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arXiv:1008.0701

Quantum Simulation of Molecular Collisions with Superconducting Qubits

Emily Pritchett, Colin Benjamin, Andrei Galiautdinov, Michael R. Geller, Andrew T. Sornborger, Phillip C. Stancil, John M. Martinis

Published Aug 4, 2010• 9 citations
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Abstract

We introduce a protocol for the fast simulation of $n$-dimensional quantum systems on $n$-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of $H_{\rm s}(t)$, an arbitrary, real, time-dependent $n\times n$ dimensional Hamiltonian that is simulated in the $n$-dimensional `single excitation' subspace of the quantum computer. A time-dependent energy/time rescaling minimizes the simulation time on hardware having a fixed coherence time. We demonstrate how three tunably coupled phase qubits simulate a three-channel molecular collision using this protocol, then study the simulation's fidelity as a function of total simulation time.

DOI
10.48550/arxiv.1008.0701

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We introduce a protocol for the fast simulation of nnn-dimensional quantum systems on nnn-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of Hs(t)H_{\rm s}(t)Hs​(t), an arbitrary, real, time-dependent n×nn\times nn×n dimensional Hamiltonian that is simulated in the nnn-dimensional `single excitation' subspace of the quantum computer. A time-dependent energy/time rescaling minimizes the simulation time on hardware having a fixed coherence time. We demonstrate how three tunably coupled phase qubits simulate a three-channel molecular collision using this protocol, then study the simulation's fidelity as a function of total simulation time.
The single excitation subspace (SES) method for universal quantum simulation is investigated for a number of diatomic molecular collision complexes. Assuming a system of nnn tunably-coupled, and fully-connected superconducting qubits, computations are performed in the nnn-dimensional SES which maps directly to an nnn-channel collision problem within a diabatic molecular wave function representation. Here we outline the approach on a classical computer to solve the time-dependent Schrödinger equation in an nnn-dimensional molecular basis - the so-called semiclassical molecular-orbital close-coupling (SCMOCC) method - and extend the treatment beyond the straight-line, constant-velocity approximation which is restricted to large kinetic energies (≳0.1\gtrsim 0.1≳0.1 keV/u). We explore various multichannel potential averaging schemes and an Ehrenfest symmetrization approach to allow for the application of the SCMOCC method to much lower collision energies (approaching 1 eV/u). In addition, a computational efficiency study for various propagators is performed to speed-up the calculations on classical computers. These computations are repeated for the simulation of the SES approach assuming typical parameters for realistic pretheshold superconducting quantum computing hardware. The feasibility of applying future SES processors to the quantum dynamics of large molecular collision systems is briefly discussed.
Current quantum computing architectures lack the size and fidelity required for universal fault-tolerant operation, limiting the practical implementation of key quantum algorithms to all but the smallest problem sizes. In this work we propose an alternative method for general-purpose quantum computation that is ideally suited for such ``prethreshold'' superconducting hardware. Computations are performed in the nnn-dimensional single-excitation subspace (SES) of a system of nnn tunably coupled superconducting qubits. The approach is not scalable, but allows many operations in the unitary group SU(nnn) to be implemented by a single application of the Hamiltonian, bypassing the need to decompose a desired unitary into elementary gates. This feature makes large, nontrivial quantum computations possible within the available coherence time. We show how to use a programmable SES chip to perform fast amplitude amplification and phase estimation, two versatile quantum subalgorithms. We also show that an SES processor is well suited for Hamiltonian simulation, specifically simulation of the Schr\"odinger equation with a real but otherwise arbitrary $n\ifmmode\times\else\texttimes\fi{}n$ Hamiltonian matrix. We discuss the utility and practicality of such a universal quantum simulator, and propose its application to the study of realistic atomic and molecular collisions.
A quantum computer will potentially solve far-reaching problems which are currently intractable on any classical computer. Many technological obstacles have prevented the realization of a quantum computer, the main obstacle being decoherence, which is the loss of quantum information. Decoherence arises from the undesired interaction between qubits and their environment. Isolated qubits have better coherence but are more difficult to control. Superconducting qubits are a promising platform since their macroscopic size allows for easy control and coupling to other qubits. While the coherence of superconducting qubits has substantially improved over the past two decades, further improvements in coherence are required.We have repeatedly and reliably increased the coherence times of superconducting qubits. Currently decoherence in these devices is dominated by coupling to material defects. These defects are present in the dielectrics used to fabricate these devices or introduced during fabrication. Using simpler resonators as a testbed, we individually isolate, characterize, and then improve each step of the more complicated fabrication of superconducting qubits. We increased the quality factor of resonators by a factor of four by first identifying the surfaces and interfaces as a major source of loss and then by optimizing the substrate preparation. Furthermore, we measure and subsequently mitigate additional defect loss, which is dependent on the position of ground plane holes used to limit the loss from magnetic vortices. Implementing these improvements led to an increase of our qubit coherence times by more than an order of magnitude.The progress made in coherence while maintaining a high degree of connectivity and controllability has been directly used in more complex circuits. One such device is a fully connected three qubit ring with both tunable qubit frequencies and adjustable qubit-qubit couplings. The considerable level of control allows us to generate the quantum dynamics resulting from a collision between Na and He atoms by encoding the problem into a time-dependent multi-qubit interaction. We compute a scattering cross section by measuring the probability of exciting the Na atom over a wide range of collision parameters. The scattering cross-section shows that there is a velocity where the excitation probability is maximized, in agreement with scattering experiments.
We describe an alternative approach to quantum computation that is ideally suited for today's sub-threshold-fidelity qubits, and which can be applied to a family of hardware models that includes superconducting qubits with tunable coupling. In this approach, the computation on an n-qubit processor is carried out in the n-dimensional single-excitation subspace (SES) of the full 2^n-dimensional Hilbert space. Because any real Hamiltonian can be directly generated in the SES [E. J. Pritchett et al., arXiv:1008.0701], high-dimensional unitary operations can be carried out in a single step, bypassing the need to decompose into single- and two-qubit gates. Although technically nonscalable and unsuitable for applications (including Shor's) requiring enormous Hilbert spaces, this approach would make practical a first-generation quantum computer capable of achieving significant quantum speedup.
A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Complementing the theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95% we are able to compute the eigenstates within an accuracy of 50 mHartree on average, a limit set by the coherence time of the tunable coupler.
Hamiltonian dynamics have been widely implemented on noisy intermediate-scale quantum devices in recent years. In contrast, experimental demonstrations of Markovian quantum dynamics remain limited, because implementing nonunitary evolution on quantum computers is challenging. Quantum collision models provide a natural approach to this problem by coupling the system to ancillas to realize dissipation. However, previous implementations of quantum collision models on quantum computers have typically been restricted to one or two system qubits and fewer than 12 time steps, owing to noise, circuit depth, the overhead of ancilla reset, and limited qubit resources. In this work, we experimentally simulate Markovian quantum processes with local and nonlocal dissipation on both trapped-ion and superconducting quantum computers. By employing hardware-specific ancilla strategies, we realize simulations with up to seven system qubits, corresponding to 13 qubits in total, and 40 time steps. Our results demonstrate that, even for the same physical model, the optimal implementation strategy depends strongly on the hardware characteristics of the quantum computer.