © VBRI Press.

Duality quantum simulation of a generalized anti-PT-symmetric two-level system

In this work, quantum simulation of the evolution of a two-level quantum system with a generalized anti-PT(APT)-symmetric Hamiltonian in arbitrary phase is investigated theoretically. The evolution is reinterpreted as a subsystem in a Hilbert space of higher dimensions, enabling it to construct any two-dimensional APT-symmetric Hamiltonian in a Hermitian quantum system. In some special phases, a two-qubit quantum computer is able to achieve the quantum simulation. However, a minimum six-dimensional Hilbert space is necessary for a general case, indicating that a qutrit is needed as an ancillary. We show how to realize the simulation process in a qubit-qutrit hybrid system using the duality quantum algorithm. We also give the flow chart and quantum circuit for a quantum computer of three qubits to realize the quantum simulation. Therefore, experimental realizations and applications can be expected in the future.

Implementation of a fixed-point quantum search by duality computer

The quantum algorithms where the operations are unitary can be implemented by an ordinary quantum computer, and nonunitary operations can be realized in the duality computer. The operations in the fixed-point quantum search proposed by Mizel (Phys. Rev. Lett., 102 (2009) 150501) are not unitary, and in this paper it is shown that this algorithm can effectively be implemented in duality quantum computer.

A Note of Coherence for Duality Quantum Computers Acting on Pure States

In this paper, we discuss the coherence for duality quantum computers under taking different unitary operators acting on pure states. Firstly, for arbitrary unitary operators, we give some general quantitative results of the coherence of output states. Secondly, for incoherence unitary operators, we obtain that the coherence of output states satisfies an inequality. In addition, we also give a conclusion of the coherence of output states under unitary permutation operators.

Duality quantum simulation of a general parity-time-symmetric two-level system

The evolution of a two-level quantum system with a general parity-time-reversal-invariant Hamiltonian is reinterpreted as a subsystem in a four-dimensional Hilbert space, which makes it possible to simulate any two-level parity-time-symmetric (PT-symmetric) quantum system using a conventional quantum mechanics system. We studied the ability to simulate and investigate novel quantum systems and phenomena using a nowadays-available Hermitian quantum computer or a duality quantum computer. The quantum circuits are given for a qubit and two qudit systems, and they would be useful for experimental implementation and applications in the future.

Duality Quantum Simulation of the Yang-Baxter Equation

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

New research progress of nuclear magnetic resonance quantum information processing

In the last 20 years, there have been lots of novel developments and remarkable achievements in quantum information processing theoretically and experimentally. Among them, the coherent control of nuclear spin dynamics is a powerful tool for the experimental implementation of quantum schemes in liquid and solid nuclear magnetic resonance (NMR) system, especially in liquid-state NMR. Compared with other quantum information processing systems, NMR platform has many advantages such as the long coherence time, the precise manipulation and well-developed quantum control techniques, which make it possible to accurately control a quantum system with up to 12-qubits. Extensive applications of liquid-state NMR spectroscopy in quantum information processing such as quantum communication, quantum computing and quantum simulation have been thoroughly studied over half a century. There are also many outstanding researches in the recent several years. So we focus on the recent researches in this review article. First, we introduce the basic principle of the liquid-state NMR quantum computing and two new methods reported in the pseudo-pure state preparation which has more advantages than the traditional methods. The quantum noise-injection methods and the quantum tomography technology in liquid-state NMR are also mentioned. Then we overview Horrow-Hassidim-Lioyd algorithm, quantum support vector machine algorithm, duality quantum computing and their implementations in liquid-state NMR system. Also, we report recent researches about quantum simulations, including quantum tunneling, high-energy physics and topological sequences. Then we display the quantum cloud platform of our group. In order to let more people, either amateurs or professionals, embrace and more importantly participate in the tidal wave of quantum science, we launch our NMR quantum cloud computing (NMRCloudQ) service. Through NMRCloudQ, we offer a direct access to a real, physical spectrometer in our laboratory and encourage users to explore quantum phenomena and demonstrate quantum algorithms. Finally, we discuss the development prospects and development bottlenecks of NMR, and point out the prospects for the future development direction.

Duality quantum algorithm efficiently simulates open quantum systems.

Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.

Duality quantum computer and the efficient quantum simulations

In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Duality quantum computer provides flexibility and clear physical picture in designing quantum algorithms, serving as a useful bridge between quantum and classical algorithms. In this review, we will show that duality quantum computer can simulate quantum systems more efficiently than ordinary quantum computers by providing descriptions of the recent efficient quantum simulation algorithms of Childs et al [Quantum Information & Computation, 12(11-12): 901-924 (2012)] for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al [Phys. Rev. Lett. 114, 090502 (2015)], which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.

Generalized duality quantum computers acting on mixed states

A generalized duality quantum computer acting on mixed states (GDQC-MS) is established, which is a device consisting of a generalized quantum wave divider, a finite number of generalized quantum operations, and a generalized quantum wave combiner. Some of the interesting properties of a GDQC are explored. For example, it is proved that the divider and the combiner of a GDQC-MS are mutually dual contractions, and when the generalized quantum operations used in a GDQC-MS are contractions, the GDQC-MS is also a contraction. In that case, the loss of an input state passing through a GDQC-MS is measured and the corresponding operator of a GDQC-MS is a generalized quantum operation.

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators.

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and nontrivial quantum geometry.