Towards Practical Quantum Variational Algorithms (1507.08969v2)

Abstract: The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state preparation can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state preparation. We test its accuracy and determine the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin-orbitals), and for small molecules. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required number of measurements is astronomically large for quantum chemistry applications to molecules, applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state preparation using short quantum circuits, to prepare trial ground states of models faster than using adiabatic state preparation.

• The paper introduces a Hamiltonian variational method that reduces variational parameters and simplifies state preparation.
• It demonstrates quicker convergence on Hubbard models compared to traditional methods like UCC.
• Numerical tests on quantum Hamiltonians and small molecules validate the method's efficiency for practical quantum chemistry simulations.

Insights into Practical Quantum Variational Algorithms

The paper "Towards Practical Quantum Variational Algorithms" addresses the strategic development of algorithms that leverage quantum computing to solve complex quantum state preparation challenges. The focus is on variational approaches that can efficiently operate on quantum systems without relying heavily on quantum error correction, given the constraints of near-term quantum devices. This research carefully evaluates the trade-off between circuit depth and fidelity, examining scenarios where shorter circuits are preferable.

Variational State Preparation and Quantum Algorithms

Variational methods such as matrix product states (MPS), MERA, and PEPS are critically examined in this paper, specifically in the context of quantum-computation-heavy variational algorithms. The paper introduces and tests the "Hamiltonian variational" method as a new technique that purportedly simplifies the state preparation process with a significantly reduced number of variational parameters. Instead of employing the typical exhaustive variational state methods, this technique promises practical applicability for Hamiltonians associated with the Hubbard model.

The comparative analysis with unitary coupled cluster (UCC) methods reveals a notable advancement: the Hamiltonian variational approach aligns with simpler interactions and fewer parameters, resulting in quicker convergence—particularly noticeable in the context of the Hubbard model systems. The paper asserts the potential practical implementability on small quantum computers.

Numerical Insights and Theoretical Implications

The authors extensively test their techniques on sets of quantum Hamiltonians and various chemical problems. The emphasis is placed on the optimization strategy for parameters, which is deeply connected to the success of the variational method. For example, their application to Hubbard ladder models, ranging up to 24 spin-orbitals, illustrates the approach's efficacy in state preparation with manageable computational demands.

Significant attention is devoted to the variational method's implications for quantum chemistry, including benchmark tests on small molecules like HeH⁺, H₂O, and BeH₂, among others. The research presents numerical evidence indicating that Hamiltonian variational states offer superior accuracy and computation efficiency compared to UCC and its variants in larger systems.

Future Prospects and Resource Implications

The methodology unambiguously points to the need for further inquiry into reducing sampling error and refining optimal parameter selections. Growing system sizes and stronger electron correlations will likely magnify the benefits of the Hamiltonian variational method relative to conventional computational tasks. The resource implications are significant: analyzing the gate count and measurement strategies that underpin feasible near-term computation on small quantum systems.

Taking into account the quantum chemistry sector, the paper reflects on the greater computational demands and paves the way for a more precise estimation of resource requirements. While the immediate applications in quantum chemistry remain challenging considering current quantum device limitations, the Hubbard model applications appear promising, holding tangible near-term benefits.

Conclusion

In summary, the research outlined in this paper contributes substantially to the quantum computing field by proposing refined variational approaches that could harness the practical capabilities of quantum devices in near-term applications. The measured understanding of quantum resource constraints combined with strategically designed algorithms forms a roadmap toward more reliable quantum variance in state preparation. While the journey toward practical quantum algorithms continues, the groundwork laid by this paper is indispensable for future progress in quantum computation.