Integer factorization using stochastic magnetic tunnel junctions

Borders, William A.; Pervaiz, Ahmed Zeeshan; Fukami, Shunsuke; Çamsarı, Kerem Y.; Ohno, Hideo; Datta, Supriyo

doi:10.1038/s41586-019-1557-9

Cited by 444 publications

(363 citation statements)

References 37 publications

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“…Ref. [18] makes similar order of magnitude energy projections as ours in the case that the SMTJ dwell time could be reduced to ≈ 1 ns. Theory [40] suggests that nanomagnets with autocorrelation times on this scale might be realizable in the limit that the barrier goes to zero.…”

Section: Appendix C: Comparison With P-bitssupporting

confidence: 58%

Energy-Efficient Stochastic Computing with Superparamagnetic Tunnel Junctions

et al. 2020

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Superparamagnetic tunnel junctions have emerged as a competitive, realistic nanotechnology to support novel forms of stochastic computation in CMOS-compatible platforms. One of their applications is to generate random bitstreams suitable for use in stochastic computing implementations. We describe a method for digitally programmable bitstream generation based on pre-charge sense amplifiers which is more energy efficient than previously explored alternatives. The energy savings offered by this digital generator survive when we use them as the fundamental units of a neural network architecture. To take advantage of the potential savings, we codesign the algorithm with the circuit, rather than directly transcribing a classical neural network into hardware. The flexibility of the neural network mathematics compensates for explicitly energy efficient choices we make at the device level. The result is a convolutional neural network design operating at ≈ 150 nJ per inference with 97 % performance on MNIST-nearly an order of magnitude more energy efficiency than comparable proposals in the recent literature. * matthew.daniels@nist.gov † mark.stiles@nist.govThe low energy, truly random behavior, ease of control, and established compatibility with complementarymetal-oxide-semiconductor (CMOS) circuitry has led to the use of SMTJs as the basis for a number of novel computing schemes [11][12][13]. SMTJs were proposed to implement the concept of probabilistic bits, or "p-bits," which were leveraged for applications as Bayesian neural networks [14][15][16], invertible Boolean logic [17,18], reservoir computing [19], and Ising network models applied to optimization problems [20,21]. SMTJs were also proposed as stochastic neural units [22] that can interact with synaptic units, emulated by crossbar arrays of mag-

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Section: Appendix C: Comparison With P-bitssupporting

confidence: 58%

Energy-Efficient Stochastic Computing with Superparamagnetic Tunnel Junctions

et al. 2020

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“…The fluctuating order parameter can be read out by utilizing magnetic tunnel junctions (MTJs) [14,35]. In MTJs, the fluctuating nanomagnets can be integrated as free layers that lead to fast resistance fluctuations [36,37].…”

Section: Discussionmentioning

confidence: 99%

“…Consequently, both fundamental and technological studies have primarily focused on the regime when the energy barrier between the stable states of the magnet is much larger than the thermal energy, referred to as the nonvolatile regime. More recently, it has been realized that the order-parameter dynamics even in the other extreme, namely the low-barrier volatile regime, can be utilized to engender useful technological functionality, including true random-number generation [11], probabilistic computing [12][13][14], optimization [15], machine learning [16] and quantum emulation [17].…”

Section: Introductionmentioning

confidence: 99%

Subnanosecond Fluctuations in Low-Barrier Nanomagnets

et al. 2019

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Fast magnetic fluctuations due to thermal torques have useful technological functionality ranging from cryptography to probabilistic computing. The characteristic time of fluctuations in typical uniaxial anisotropy magnets studied so far is bounded from below by the well-known energy relaxation mechanism. This time scales as α −1 , where α parameterizes the strength of dissipative processes. Here, we theoretically analyze the fluctuating dynamics in easy-plane and antiferromagnetically coupled nanomagnets. We find in such magnets, the dynamics are strongly influenced by fluctuating intrinsic fields, which give rise to an additional dephasing-type mechanism for washing out correlations. In particular, we establish two time scales for characterizing fluctuations (i) the average time for a nanomagnet to reverse-which for the experimentally relevant regime of low damping is governed primarily by dephasing and becomes independent of α, (ii) the time scale for memory loss of a single nanomagnet-which scales as α −1/3 and is governed by a combination of energy dissipation and dephasing mechanism. For typical experimentally accessible values of intrinsic fields, the resultant thermal-fluctuation rate is increased by multiple orders of magnitude when compared with the bound set solely by the energy relaxation mechanism in uniaxial magnets. This could lead to higher operating speeds of emerging devices exploiting magnetic fluctuations.

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“…Quantum computation has the potential to outperform conventional computation for certain challenging problems [1]. Many groups are developing the building blocks of a quantum computer, exploring several different physical systems in the search for the best architecture [2][3][4][5][6][7][8][9][10][11][12][13][14]. One of the challenges is the problem of scalability [15]: it is difficult to engineer a quantum system with a large number of individually controllable qubits that together form a large Hilbert space and are free from external perturbations and loss.…”

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confidence: 99%

Ultracold polar molecules as qudits

et al. 2020

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We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of 40 Ca 19 F and 87 Rb 133 Cs, which are examples of molecules with 2 Σ and 1 Σ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a four-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension d=4 to perform the Deutsch algorithm.

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Integer factorization using stochastic magnetic tunnel junctions

Cited by 444 publications

References 37 publications

Energy-Efficient Stochastic Computing with Superparamagnetic Tunnel Junctions

Energy-Efficient Stochastic Computing with Superparamagnetic Tunnel Junctions

Subnanosecond Fluctuations in Low-Barrier Nanomagnets

Ultracold polar molecules as qudits

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