[Paper Review] Universal digital photonic single-qubit quantum channel simulator

Lu He, Chang Liu+10 more|arXiv (Cornell University)|May 12, 2015

Quantum Computing Algorithms and Architecture3 citations

TL;DR

This paper presents the first experimental digital quantum simulator for arbitrary single-qubit quantum channels, using a universal set of single-qubit gates and a single two-qubit entangling gate. The simulator enables efficient and accurate compilation and programming of any single-qubit channel, generalizing Hamiltonian-based simulators to channel-based digital quantum simulation with broad applications in quantum computation and simulation.

ABSTRACT

Quantum simulators, which exploit quantum effects to reveal unknown or difficult-to-compute properties of a model of interest, play a significant role in quantum information science. Quantum simulation of the dynamics of many-body system has been widely studied for various quantum computing systems, including cold atoms, trapped ions and photons. However, simulation of quantum channels, which describes one of the most general quantum processes in realistic systems, has not yet been fully explored, even for single-qubit channels. Here we report the first experimental digital quantum simulator of arbitrary single-qubit channels. We built this simulator with a set of single-qubit gates together with a single two-qubit entangling gate. We show that any single-qubit channel can be efficiently and accurately programmed and compiled by our simulator. Our scheme generalizes Hamiltonian-based simulators to channel-based digital quantum simulators, which could have important applications in quantum computation and quantum simulation.

Motivation & Objective

• To develop a universal digital quantum simulator capable of emulating any single-qubit quantum channel.
• To overcome the limitations of existing Hamiltonian-based quantum simulators, which do not fully address general quantum processes like quantum channels.
• To enable efficient and accurate programming and compilation of arbitrary single-qubit channels in a physical quantum system.
• To extend digital quantum simulation beyond unitary dynamics to include non-unitary, open quantum system processes such as decoherence and dissipation.

Proposed method

• The simulator employs a universal set of single-qubit quantum gates to construct the desired quantum channel dynamics.
• A single two-qubit entangling gate is used to mediate non-unitary operations required for simulating general quantum channels.
• The channel is compiled into a sequence of quantum operations using a digital simulation framework, enabling programmable implementation.
• The approach generalizes digital quantum simulation from unitary evolution to arbitrary completely positive trace-preserving maps.
• The architecture is designed to be scalable and adaptable to various quantum platforms, including photonic systems.
• The simulator leverages the Stinespring dilation theorem to represent any quantum channel as a unitary evolution on an enlarged Hilbert space.

Experimental results

Research questions

• RQ1 Can a digital quantum simulator be constructed to accurately emulate any arbitrary single-qubit quantum channel?
• RQ2 How can a universal set of quantum gates be combined with a single two-qubit entangling gate to simulate general quantum channels?
• RQ3 What is the efficiency and accuracy of compiling arbitrary single-qubit channels using this digital simulation framework?
• RQ4 How does this approach extend the scope of digital quantum simulation beyond unitary evolution to include non-unitary, open-system dynamics?
• RQ5 What are the practical implications of this simulator for quantum computation and quantum simulation in realistic noisy environments?

Key findings

• The proposed simulator successfully emulates any single-qubit quantum channel with high accuracy using a minimal gate set.
• The inclusion of a single two-qubit entangling gate enables the simulation of non-unitary dynamics essential for modeling open quantum systems.
• The digital compilation method allows for efficient programming of arbitrary channels, demonstrating scalability in principle.
• The scheme generalizes Hamiltonian-based simulators to channel-based digital quantum simulation, broadening the scope of quantum simulation.
• The experimental realization confirms the feasibility of simulating general quantum processes in photonic quantum systems.
• The approach provides a universal framework for simulating arbitrary single-qubit channels, enabling new applications in quantum error mitigation and noise characterization.