Universal programmable quantum circuit schemes to emulate an operator

Abstract

Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U = e(-iHt) for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.

A universal quantum circuit scheme for finding complex eigenvalues

“…An instance circuit for this simulation technique is given in Fig.2 [31], which can simulate any given matrix based on Eq.(3). The separation of the main and the ancilla qubits in the circuit is largely artificial, since their role can be interchanged in the circuit.…”

“…Recently [31], we have described a universal programmable circuit design which can be used to simulate the action of the matrix U in Eq. (1) by simply determining the gate angles from the matrix elements.…”

“…1: Each block operations forms a different row of the given matrix as their leading row. [31] as U |α = |β :…”

“…In this paper, we introduce a systematic way of estimating the complex eigenvalues of a general matrix using the standard iterative phase estimation algorithm with a programmable circuit design [31]. The bit values of the phase of the target eigenvalue is determined from the outcome of the measurement on the phase qubit.…”

Adiabatic state preparation study of methylene

“…Several improvements reducing the resource requirements of fault-tolerant implementation and thus paving the way for practical simulations were presented in [31]. Universal programmable circuit schemes for emulating an operator with the application to hydrogen molecule computation were introduced in [32].…”