We present a real-time quantum Monte Carlo algorithm that simulates the dynamics of open quantum systems by stochastically compressing and evolving the density matrix under both Markovian and non-Markovian master equations. Our algorithm uses population dynamics to continuously suppress the sign problem, preventing its accumulation throughout the evolution for a broad class of noisy-circuit Liouvillians of practical and experimental interest. We apply it to a variety of quantum circuits and demonstrate significant speedups and scaling improvements over state-of-the-art quantum trajectory methods and convergence to exact solutions even in non-Markovian regimes where trajectory methods fail. Our approach improves the efficiency of classical simulation of gate-based quantum computing, quantum annealing, and general open system dynamics.
We present a real-time quantum Monte Carlo algorithm that simulates the dynamics of open quantum systems by stochastically compressing and evolving the density matrix under both Markovian and non-Markovian master equations. Our algorithm uses population dynamics to continuously suppress the sign problem, preventing its accumulation throughout the evolution for a broad class of noisy-circuit Liouvillians of practical and experimental interest. We apply it to a variety of quantum circuits and demonstrate significant speedups and scaling improvements over state-of-the-art quantum trajectory methods and convergence to exact solutions even in non-Markovian regimes where trajectory methods fail. Our approach improves the efficiency of classical simulation of gate-based quantum computing, quantum annealing, and general open system dynamics.
Quantum Monte Carlo and quantum simulation are both important tools for
understanding quantum many-body systems. As a classical algorithm, quantum
Monte Carlo suffers from the sign problem, preventing its applications to most
fermion systems and real-time dynamics. In contrast, on a quantum computer, we
can simulate time evolution of general systems with local interactions, yet
such algorithms usually require the development of fault-tolerant quantum
technologies. In this paper, we introduce a novel non-variational algorithm
using quantum computing as a subroutine to accelerate quantum Monte Carlo. On a
fault-tolerant quantum computer, the complexity of our algorithm is polynomial
as the same as conventional quantum simulation algorithms. On a noisy quantum
computer, our algorithm incorporating error mitigation eases the sign problem.
Even when the circuit noise is significant, our algorithm can reduce the Monte
Carlo variance by orders of magnitude.
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems.As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems and real-time dynamics.In this paper, we introduce a novel nonvariational algorithm using quantum simulation as a subroutine to accelerate quantum Monte Carlo by easing the sign problem.The quantum subroutine can be implemented with shallow circuits and, by incorporating error mitigation, can reduce the Monte Carlo variance by several orders of magnitude even when the circuit noise is significant.As such, the proposed quantum algorithm is applicable to near-term noisy quantum hardware.
Strong coupling and environmental memory render many open quantum systems intractable to classical computation. To overcome this barrier, we present a variational quantum algorithm capable of solving generalized form time-local quantum master equations directly on noisy intermediate-scale quantum (NISQ) processors. Our approach combines four key innovations: (1) a pair-vector stochastic Schrödinger equation to unravel time-local quantum master equations, (2) deterministic evolution projected onto parameterized circuits via McLachlan's principle and stochastic jump implementation via singular-value decomposition, (3) using Hadamard tests circuits to measure the jump rates and the element of reduced density matrices, and (4) using no-evolution sampling to sample trajectories. The resulting protocol remains resilient under realistic hardware noise. We validate it on both classical simulators and a 66-qubit superconducting processor for solving the Redfield master equation and fourth-order time-local non-Markovian master equation and find that it can successfully capture key features of complex open quantum dynamics-including non-Markovian oscillations and strong-coupling effects. Our approach establishes a practical pathway toward scalable simulations of open quantum systems in the NISQ era.
Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.
We present an alternative approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from density-matrix quantum Monte Carlo in dealing with the sign problem and incorporates additional features. First of all, the dynamics is transferred to the Laplace representation where an exact equation can be derived and solved using an evolution step that, unlike most Monte Carlo methods, is not a priori physically bounded. Moreover, the spawning events are formulated in terms of two-process stochastic unravellings of quantum master equations, a formalism that is particularly useful when working with density matrices. Last, our approach is perturbative in nature, with the free part being integrated exactly and, as such, the convergence is greatly accelerated when the interaction parameter is small. We benchmark our method by applying it to two case studies in condensed-matter physics, perform some ground-state calculations, show its accuracy, and further discuss its efficiency.
Many-body open quantum systems are exposed to an essentially uncontrollable environment that acts as a source of decoherence and dissipation. As the exact treatment of such models is generally unfeasible, it is favourable to formulate an approximate description by means of the dynamics of the reduced density operator of the system. When studying models with a weak coupling to a memoryless environment, the existence of such solution is granted and the reduced dynamics is governed by the Lindblad quantum master equation. In recent years, open quantum systems have evolved into a major field of studies. Focus of these studies are the characterization of emergent phenomena and dissipative phase transitions, as well as the ongoing debate about whether quantum computing schemes are still hard to simulate classically --- and thus achieve quantum supremacy --- when in presence of some degree of noise-induced decoherence. However, the challenge posed by this task lies in the complexity of the density matrix that increases exponentially with the system size, and the quest for efficient numerical methods is a research field that is still in its infancy. Here, we first develop a real-time full configuration interaction quantum Monte Carlo technique that stems from a class of methods generally known as projector Monte Carlo. The approach enables the stochastic sampling of the Lindblad time evolution of the density matrix thanks to a massively parallel algorithm, thus providing estimates of observables on the non-equilibrium steady state. We present the underlying theory and introduce an initiator technique and importance sampling to reduce statistical error. We demonstrate the efficiency of the approach by applying it to the dissipative two-dimensional XYZ spin-1/2 model on a lattice. As the importance sampling of projector approaches is often combined with variational results, we then introduce a novel method that is based on the variational Monte Carlo methods and on a neural network representation of the density matrix. Thanks to the stochastic reconfiguration scheme, the application of the variational principle is translated into the actual integration of the Lindblad quantum master equation. We test the effectiveness of the method by modeling the steady state of the dissipative two-dimensional XYZ spin-1/2 model through a dissipative phase transition, and also the real-time dynamics of the dissipative Ising model. In addition, we discuss the application of the developed methods and the open questions of the field.