Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneralized quantum circuit differentiation rules
86
0
0.0
(
0
)
Added by
Oleksandr Kyriienko
Publication date
2021
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here, we propose the rules for differentiating quantum circuits (unitaries) with arbitrary generators. Unlike the standard parameter shift rule valid for unitaries generated by operators with spectra limited to at most two unique eigenvalues (represented by involutory and idempotent operators), our approach also works for generators with a generic non-degenerate spectrum. Based on a spectral decomposition, we derive a simple recipe that allows explicit derivative evaluation. The derivative corresponds to the weighted sum of measured expectations for circuits with shifted parameters. The number of function evaluations is equal to the number of unique positive non-zero spectral gaps (eigenvalue differences) for the generator. We apply the approach to relevant examples of two-qubit gates, among others showing that the fSim gate can be differentiated using four measurements. Additionally, we present generalized differentiation rules for the case of Pauli string generators, based on distinct shifts (here named as the triangulation approach), and analyse the variance for derivative measurements in different scenarios. Our work offers a toolbox for the efficient hardware-oriented differentiation needed for circuit optimization and operator-based derivative representation.
rate research
Read More
Generative adversarial learning is one of the most exciting recent breakthroughs in machine learning---a subfield of artificial intelligence that is currently driving a revolution in many aspects of modern society. It has shown splendid performance in a variety of challenging tasks such as image and video generations. More recently, a quantum version of generative adversarial learning has been theoretically proposed and shown to possess the potential of exhibiting an exponential advantage over its classical counterpart. Here, we report the first proof-of-principle experimental demonstration of quantum generative adversarial learning in a superconducting quantum circuit. We demonstrate that, after several rounds of adversarial learning, a quantum state generator can be trained to replicate the statistics of the quantum data output from a digital qubit channel simulator, with a high fidelity ($98.8%$ on average) that the discriminator cannot distinguish between the true and the generated data. Our results pave the way for experimentally exploring the intriguing long-sought-after quantum advantages in machine learning tasks with noisy intermediate-scale quantum devices.
We propose a scheme to simulate the exciton energy transfer (EET) of photosynthetic complexes in a quantum superconducting circuit system. Our system is composed of two pairs of superconducting charge qubits coupled to two separated high-Q superconducting transmission line resonators (TLRs) connected by a capacitance. When the frequencies of the qubits are largely detuned with those of the TLRs, we simulate the process of the EET from the first qubit to the fourth qubit. By tuning the couplings between the qubits and the TLRs, and the coupling between the two TLRs, we can modify the effective coupling strengths between the qubits and thus demonstrate the geometric effects on the EET. It is shown that a moderate clustered geometry supports optimal EET by using exciton delocalization and energy matching condition. And the population loss during the EET has been trapped in the two TLRs.
We present a method that outputs a sequence of simple unitary operations to prepare a given quantum state that is a generalized coherent state. Our method takes as inputs the expectation values of some relevant observables on the state to be prepared. Such expectation values can be estimated by performing projective measurements on $O(M^3 log(M/delta)/epsilon^2)$ copies of the state, where $M$ is the dimension of an associated Lie algebra, $epsilon$ is a precision parameter, and $1-delta$ is the required confidence level. The method can be implemented on a classical computer and runs in time $O(M^4 log(M/epsilon))$. It provides $O(M log(M/epsilon))$ simple unitaries that form the sequence. The number of all computational resources is then polynomial in $M$, making the whole procedure very efficient in those cases where $M$ is significantly smaller than the Hilbert space dimension. When the algebra of relevant observables is determined by some Pauli matrices, each simple unitary may be easily decomposed into two-qubit gates. We discuss applications to quantum state tomography and classical simulations of quantum circuits.
Superconducting circuits have become a leading quantum technology for testing fundamentals of quantum mechanics and for the implementation of advanced quantum information protocols. In this chapter, we revise the basic concepts of circuit network theory and circuit quantum electrodynamics for the sake of digital and analog quantum simulations of quantum field theories, relativistic quantum mechanics, and many-body physics, involving fermions and bosons. Based on recent improvements in scalability, controllability, and measurement, superconducting circuits can be considered as a promising quantum platform for building scalable digital and analog quantum simulators, enjoying unique and distinctive properties when compared to other advanced platforms as trapped ions, quantum photonics and optical lattices.
Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the systems complexity increases and it is thus desirable to have accurate yet affordable methods for their simulation. Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g. the Meyer-Miller-Stock-Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space, and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the identity operator and other operators on an equal footing. As numerical benchmarks on two Linear Vibronic Coupling models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independently of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
