Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators

Abstract

Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a non-unitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here we present a general algorithm for implementing the action of any non-unitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating non-unitary operations on intermediate-term and future quantum devices.

References in corpus (29)

• Charge insensitive qubit design derived from the Cooper pair box
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Synthesis of Quantum Logic Circuits
• Variational ansatz-based quantum simulation of imaginary time evolution
• A simple all-microwave entangling gate for fixed-frequency superconducting qubits
• IBM Q Experience as a versatile experimental testbed for simulating open quantum systems
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Variational quantum simulation of general processes
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Quantum Circuits for Isometries
• Constructing neural stationary states for open quantum many-body systems
• A quantum algorithm for evolving open quantum dynamics on quantum computing devices
• Quantum circuits with uniformly controlled one-qubit gates
• Quantum master equation approach to quantum transport through mesoscopic systems
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Decompositions of general quantum gates
• Structure of eigenstates and quench dynamics at an excited state quantum phase transition
• Decoherence as a signature of an excited state quantum phase transition
• A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex
• Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
• Universal simulation of Markovian open quantum systems
• Extending the applicability of Redfield theories into highly non-Markovian regimes
• Digital quantum simulation of many-body non-Markovian dynamics
• Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables
• Quantum simulation of non-Markovianity using the quantum Zeno effect
• Synthesis of Ternary Quantum Logic Circuits by Decomposition
• Simulation of Thermal Relaxation in Spin Chemistry Systems on a Quantum Computer Using Inherent Qubit Decoherence

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• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits
• Quantum Simulation of the Radical Pair Dynamics of the Avian Compass
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• Digital Quantum Simulation of the Spin-Boson Model under Open System Dynamics
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• Simulating noisy quantum channels via quantum state preparation algorithms
• Optimized noise-assisted simulation of the Lindblad equation with time-dependent coefficients on a noisy quantum processor
• Simulation of open quantum systems via low-depth convex unitary evolutions
• Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor
• Locally purified density operators for noisy quantum circuits
• Singular value decomposition quantum algorithm for quantum biology
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials
• Structure-preserving numerical schemes for Lindblad equations
• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
• Simulating open-system molecular dynamics on analog quantum computers
• Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
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• Assisted quantum simulation of open quantum systems
• Non-markovian neural quantum propagator and its application to the simulation of ultrafast nonlinear spectra
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• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Towards robust variational quantum simulation of Lindblad dynamics via stochastic Magnus expansion
• Collisional S-Matrix for the Vibrational Dynamics of H+H2 by Quantum Computing
• A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics
• Digital Quantum Simulation of the Lindblad Master Equation and Its Nonlinear Extensions via Quantum Trajectory Averaging
• Quantum implementation of non-unitary operations with biorthogonal representations
• Quantum State Driving along Arbitrary Trajectories
• Quantum Approximation of Normalized Schatten Norms and Applications to Learning
• Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians
• Probabilistic Unitary Formulation of Open Quantum System Dynamics
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Quantum algorithms based on quantum trajectories
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Quantum Simulation via Stochastic Combination of Unitaries
• Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations
• Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time
• Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians
• Non-normality and dissipation in Markovian quantum dynamics: Implications for quantum simulation
• Krein space quantization and New Quantum Algorithms
• Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators
• Many-Fermion Simulation from the Contracted Quantum Eigensolver without Fermionic Encoding of the Wave Function