Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userError Bounds for Variational Quantum Time Evolution
69
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Variational quantum time evolution (VarQTE) allows us to simulate dynamical quantum systems with parameterized quantum circuits. We derive a posteriori, global phase-agnostic error bounds for real and imaginary time evolution based on McLachlans variational principle that can be evaluated efficiently. Rigorous error bounds are crucial in practice to adaptively choose variational circuits and to analyze the quality of optimization algorithms. The power of the new error bounds, as well as, the performance of VarQTE are demonstrated on numerical examples.
rate research
Read More
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not optimal either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noisy intermediate scale quantum regime, we show how to systematically compile the circuit following an optimising process seeking to minimise the number of noisy operations that are allowed by the noisy quantum hardware or to obtain the highest fidelity of the encoded state with noisy gates. We demonstrate our method by deriving novel encoders for logic states of the five qubit code and the seven qubit Steane code. We describe ways to augment the discovered circuits with error detection. Our method is applicable quite generally for compiling the encoding circuits of quantum error correcting codes.
Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal with noise that can be applied to these algorithms. Recent work introduced a technique for mitigating expectation values against correlated measurement errors that can be applied to measurements of 10s of qubits. We apply these techniques to VQAs and demonstrate its effectiveness in improving estimates to the cost function. Moreover, we use the data resulting from this technique to experimentally characterize measurement errors in terms of the device connectivity on devices of up to 20 qubits. These results should be useful for better understanding the near-term potential of VQAs as well as understanding the correlations in measurement errors on large, near-term devices.
The road to computing on quantum devices has been accelerated by the promises that come from using Shors algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as O(n^{5}d), where n is the bit-length of the number to be factorized and $d$ is the depth of the circuit. We use a single layer of entangling gates to factorize several numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the methods performance by implementing it on the IBMQ Lima hardware.
Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but not non-unitary imaginary time evolution. We propose a variational algorithm for simulating imaginary time evolution on a hybrid quantum computer. We use this algorithm to find the ground-state energy of many-particle systems; specifically molecular hydrogen and lithium hydride, finding the ground state with high probability. Our method can also be applied to general optimisation problems and quantum machine learning. As our algorithm is hybrid, suitable for error mitigation and can exploit shallow quantum circuits, it can be implemented with current quantum computers.
Quantum error mitigation techniques are at the heart of quantum hardware implementation, and are the key to performance improvement of the variational quantum learning scheme (VQLS). Although VQLS is partially robust to noise, both empirical and theoretical results exhibit that noise would rapidly deteriorate the performance of most variational quantum algorithms in large-scale problems. Furthermore, VQLS suffers from the barren plateau phenomenon---the gradient generated by the classical optimizer vanishes exponentially with respect to the qubit number. Here we devise a resource and runtime efficient scheme, the quantum architecture search scheme (QAS), to maximally improve the robustness and trainability of VQLS. In particular, given a learning task, QAS actively seeks an optimal circuit architecture to balance benefits and side-effects brought by adding more quantum gates. Specifically, while more quantum gates enable a stronger expressive power of the quantum model, they introduce a larger amount of noise and a more serious barren plateau scenario. Consequently, QAS can effectively suppress the influence of quantum noise and barren plateaus. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. Numerical and experimental results show that QAS significantly outperforms conventional variational quantum algorithms with heuristic circuit architectures. Our work provides practical guidance for developing advanced learning-based quantum error mitigation techniques on near-term quantum devices.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
