Linear and logarithmic time compositions of quantum many-body operators

Abstract

We develop a generalized framework for constructing many-body-interaction operations either in linear time, or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given in particular for Pauli strings, many-control Toffoli gates, number-~and parity-conserving interactions, Unitary Coupled Cluster operations, and sparse matrix generators. We provide a linear time protocol that works by creating a superposition of exponentially many different possible operator strings and then uses dynamical decoupling methodology to undo all the unwanted terms. A logarithmic time protocol overcomes the speed limit of the first by using ancilla registers to condition evolution to the support of the desired many-body interaction before using parallel chaining operations to expand the string length. The two techniques improve substantially on current strategies (reductions in time and space can range from linear to exponential), are applicable to different physical interaction mechanisms such as CNOT, $XX$, and $XX+YY$, and generalize to a wide range of many-body operators.

arXiv comment8 pages, 4 figures

References in corpus (30)

• The Quantum Internet
• A variational eigenvalue solver on a quantum processor
• Elementary gates for quantum computation
• Quantum algorithm for solving linear systems of equations
• Simulated Quantum Computation of Molecular Energies
• 14-qubit entanglement: creation and coherence
• Multi-particle entanglement of hot trapped ions
• Entanglement and quantum computation with ions in thermal motion
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Simulating chemistry using quantum computers
• Digital quantum simulation of fermionic models with a superconducting circuit
• Gate count estimates for performing quantum chemistry on small quantum computers
• High-order quantum algorithm for solving linear differential equations
• On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization
• Adiabatic Quantum Simulation of Quantum Chemistry
• Techniques for the Synthesis of Reversible Toffoli Networks
• Fast Quantum Modular Exponentiation
• Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization
• Improved Quantum Cost for n-bit Toffoli Gates
• Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
• Indirect Interaction of Solid-State Qubits via Two-Dimensional Electron Gas
• Simulating Quantum Dynamics On A Quantum Computer
• Charting the circuit QED design landscape using optimal control theory
• Efficient Grover search with Rydberg blockade
• Improved error thresholds for measurement-free error correction
• A Quantum Computer Architecture using Nonlocal Interactions
• An $\Theta (\sqrt{n})$-depth Quantum Adder on a 2D NTC Quantum Computer Architecture
• A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
• Graph Concatenation for Quantum Codes
• On the Effect of Quantum Interaction Distance on Quantum Addition Circuits

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