We developed quantum computer algorithms which utilize quantum effects to

- Accelerate machine learning – particularly, deep learning
- Perform tensor operations on a quantum computer
- Simulate quantum chemistry and materials science

In our work, we have taken part in several experimental collaborations which have realized prototypes of our algorithms.

In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. We’ve considered both gate-model as well as adiabatic quantum simulation, together with experimental realizations.

In short. Quantum effects are a feature, not a bug and quantum effects are inherently good at simulating themselves. The area of quantum simulation considers dedicated quantum systems as well as quantum computer algorithms which simulate physics and quantum chemistry.

**Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register**

with Ya Wang et al.

ACS Nano 9, 7769 (2015)

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Ab initiocomputation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which have the potential to vastly accelerate research throughput in fields ranging from material science to drug discovery. Using a solid-state quantum register realized in a nitrogen-vacancy (NV) defect in diamond, we compute the bond dissociation curve of the minimal basis helium hydride cation, HeH^{+}. Moreover, we report an energy uncertainty (given our model basis) of the order of 10^{–14}hartree, which is 10 orders of magnitude below the desired chemical precision. As NV centers in diamond provide a robust and straightforward platform for quantum information processing, our work provides an important step toward a fully scalable solid-state implementation of a quantum chemistry simulator.arXiv:1405.2696 [quant-ph]

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**Adiabatic Quantum Simulators**

with Ville Bergholm, James Whitfield, Joe Fitzsimons and Alan Aspuru-Guzik

AIP Advances 1, 022126 (2011)

**Simulation of Electronic Structure Hamiltonians using Quantum Computers **

with James Whitfield and Alan Aspuru-Guzik

Molecular Physics 109, 735 (2011) – **James Whitfield received the Longuet-Higgins Authors Prize for this work**, [*Molecular Physics*109:5, 735 (2010)], Announcement of the winner of the Longuet-Higgins Author’s Prize, editorial by Tim Softley

**Towards Quantum Chemistry on a Quantum Computer **

with Ben Lanyon, et al.,

Nature Chemistry 2, 106 (2009)

**High fidelity Spin Entanglement using Optimal Control**

with Florian Dolde et al.

Nature Communications 5, 3371 (2014)

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Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.

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**Solving Search Problems by Strongly Simulating Quantum Circuits**

with Tomi Johnson, Stephen Clark and Dieter Jaksch

Scientific Reports 3, 1235 (2013)

**Chiral Quantum Walks**

Dawei Lu, Jacob D. Biamonte, Jun Li, Hang Li, Tomi H. Johnson, Ville Bergholm, Mauro Faccin, Zoltán Zimborás, Raymond Laflamme, Jonathan Baugh, Seth Lloyd

Physical Review A 93, 042302 (2016)

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Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal theory, classifying Hamiltonians and quantum circuits as time-symmetric or not in terms of the elements and geometries of their underlying networks. Many of the typical circuits of quantum information science are found to exhibit time-asymmetry. Moreover, we show that time-asymmetry in circuits can be controlled using local gates only, and can simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a fundamental example in which controlled time-reversal asymmetry in a palindromic quantum circuit leads to near-perfect transport. Our results pave the way for using time-symmetry breaking to control coherent transport, and imply that time-asymmetry represents an omnipresent yet poorly understood effect in quantum information science.

arXiv:1405.6209 [quant-ph]

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