Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum optimization using variational algorithms on near-term quantum devices
91
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.
rate research
Read More
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.
Quantum entanglement is a key resource in quantum technology, and its quantification is a vital task in the current Noisy Intermediate-Scale Quantum (NISQ) era. This paper combines hybrid quantum-classical computation and quasi-probability decomposition to propose two variational quantum algorithms, called Variational Entanglement Detection (VED) and Variational Logarithmic Negativity Estimation (VLNE), for detecting and quantifying entanglement on near-term quantum devices, respectively. VED makes use of the positive map criterion and works as follows. Firstly, it decomposes a positive map into a combination of quantum operations implementable on near-term quantum devices. It then variationally estimates the minimal eigenvalue of the final state, obtained by executing these implementable operations on the target state and averaging the output states. Deterministic and probabilistic methods are proposed to compute the average. At last, it asserts that the target state is entangled if the optimized minimal eigenvalue is negative. VLNE builds upon a linear decomposition of the transpose map into Pauli terms and the recently proposed trace distance estimation algorithm. It variationally estimates the well-known logarithmic negativity entanglement measure and could be applied to quantify entanglement on near-term quantum devices. Experimental and numerical results on the Bell state, isotropic states, and Breuer states show the validity of the proposed entanglement detection and quantification methods.
Now that ever more sophisticated devices for quantum computing are being developed, we require ever more sophisticated benchmarks. This includes a need to determine how well these devices support the techniques required for quantum error correction. In this paper we introduce the texttt{topological_codes} module of Qiskit-Ignis, which is designed to provide the tools necessary to perform such tests. Specifically, we use the texttt{RepetitionCode} and texttt{GraphDecoder} classes to run tests based on the repetition code and process the results. As an example, data from a 43 qubit code running on IBMs emph{Rochester} device is presented.
We describe a resource-efficient approach to studying many-body quantum states on noisy, intermediate-scale quantum devices. We employ a sequential generation model that allows us to bound the range of correlations in the resulting many-body quantum states. From this, we characterize situations where the estimation of local observables does not require the preparation of the entire state. Instead smaller patches of the state can be generated from which the observables can be estimated. This can potentially reduce circuit size and number of qubits for the computation of physical properties of the states. Moreover, we show that the effect of noise decreases along the computation. Our results apply to a broad class of widely studied tensor network states and can be directly applied to near-term implementations of variational quantum algorithms.
Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications, although fault-tolerant quantum computers will likely not be available for several years. Currently available quantum devices have serious constraints, including limited qubit numbers and noise processes that limit circuit depth. Variational Quantum Algorithms (VQAs), which employ a classical optimizer to train a parametrized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisioned for quantum computers, and they appear to the best hope for obtaining quantum advantage. Nevertheless, challenges remain including the trainability, accuracy, and efficiency of VQAs. In this review article we present an overview of the field of VQAs. Furthermore, we discuss strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
