May 30, 2014

More published evidence of Quantum Entanglement with Dwave Systems Qubits

A new paper published today in Phys Rev X demonstrates eight qubit entanglement in a D-Wave processor, which is a world record for solid state qubits. This is an exceptional paper with an important result. The picture below measures a quantity that, if negative, verifies entanglement. The quantity s is the time — the quantum annealing procedure goes from the left to the right, with entanglement maximized near the area where the energy gap is smallest.

Upper limit of the quantity Tr[WABρ] versus s for several bipartitions A-B of the eight-qubit system. When this quantity is less than 0, the system is entangled with respect to this bipartition. The solid dots show the upper limit on Tr[WABρ] for the median bipartition. The open dots above and below these are derived from the two bipartitions that give the highest and lowest upper limits on Tr[WABρ], respectively. For the points at s greater than 0.3, the measurements of P1 and P2 do not constrain ρ enough to certify entanglement.

Quantum algorithms hold the promise of helping to solve a broad range of problems that are simply intractable with classical algorithms. The advantage of quantum calculations stems from exploiting the strange and nonintuitive properties of quantum systems: tunneling, superposition, quantum coherence, and entanglement. Building a general-purpose quantum computer, however, is extremely challenging; a more scalable and feasible approach may involve implementing a single, simpler quantum algorithm, such as quantum annealing. It is critical to demonstrate that such a scalable processor has access to quantum-mechanical resources such as coherence and entanglement. We build a processor based on quantum annealing and verify that specific two- and eight-qubit systems become entangled, a necessary and significant step in developing quantum annealing into a viable quantum-computing technology.

We run quantum annealing on a processor chip composed of magnetically coupled superconducting flux qubits. The chip is mounted on the mixing chamber of a dilution refrigerator held at 12.5 mK. We use qubit tunneling spectroscopy to infer nonclassical correlations in two- and eight-qubit systems based on eigenspectra and level occupations, effects that persist even at thermal equilibrium. Our measurements of spectral lines are dominated by the noise of the qubit tunneling spectroscopy probe, however, and we expect that follow-up experiments with improved probes will enable larger systems of qubits to be studied.

Our work provides promise that quantum annealing is a viable approach to realizing quantum-computing technologies. Moreover, our technique represents an effective way of studying quantum behavior in a practical processor, helping us to further understand the capabilities of quantum algorithms.

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have built a series of architecturally scalable QA processors consisting of networks of manufactured interacting spins (qubits). Here, we use qubit tunneling spectroscopy to measure the energy eigenspectrum of two- and eight-qubit systems within one such processor, demonstrating quantum coherence in these systems. We present experimental evidence that, during a critical portion of QA, the qubits become entangled and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that QA is a viable technology for large scale quantum computing.

An illustration of entanglement between two qubits during QA with hi=0 and J less than 0. We plot calculations of the two-qubit ground-state wave-function modulus squared in the basis of Φq1 and Φq2, the flux through the bodies of q1 and q2, respectively. The color scale encodes the probability density with red corresponding to high probability density and blue corresponding to low probability density. We use Hamiltonian (1) and the energies in Fig. 1(d) for the calculation. The four quadrants represent the four possible states of the two-qubit system in the computation basis. We also plot the single-qubit potential energy (U versus Φq1) calculated from measured device parameters. (a) At s=0 (Δ≫2|J|E∼0), the qubits weakly interact and are each in their ground state (1/2)(|↑⟩+|↓⟩), which is delocalized in the computation basis. The wave function shows no correlation between q1 and q2 and, therefore, their wave functions are separable. (b) At intermediate s (Δ∼2|J|E), the qubits are entangled. The state of one qubit is not separable from the state of the other, as the ground state of the system is approximately |+⟩≡(|↑↑⟩+|↓↓⟩)/2. A clear correlation is seen between q1 and q2. (c) As s→1, Δ≪2|J|E, and the ground state of the system approaches |+⟩. However, the energy gap g between the ground state (|+⟩) and the first excited state (|-⟩) is closing. When the qubits are coupled to a bath with temperature T and g less than kBT, the system is in a mixed state of |+⟩ and |-⟩ and entanglement is extinguished.

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