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arXiv:2111.12207 · Physical Review A

Quantum state preparation by adiabatic evolution with custom gates

E. A. Coello Pérez, Joey Bonitati, Dean Lee, Sofia Quaglioni, Kyle Wendt

Published Mar 2, 2022• 23 citations
arXivHTMLPDF

Abstract

Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These implementation times can be significantly reduced by realizing these circuits with custom gates. Using classical computing, we model the output of a realistic two-qubit processor implementing the adiabatic evolution of a two-spin system by means of custom gates. This modeled output is then compared with the results of quantum simulations solving the same problem on IBM Quantum (IBMQ) systems. When used to emulate the behavior of the IBMQ quantum circuit, our realistic model yields state fidelities ranging from 65% to 85%, similar to the actual performance of a diverse set of IBMQ devices. When we reduced the implementation time by using custom gates, however, the loss of fidelity was reduced by at least a factor of 4, allowing us to accurately extract the energy of the target state. This improvement is enough to render adiabatic evolution useful for quantum state preparation for small systems or as a preconditioner for other state preparation methods.

DOI
10.1103/physreva.105.032403

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Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These implementation times can be significantly reduced by realizing these circuits with custom gates. Using classical computing, we model the output of a realistic two-qubit processor implementing the adiabatic evolution of a two-spin system by means of custom gates. This modeled output is then compared with the results of quantum simulations solving the same problem on IBM Quantum (IBMQ) systems. When used to emulate the behavior of the IBMQ quantum circuit, our realistic model yields state fidelities ranging from 65% to 85%, similar to the actual performance of a diverse set of IBMQ devices. When we reduced the implementation time by using custom gates, however, the loss of fidelity was reduced by at least a factor of 4, allowing us to accurately extract the energy of the target state. This improvement is enough to render adiabatic evolution useful for quantum state preparation for small systems or as a preconditioner for other state preparation methods.
The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. Using the adiabatic theorem for state preparation, whose error decreases exponentially as a function of the preparation time, we derive an explicit analytic expression for the dependence of the characteristic time on the Hamiltonian used in the adiabatic evolution. Exploiting this knowledge, we then design a preconditioning term that modifies the adiabatic preparation, thus reducing its characteristic time and hence giving an exponential advantage in state preparation. We prove the efficiency of our method with extensive numerical experiments on prototypical spin models, which gives a promising strategy to perform quantum simulations of manybody models via Trotter evolution on near-term quantum processors.
Single quantum rotation gates can be perfectly implemented in a closed system using the controlled adiabatic evolutions process proposed by Itay Hen that may lead to build some quantum circuit blocks [Phys. Rev. A, 022309 (2015)]. These adiabatic evolutions yield to vanishing geometric phases. In this work, we extended Itay’s work by considering a more realistic model where the qubits are subjected to decoherence effects during the adiabatic evolution process. We demonstrate that, in the case of an open system, the decoherence leads to nonvanishing geometric phases and drastically reduces the performance of the quantum rotation gates bellow the fidelity target (0.999).
For practical usage of quantum systems in solving real-world problems, large amounts of classical data are required to be transferred/encoded to the quantum domain. Arbitrary classical data is usually encoded onto quantum devices by synthesizing and initializing a corresponding quantum state. Current techniques of arbitrary state synthesis, however, produce deep and complex quantum circuits, leading to low state fidelity and possible violations of decoherence constraints. In this work, we propose an improved methodology and optimized circuits for synthesizing any arbitrary quantum state from given classical data. Compared to existing methods, the proposed methodology results in circuits with lower gate count, lower circuit depth, and high state fidelity. The proposed methods are evaluated by simulation in MATLAB and IBM qasm, and realistic implementation on an IBM quantum device. The experimental results show a reduction in gate count and circuit depth by a factor of two over existing methods.
Demonstrations of quantum advantage for certain sampling problems have generated considerable excitement for quantum computing and have further spurred the development of circuit-model quantum computers, which represent quantum programs as a sequence of quantum gates acting on a finite number of qubits. Amongst this excitement, analog quantum computation has become less prominent, with the expectation that circuit-model quantum computers will eventually be sufficient for emulating analog quantum computation and thus rendering analog quantum computation obsolete. In this work we explore the basic requirements for emulating a specific analog quantum computation in the circuit model: the preparation of a biased superposition of degenerate ground states of an Ising Hamiltonian using an adiabatic evolution. We show that the overhead of emulation is substantial even for this simple problem. This supports using analog quantum computation for solving time-dependent Hamiltonian dynamics in the short term and midterm, assuming analog errors can be made low enough and coherence times long enough to solve problems of practical interest.
Fundamental quantum gates can be implemented effectively using adiabatic quantum computation or circuit model. Recently, Hen combined the two approaches to introduce a new model called controlled adiabatic evolutions [I. Hen, Phys. Rev. A, 91(2) (2015) 022309]. This model was specifically designed to implement one and two-qubit controlled gates. Later, Santos extended Hen’s work to implement [Formula: see text]-qubit controlled gates [A. C. Santos and M. S. Sarandy, Sci. Rep., 5 (2015) 15775]. In this paper, we discuss the implementation of each of the usual quantum gates, as well as demonstrate the possibility of preparing Bell’s states using the controlled adiabatic evolutions approach. We conclude by presenting the fidelity results of implementing single quantum gates and Bell’s states in open systems.
Abstract Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term devices, a number of hybrid approaches have been pursued in which a parameterized quantum circuit prepares and measures quantum states and a classical optimization algorithm minimizes an objective function that encompasses the solution to the problem of interest. In this work, we propose a different approach starting by analyzing how a small perturbation of a Hamiltonian affects the parameters that minimize the energy within a family of parameterized quantum states. We derive a set of equations that allow us to compute the new minimum by solving a constrained linear system of equations that is obtained from measuring a series of observables on the unperturbed system. We then propose a discrete version of adiabatic quantum computing that can be implemented in a near-term device while at the same time is insensitive to the initialization of the parameters and to other limitations hindered in the optimization part of variational quantum algorithms. We compare our proposed algorithm with the variational quantum eigensolver on two classical optimization problems, namely MaxCut and number partitioning, and on a quantum-spin configuration problem, the transverse-field ising chain model, and confirm that our approach demonstrates superior performance.