Simulation of single-qubit open quantum systems

Abstract

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels $\{T_t\}$ specified by a generator $\mathcal{L}$. This algorithm requires only $\mathcal{O}((||\mathcal{L}|{|}_{(1\to 1)}t{)}^{3/2}/{\epsilon }^{1/2})$ single qubit and CNOT gates and approximates the channel $T_t=e^{t\mathcal{L}}$ up to chosen accuracy $\epsilon$. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilised which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a non-unitary single-qubit quantum channel.

Revised version. Restricted recombination method to first order Suzuki-Lie-Trotter integrators, and added discussion concerning issues with application of higher order integrators within the open quantum systems setting

References in corpus (9)

• An Open-System Quantum Simulator with Trapped Ions
• Dissipative preparation of entanglement in optical cavities
• Using Quantum Computers for Quantum Simulation
• Quantum algorithm for simulating the dynamics of an open quantum system
• Simulation of indivisible qubit channels in collision models
• Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
• Dissipative preparation of large W states in Optical Cavities
• Some Open Problems in Quantum Information Theory
• Dissipative preparation of generalised Bell states

Cited by in corpus (26)

• Collision models can efficiently simulate any multipartite Markovian quantum dynamics
• Characterizing non-Markovianity via quantum interferometric power
• Universal simulation of Markovian open quantum systems
• Learning models of quantum systems from experiments
• Digital quantum simulation of many-body non-Markovian dynamics
• Quantum simulation of dissipative collective effects on noisy quantum computers
• Quantum simulation of quantum channels in nuclear magnetic resonance
• Gaussian interferometric power as a measure of continuous variable non-Markovianity
• Efficient simulation of sparse Markovian quantum dynamics
• Superdiffusive quantum stochastic walk definable of arbitrary directed graph
• Quantum simulation of non-Markovianity using the quantum Zeno effect
• Experimental repetitive quantum channel simulation
• Nitrogen-Vacancy Center as Open-Quantum-System Simulator
• Quantum simulations of dissipative dynamics: time-dependence instead of size
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Variational Quantum Algorithms for Steady States of Open Quantum Systems
• Dissipative Bose-Einstein condensation in contact with a thermal reservoir
• Experimental demonstration of a measurement-based realisation of a quantum channel
• Error-mitigated deep-circuit quantum simulation of open systems: steady state and relaxation rate problems
• Quantum circuit simulation of superchannels
• Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems
• Optimal quantum simulation of open quantum systems
• Weighted Quantum Channel Compiling through Proximal Policy Optimization
• Digital Simulation of Single Qubit Markovian Open Quantum Systems: A Tutorial
• Experimental simulation of quantum superchannels
• Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators