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Journal of Physics Conference Series

How can the D-Wave machine exhibit long-time quantum behaviour

D. Drakova, G. Doyen

Published Jul 3, 2015• 1 citation
Publisher

Abstract

Extensive experiments have demonstrated quantum behaviour in the long-time operation of the D-Wave quantum computer. The decoherence time of a single flux qubit is reported to be on the order of nanoseconds [1], which is much shorter than the time required to carry out a computation on the timescale of seconds [2, 3]. Previous judgements of whether the D-Wave device should be thought of as a quantum computer have been based on correlations of the input-output behaviour of the D-Wave machine with a quantum model, called simulated quantum annealing, or classical models, called simulated annealing and classical spin dynamics [4]. Explanations for a factor of 10 8 discrepancy between the single flux qubit decoherence time and the long-time coherent quantum behaviour of many integrated flux qubits of the D-Wave device have not been offered so far. In our contribution we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to environmental particles of high density of states, called gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included. This adiabatic evolution is, however, a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schrödinger's time dependent equation in 4 dimensional spacetime. Compared to Schrödinger's time development in 4D, the evolution is considerably slowed down, though still adiabatic. The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain the factor of 10 8 discrepancy between decoherence time and quantum computation time. The observation and our explanation are in anology to the 108 discrepancy factor found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schrödinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included.

DOI
10.1088/1742-6596/626/1/012057

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Extensive experiments have demonstrated quantum behaviour in the long-time operation of the D-Wave quantum computer. The decoherence time of a single flux qubit is reported to be on the order of nanoseconds [1], which is much shorter than the time required to carry out a computation on the timescale of seconds [2, 3]. Previous judgements of whether the D-Wave device should be thought of as a quantum computer have been based on correlations of the input-output behaviour of the D-Wave machine with a quantum model, called simulated quantum annealing, or classical models, called simulated annealing and classical spin dynamics [4]. Explanations for a factor of 10 8 discrepancy between the single flux qubit decoherence time and the long-time coherent quantum behaviour of many integrated flux qubits of the D-Wave device have not been offered so far. In our contribution we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to environmental particles of high density of states, called gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included. This adiabatic evolution is, however, a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schrödinger's time dependent equation in 4 dimensional spacetime. Compared to Schrödinger's time development in 4D, the evolution is considerably slowed down, though still adiabatic. The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain the factor of 10 8 discrepancy between decoherence time and quantum computation time. The observation and our explanation are in anology to the 108 discrepancy factor found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schrödinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included.
Extensive experiments have demonstrated quantum behaviour in the long-time operation of the D-Wave quantum computer. The decoherence time of a single flux qubit is reported to be on the order of nanoseconds, which is much shorter than the time required to carry out a computation on the timescale of seconds. In our contribution we investigate a model of four qubits with one qubit coupled to a phonon and (optionally) to environmental particles of high density of states, called gravonons. The calculations indicate that when no gravonons are present, the current in the qubit is flipped at some time and adiabatic evolution is discontinued. The time dependent wave functional becomes a non-correctable superposition of many excited states. The results demonstrate the possibility of effectively suppressing the current flip and allowing for continued adiabatic evolution when the entanglement to gravonons is included. This adiabatic evolution is, however, a coherent evolution in high dimensional spacetime and cannot be understood as a solution of Schrödinger's time dependent equation in four dimensional spacetime. Compared to Schrödinger's time development, the evolution is considerably slowed down, though still adiabatic. The properties of our model reflect correctly the experimentally found behaviour of the D-Wave machine and explain the factor of 10810^8108 discrepancy between decoherence time and quantum computation time. The observation and our explanation are in analogy to the 10810^8108 discrepancy factor found, when comparing experimental results on adsorbate quantum diffusion rate with predictions of Schrödinger's time dependent equation, which can also be resolved in a model with the coupling to gravonons included.
Long lasting coherence in photosynthetic pigment-protein complexes has been observed even at physiological temperatures. Experiments have demonstrated quantum coherent behaviour in the long-time operation of the D-Wave quantum computer as well. Quantum coherence is the common feature between the two phenomena. An explanations for eight orders of magnitude discrepancy between the single flux qubit coherence time and the long-time quantum behaviour of an array of thousand flux qubits in the quantum computer was suggested within a theory where the flux qubits are coupled to an environment of particles called gravonons of high density of states The coherent evolution is in high dimensional spacetime and can be understood as a solution of Schroedinger's time-dependent equation. Explanations for the quantum beats observed in 2D Fourier transform electronic spectroscopy of the Fenna-Matthews-Olson (FMO) protein complex in the green sulfur bacteria are presently sought in constructing transport theories based on quantum master equations where 'good' molecular vibrations ('coloured noise') in the chlorophyll and the surrounding protein scaffold knock the exciton oscillations back into coherence. These 'good' vibrations are claimed to have developed in three billion years of natural selection. These theories, however, face the discomforting experimental observation that "attempts to scramble vibrational modes or to shift resonances with isotopic substitution miserably failed to affect the beating signals". As a possible way out of this dilemma we adopted the formalism of the quantum computation to the quantum beats in the FMO protein complex.
Quantum annealing represents an essential milestone towards the goal of adiabatic quantum computing. In quantum annealing, the computation involves finding the ground state of a classical Ising-like Hamiltonian realized as interactions between qubits. Quantum fluctuations are introduced to allow the wavefunction of the qubits to explore the energy landscape, the hope being that the wavefunction finds a minimum energy configuration and possibly giving the result of the computation. While quantum annealing likely may not be as powerful as adiabatic quantum computing, it is possible that it may be better at optimization compared to analogous classical algorithms. In physical realizations of quantum annealing, there are still questions as to the role of quantum fluctuations in the operation of a device given the short coherence times of the individual qubits. These questions have consistently posed a serious theoretical challenge making it difficult to verify experimental results. Here we simplify the problem by considering a system of qubits with ferromagnetic interactions, modeling the decoherence effects as classical noise in the transverse-field of each qubit. We compare the calculations to data collected from a system of manufactured qubits produced by D-wave Systems by performing a finite-size scaling analysis that captures the competition between quantum fluctuations of the transverse-field and bit-flip errors from the noise. We argue that on time-scales larger than the single-qubit decoherence time, the device produces the expected quantum fluctuations for the many-body system. Using this finite-size scaling, one can diagnose sources of noise in the system. Hopefully, in the near future, these devices will not only be realizing coherent quantum annealing but will likely be useful as another example of synthetic quantum matter.
Abstract Quantum annealing has been demonstrated with superconducting qubits. Such a quantum annealer has been used to solve combinational optimization problems. Moreover, it serves as a quantum simulator for investigating the properties of the quantum many-body systems. However, the coherence properties of actual devices provided by D-Wave Quantum Inc. have not been explored sufficiently. Here, we measure the energy relaxation of the excited state in quantum annealing with the D-Wave device. Specifically, we investigate the incoherent decay rate of the first excited states of a fully connected Ising model with a transverse field. We find that the decay rate of the excited states of the model is orders of magnitude smaller than that of the excited state of a single qubit, and we qualitatively explain this phenomenon by using theoretical methods. Since our numerical simulations show that the first excited state during QA for the model is entangled, our experimental results indicate that the long-lived entangled state can be generated during QA with the D-Wave machine.
A recent experiment [T. Lanting et al., Phys. Rev. X 4, 021041 (2014)] claimed to provide evidence of up to eight-qubit entanglement in a D-Wave quantum annealing device. However, entanglement was measured using qubit tunneling spectroscopy, a technique that provides indirect access to the state of the system at intermediate times during the anneal by performing measurements at the end of the anneal with a probe qubit. In addition, an underlying assumption was that the quantum transverse-field Ising Hamiltonian, whose ground states are already highly entangled, is an appropriate model of the device and not some other (possibly classical) model. This begs the question of whether alternative classical or semiclassical models would be equally effective at predicting the observed spectrum and thermal state populations. To check this, we consider a recently proposed classical rotor model with classical Monte Carlo updates, which has been successfully employed in describing features of earlier experiments involving the device. We also consider simulated quantum annealing with quantum Monte Carlo updates, an algorithm that samples from the instantaneous Gibbs state of the device Hamiltonian. Finally, we use the quantum adiabatic master equation, which cannot be efficiently simulated classically and which has previously been used to successfully capture the open-system quantum dynamics of the device. We find that only the master equation is able to reproduce the features of the tunneling spectroscopy experiment, while both the classical rotor model and simulated quantum annealing fail to reproduce the experimental results. We argue that this bolsters the evidence for the reported entanglement.
Abstract : Quantum annealing is a general strategy for solving difficult optimization problems with the aid of quantum adiabatic evolution [1, 2]. Both analytical and numerical evidence suggests that under idealized, closed system conditions, quantum annealing can outperform classical thermalization-based algorithms such as simulated annealing [3, 4]. Do engineered quantum annealing devices effectively perform classical thermalization when coupled to a decohering thermal environment? To address this we establish, using superconducting flux qubits with programmable spin-spin couplings, an experimental signature which is consistent with quantum annealing, and at the same time inconsistent with classical thermalization, in spite of a decoherence timescale which is orders of magnitude shorter than the adiabatic evolution time. This suggests that programmable quantum devices, scalable with current superconducting technology, implement quantum annealing with a surprising robustness against noise and imperfections.