Magic State Distillation and Gate Compilation in Quantum Algorithms for Quantum Chemistry

Abstract

Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which implies the need for quantum error correction and fault-tolerant quantum computation. Arbitrary fault-tolerant operations can be constructed from a small, universal set of fault-tolerant operations by gate compilation. Quantum chemistry algorithms are compiled by decomposing the dynamics of the coupled spin-system using a Trotter formula, synthesizing the decomposed dynamics using Clifford operations and single-qubit rotations, and finally approximating the single-qubit rotations by a sequence of fault-tolerant single-qubit gates. Certain fault-tolerant gates rely on the preparation of specific single-qubit states referred to as magic states. As a result, gate compilation and magic state distillation are critical for solving quantum chemistry problems on a quantum computer. We review recent progress that has improved the efficiency of gate compilation and magic state distillation by orders of magnitude.

17 pages, 3 figures, 1 table in Int. J. Quantum Chem. 2014

References in corpus (38)

• A variational eigenvalue solver on a quantum processor
• Elementary gates for quantum computation
• Surface codes: Towards practical large-scale quantum computation
• Quantum Simulation
• Quantum Teleportation is a Universal Computational Primitive
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Simulated Quantum Computation of Molecular Energies
• Two-Bit Gates are Universal for Quantum Computation
• Fermionic quantum computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Efficient quantum algorithms for simulating sparse Hamiltonians
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Simulating Physical Phenomena by Quantum Networks
• Magic state distillation with low overhead
• Resilient Quantum Computation: Error Models and Thresholds
• Gate count estimates for performing quantum chemistry on small quantum computers
• Single-qubit-gate error below 10^-4 in a trapped ion
• Exponential improvement in precision for simulating sparse Hamiltonians
• Exact synthesis of multiqubit Clifford+T circuits
• Simulating chemistry efficiently on fault-tolerant quantum computers
• Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits
• Exploiting locality in quantum computation for quantum chemistry
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance
• A trapped-ion based quantum byte with $10^{-5}$ next-neighbour cross-talk
• A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits
• Randomized benchmarking of atomic qubits in an optical lattice
• 2-D color code quantum computation
• Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
• A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations
• Floating Point Representations in Quantum Circuit Synthesis
• Optimising the Solovay-Kitaev algorithm
• Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code

Cited by in corpus (9)

• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Scalable Quantum Simulation of Molecular Energies
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Quantifying magic for multi-qubit operations
• Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry
• An efficient magic state approach to small angle rotations
• Quantum chemistry and charge transport in biomolecules with superconducting circuits
• Everything You Always Wanted to Know About Quantum Circuits