Noisy Intermediate-scale Quantum Machines Research Articles

A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz.

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilize even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning of the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE); however, there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz, a parametrized quantum state over which we optimize during VQE; it is not initially clear how a splitting of the Hamiltonian should be reflected in the CS-VQE ansätze. We propose a "noncontextual projection" approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator and demonstrate chemically precise ground state energy calculations for a suite of small molecules at a significant reduction in the required qubit count and circuit depth.

Indexed improvements for real-time trotter evolution of a (1 + 1) field theory using NISQ quantum computers

Today’s quantum computers offer the possibility of performing real-time calculations for quantum field theory scattering processes motivated by high energy physics. In order to follow the successful roadmap which has been established for the calculation of static properties at Euclidean time, it is crucial to develop new algorithmic methods to deal with the limitations of current noisy intermediate-scale quantum (NISQ) devices and to establish quantitative measures of the progress made with different devices. In this paper, we report recent progress in these directions. We show that nonlinear aspects of the trotter errors allow us to take much larger step then suggested by low-order analysis. This is crucial to reach physically relevant time scales with today’s NISQ technology. We propose to use an index averaging absolute values of the difference between the accurately calculated trotter evolution of site occupations and their actual measurements on NISQ machines (G index) as a measure to compare results that have been obtained from different hardware platforms. Using the transverse Ising model in one spatial dimension with four sites we apply this metric across several hardware platforms. We study the results including readout mitigation and Richardson extrapolations and show that the mitigated measurements are very effective based on the analysis of the trotter step size modifications. We discuss how this advance in the trotter step size procedures can improve quantum computing physics scattering results and how this technical advance can be applied to other machines and noise mitigation methods.

Resource Estimation for Quantum Variational Simulations of the Hubbard Model

As the advances in quantum hardware bring us into the noisy intermediate-scale quantum (NISQ) era, one possible task we can perform without quantum error correction using NISQ machines is the variational quantum eigensolver (VQE) due to its shallow depth. A specific problem that we can tackle is the strongly interacting Fermi-Hubbard model, which is classically intractable and has practical implications in areas like superconductivity. In this Article, we outline the details about the gate sequence, the measurement scheme and the relevant error mitigation techniques for the implementation of the Hubbard VQE on a NISQ platform. We perform resource estimation for both silicon spin qubits and superconducting qubits for a 50-qubit simulation, which cannot be solved exactly via classical means, and find similar results. The number of two-qubit gates required is on the order of 20000. Hence, to suppress the mean circuit error count to a level such that we can obtain meaningful results with the aid of error mitigation, we need to achieve a two-qubit gate error rate of $\sim 10^{-4}$. When searching for the ground state, we need a few days for one gradient-descent iteration, which is impractical. This can be reduced to around $10$ minutes if we distribute our task among hundreds of quantum processing units. Hence, implementing a 50-qubit Hubbard model VQE on a NISQ machine can be on the brink of being feasible in near term, but further optimisation of our simulation scheme, improvements in the gate fidelity, improvements in the optimisation scheme and advances in the error mitigation techniques are needed to overcome the remaining obstacles. The scalability of the hardware platform is also essential to overcome the runtime issue via parallelisation, which can be done on one single silicon multi-core processor or across multiple superconducting processors.

Variational quantum unsampling on a quantum photonic processor

A promising route towards the demonstration of near-term quantum advantage (or supremacy) over classical systems relies on running tailored quantum algorithms on noisy intermediate-scale quantum machines. These algorithms typically involve sampling from probability distributions that—under plausible complexity-theoretic conjectures—cannot be efficiently generated classically. Rather than determining the computational features of output states produced by a given physical system, we investigate what features of the generating system can be efficiently learnt given direct access to an output state. To tackle this question, here we introduce the variational quantum unsampling protocol, a nonlinear quantum neural network approach for verification and inference of near-term quantum circuit outputs. In our approach, one can variationally train a quantum operation to unravel the action of an unknown unitary on a known input state, essentially learning the inverse of the black-box quantum dynamics. While the principle of our approach is platform independent, its implementation will depend on the unique architecture of a specific quantum processor. We experimentally demonstrate the variational quantum unsampling protocol on a quantum photonic processor. Alongside quantum verification, our protocol has broad applications, including optimal quantum measurement and tomography, quantum sensing and imaging, and ansatz validation. The variational quantum unsampling protocol provides a way to realize verification and inference of near-term quantum circuit outputs. This protocol is then experimentally verified on a quantum photonic processor.

Variational Quantum Circuits for Deep Reinforcement Learning

The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. However, the existing quantum computing platforms are hard to simulate classical deep learning models or problems because of the intractability of deep quantum circuits. Thus, it is necessary to design feasible quantum algorithms for quantum machine learning for noisy intermediate scale quantum (NISQ) devices. This work explores variational quantum circuits for deep reinforcement learning. Specifically, we reshape classical deep reinforcement learning algorithms like experience replay and target network into a representation of variational quantum circuits. Moreover, we use a quantum information encoding scheme to reduce the number of model parameters compared to classical neural networks. To the best of our knowledge, this work is the first proof-of-principle demonstration of variational quantum circuits to approximate the deep Q-value function for decision-making and policy-selection reinforcement learning with experience replay and target network. Besides, our variational quantum circuits can be deployed in many near-term NISQ machines.

Scalar quantum field theories as a benchmark for near-term quantum computers

Quantum field theory (QFT) simulations are a potentially important application for noisy intermediate scale quantum (NISQ) computers. The ability of a quantum computer to emulate a QFT, therefore, constitutes a natural application-centric benchmark. Foundational quantum algorithms to simulate QFT processes rely on fault-tolerant computational resources, but to be useful on NISQ machines, error-resilient algorithms are required. Here we outline and implement a hybrid algorithm to calculate the lowest energy levels of the paradigmatic 1+1--dimensional interacting scalar QFT. We calculate energy splittings and compare results with experimental values obtained on currently available quantum hardware. We show that the accuracy of mass-renormalization calculations represents a useful metric with which near-term hardware may be benchmarked. We also discuss the prospects of scaling the algorithm to full simulation of interacting QFTs on future hardware.

Formal constraint-based compilation for noisy intermediate-scale quantum systems

Noisy, intermediate-scale quantum (NISQ) systems are expected to have a few hundred qubits, minimal or no error correction, limited connectivity and limits on the number of gates that can be performed within the short coherence window of the machine. The past decade’s research on quantum programming languages and compilers is directed towards large systems with thousands of qubits. For near term quantum systems, it is crucial to design tool flows which make efficient use of the hardware resources without sacrificing the ease and portability of a high-level programming environment. In this paper, we present a compiler for the Scaffold quantum programming language in which aggressive optimization specifically targets NISQ machines with hundreds of qubits. Our compiler extracts gates from a Scaffold program, and formulates a constrained optimization problem which considers both program characteristics and machine constraints. Using the Z3 SMT solver, the compiler maps program qubits to hardware qubits, schedules gates, and inserts CNOT routing operations while optimizing the overall execution time. The output of the optimization is used to produce target code in the OpenQASM language, which can be executed on existing quantum hardware such as the 16-qubit IBM machine. Using real and synthetic benchmarks, we show that it is feasible to synthesize near-optimal compiled code for current and small NISQ systems. For large programs and machine sizes, the SMT optimization approach can be used to synthesize compiled code that is guaranteed to finish within the coherence window of the machine.