Efficient diabatic quantum algorithm in number factorization

Shi, Anqi; Guan, Haoyu; Zhang, Wenxian

doi:10.1016/j.physleta.2020.126745

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…Quantum annealing for the PFP is one such interesting task that was reported recently. [19][20][21][22] With the progress of PFP on quantum annealers, it is quite natural to explore the solvability of the DLP on the same computing platform. Thus, we are motivated to make an initial step towards solving the DLP using quantum annealers.…”

Section: Motivationmentioning

confidence: 99%

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An initial step toward a quantum annealing approach to the discrete logarithm problem

Mahasinghe

Jayasinghe

2022

Security and Privacy

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The discrete logarithm problem over a multiplicative group of integer modulo n is the key ingredient in the ElGamal encryption system. This problem has been proven to be tractable in polynomial time on a quantum computer by Shor's algorithm. This algorithm makes use of basic quantum gates, circuits, measurements and it has been experimented in the circuit-gate framework of quantum computing. On the other hand, the adiabatic framework of quantum computing with the quantum annealers such as the D-Wave machine that simulates the adiabatic process has become very popular, showing its potential for making a practical pathway to achieve quantum speedup. Furthermore, much progress has been reported recently on the tractability of the integer factoring problem, which is the other widely-used encryption method, on quantum annealers. In this context, it is important to explore the tractability of the discrete logarithm problem too using quantum annealers. In this work we present a first step made in this direction, by converting the discrete logarithm problem over a multiplicative group into the problem of minimizing a binary quadratic form, a standard problem format acceptable to a quantum annealer. Our formulation was tested for small-scale problem instances using the quantum-classical hybrid platform PyQUBO and we discuss the computational challenges and propose several potential improvements to the formulation.

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Section: Motivationmentioning

confidence: 99%

“…Thus, the DLP and PFP have an inseparable connection. Quantum annealing for the PFP is one such interesting task that was reported recently 19‐22 . With the progress of PFP on quantum annealers, it is quite natural to explore the solvability of the DLP on the same computing platform.…”

Section: Introductionmentioning

confidence: 99%

An initial step toward a quantum annealing approach to the discrete logarithm problem

Mahasinghe

Jayasinghe

2022

Security and Privacy

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“…Due to the uncertainty surrounding adiabatic methods, in recent years there has been explored other strategies such as non-adiabatic or diabatic quantum computing [24,[37][38][39][40]. In the diabatic case, transitions between the ground and excited states are allowed in regions where the gap becomes exponentially small, therefore avoiding the time complexity carried by adiabatic evolution.…”

Section: Introductionmentioning

confidence: 99%

Why adiabatic quantum annealing is unlikely to yield speed-up

Villanueva,

Najafi,

Kappen

2023

J. Phys. A: Math. Theor.

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We study quantum annealing for combinatorial optimization with Hamiltonian $H = H_0 + z H_f$ where $H_f$ is diagonal, $H_0=-\ket{\phi}\bra{\phi}$ is the equal superposition state projector and $z$ the annealing parameter.We analytically compute the minimal spectral gap, which is $\Omega(1/\sqrt{N})$ with $N$ the total number of states, and its location $z_*$.We show that quantum speed-up requires an annealing schedule which demands a precise knowledge of $z_*$, which can be computed only if the density of states of the optimization problem is known.However, in general the density of states is intractable to compute, making quadratic speed-up unfeasible for any practical combinatorial optimization problems. We conjecture that it is likely that this negative result also applies for any other instance independent transverse Hamiltonians such as $H_0 = -\sum_{i=1}^n \sigma_i^x$.

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“…We consider the factorization problem that is solved once the success probability is higher or equal to 1/8 and record the evolution time 𝑇 . [35,36] Numerically, we find that the success evolution time 𝑇 falls into two categories: [36] (i) one is 𝑇 < 10 which we call the factorization problem "easy", (ii) the other is 𝑇 > 100 (calculation stops at 𝑇 > 100 due to insufficient computational power) which we call the factorization problem "hard". In fact, the success evolution time is estimated to be larger than 500 for all the hard problems we calculated.…”

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confidence: 99%

Long-Range Interaction Enhanced Adiabatic Quantum Computers

Shi¹,

Guan²,

Zhang³

et al. 2020

Chinese Phys. Lett.

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A quantum computer is not necessarily alone, e.g., thousands and millions of quantum computers are simultaneously working together for adiabatic quantum computers based on nuclear spins. Long-range interaction is inevitable between these nuclear spin qubits. Here we investigate the effect of long-range dipolar interaction between different adiabatic quantum computers. Our analytical and numerical results show that the dipolar interaction can enhance the final fidelity in adiabatic quantum computation for solving the factorization problem, when the overall interaction is negative. The enhancement will become more prominent if a single quantum computer encounters an extremely small energy gap which occurs more likely for larger-size systems.

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Efficient diabatic quantum algorithm in number factorization

Cited by 4 publications

References 27 publications

An initial step toward a quantum annealing approach to the discrete logarithm problem

An initial step toward a quantum annealing approach to the discrete logarithm problem

Why adiabatic quantum annealing is unlikely to yield speed-up

Long-Range Interaction Enhanced Adiabatic Quantum Computers

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