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: 10.48550/arxiv.1503.08955

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

D. Drakova, G. Doyen

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 [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.

Journal of Physics Conference SeriesJul 3, 20151 citation

How can the green sulfur bacteria use quantum computing for light harvesting?

D. Drakova, G. Doyen

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.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.

arXiv:1605.06149May 11, 20162 citations

A microscopic model of wave-function dephasing and decoherence in the double-slit experiment

Satish Ramakrishna

The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.

arXiv:1911.08586Scientific ReportsOct 25, 20213 citations

EVALUATION OF DECOHERENCE FOR QUANTUM COMPUTING ARCHITECTURES: QUBIT SYSTEM SUBJECT TO TIME-DEPENDENT CONTROL

DMITRY SOLENOV, VLADIMIR PRIVMAN

We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.

arXiv:cond-mat/0506286International Journal of Modern Physics BMay 20, 20068 citations

Behavior of a persistent current qubit in a time-dependent electromagnetic field

Jason F. Ralph, Terrence D. Clark, M. J. Everitt +4 more

This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEJul 26, 20011 citation

Finite-size scaling in quantum annealing with decoherence

Phillip Weinberg

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.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.

Jan 1, 20200 citations

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discrepancy between decoherence time and quantum computation time. The observation and our explanation are in analogy to the

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