1D to 3D Crossover of a Spin-Imbalanced Fermi Gas

We have characterized the one-dimensional (1D) to three-dimensional (3D) crossover of a two-component spin-imbalanced Fermi gas of 6-lithium atoms in a 2D optical lattice by varying the lattice tunneling and the interactions. The gas phase separates, and we detect the phase boundaries using in situ imaging of the inhomogeneous density profiles. The locations of the phases are inverted in 1D as compared to 3D, thus providing a clear signature of the crossover. By scaling the tunneling rate with respect to the pair binding energy, we observe a collapse of the data to a universal crossover point at a scaled tunneling value of 0.025(7).Comment: 5 pages, 4 figure

Phase diagram of a strongly interacting spin-imbalanced Fermi gas

We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of Li6 atoms in a harmonic trap. These results agree with, and extend, previous experimental measurements. Measurements of the critical polarization at which the balanced superfluid core vanishes generally agree with previous experimental results and with quantum Monte Carlo (QMC) calculations in the Bardeen-Cooper-Schrieffer and unitary regimes. We disagree with the QMC results in the Bose-Einstein condensate regime, however, where the measured critical polarizations are greater than theoretically predicted. We also measure the equation of state in the crossover regime for a gas with equal numbers of the two fermion spin states

Quantum Computation of Hydrogen Bond Dynamics and Vibrational Spectra

Calculating the observable properties of chemical systems is often classically intractable, and is widely viewed as a promising application of quantum information processing. This is because a full description of chemical behavior relies upon the complex interplay of quantum-mechanical electrons and nuclei, demanding an exponential scaling of computational resources with system size. While considerable progress has been made in mapping electronic-structure calculations to quantum hardware, these approaches are unsuitable for describing the quantum dynamics of nuclei, proton- and hydrogen-transfer processes, or the vibrational spectra of molecules. Here, we use the QSCOUT ion-trap quantum computer to determine the quantum dynamics and vibrational properties of a shared proton within a short-strong hydrogen-bonded system. For a range of initial states, we experimentally drive the ion-trap system to emulate the quantum trajectory of the shared proton wavepacket as it evolves along the potential surface generated by the nuclear frameworks and electronic structure. We then extract the characteristic vibrational frequencies for the shared proton motion to spectroscopic accuracy and determine all energy eigenvalues of the system Hamiltonian to > 99.9% fidelity. Our approach offers a new paradigm for studying the quantum chemical dynamics and vibrational spectra of molecules, and when combined with quantum algorithms for electronic structure, opens the possibility to describe the complete behavior of molecules using exclusively quantum computation techniques.Comment: 10 pages, 4 figure

Error mitigation, optimization, and extrapolation on a trapped ion testbed

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors around 1% per gate for two-qubit gates. These errors significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called Richardson extrapolation can reduce these errors without incurring a qubit overhead. We demonstrate and optimize this method on the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device to solve an electronic structure problem. We explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) optimization algorithm for calculating the ground state of the HeH+ molecule at 0.8 Angstrom. We test two methods of scaling noise for extrapolation: time-stretching the two-qubit gates and inserting two-qubit gate identity operations into the ansatz circuit. We find the former fails to scale the noise on our particular hardware. Scaling our noise with global gate identity insertions and extrapolating only after a variational optimization routine, we achieve an absolute relative error of 0.363% +- 1.06 compared to the true ground state energy of HeH+. This corresponds to an absolute error of 0.01 +- 0.02 Hartree; outside chemical accuracy, but greatly improved over our non error mitigated estimate. We ultimately find that the efficacy of this error mitigation technique depends on choosing the right implementation for a given device architecture and sampling budget.Comment: 16 pages, 11 figure

Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally