Practical Quantum Chemistry on Near Term Quantum Computers

Solutions to the time-independent Schrödinger equation for molecular systems allow chemical properties to be studied without the direct need for the material. However, the dimension of this problem grows exponentially with the size of the quantum system under consideration making conventional treatment intractable. Quantum computers can efficiently represent and evolve quantum states. Their use offers a possible way to perform simulations on molecules previously impossible to model. However, given the constraints of current quantum computers even studying small systems is limited by the number of qubits, circuit depth and runtime of a chosen quantum algorithm. The work in this thesis is to explore and provide new tools to make chemical simulation more practical on near-term devices. First, the unitary partitioning measurement reduction strategy is explored. This reduces the runtime of the variational quantum eigensolver algorithm (VQE). We then apply this reduction technique to the contextual subspace method, which approximates a problem by introducing artificial symmetries based on the solution of noncontextual version of the problem that reduces the number of qubits required for simulation. We provide a modification to the original algorithm that makes an exponentially scaling part of the technique quadratic. Finally, we develop the projection-based embedding (PBE) technique to allow chemical systems to be studied using state-of-the-art classical methods in conjuncture with quantum computing protocols in a multiscale hierarchy. This allows molecular problems much larger than conventionally studied on quantum hardware to be approached

Implementation of Measurement Reduction for the Variational Quantum Eigensolver

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware.Comment: Revised order of paper, and further background details about the LCU method added. A unary implementation of LCU is also explored. Results unchange

Benchmarking Noisy Intermediate Scale Quantum Error Mitigation Strategies for Ground State Preparation of the HCl Molecule

Due to numerous limitations including restrictive qubit topologies, short coherence times and prohibitively high noise floors, few quantum chemistry experiments performed on existing noisy intermediate-scale quantum hardware have achieved the high bar of chemical precision, namely energy errors to within 1.6 mHa of full configuration interaction. To have any hope of doing so, we must layer contemporary resource reduction techniques with best-in-class error mitigation methods; in particular, we combine the techniques of qubit tapering and the contextual subspace variational quantum eigensolver with several error mitigation strategies comprised of measurement-error mitigation, symmetry verification, zero-noise extrapolation and dual-state purification. We benchmark these strategies across a suite of eight 27-qubit IBM Falcon series quantum processors, taking preparation of the HCl molecule's ground state as our testbed.Comment: 18 pages, 15 figures, 4 tables, supplementary GitHub repository: https://github.com/TimWeaving/quantum-error-mitigatio

A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilize even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning of the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE); however, there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz, a parametrized quantum state over which we optimize during VQE; it is not initially clear how a splitting of the Hamiltonian should be reflected in the CS-VQE ansätze. We propose a "noncontextual projection" approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator and demonstrate chemically precise ground state energy calculations for a suite of small molecules at a significant reduction in the required qubit count and circuit depth

A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE), but there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz - a parametrized quantum state over which we optimize during VQE. It is not initially clear how a splitting of the Hamiltonian should be reflected in our CS-VQE ans\"atze. We propose a 'noncontextual projection' approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator, with results obtained herein for a suite of trial molecules.Comment: 42 pages, 4 figure