Minimizing entanglement entropy for enhanced quantum state preparation

Abstract

Quantum state preparation is an important subroutine in many quantum algorithms. The goal is to encode classical information directly to the quantum state so that it is possible to leverage quantum algorithms for data processing. However, quantum state preparation of arbitrary states scales exponentially in the number of two-qubit gates, and this makes quantum state preparation a very difficult task on quantum computers, especially on near-term noisy devices. This represents a major challenge in achieving quantum advantage. We present and analyze a novel two-step state preparation method where we first minimize the entanglement entropy of the target quantum state, thus transforming the state to one that is easier to prepare. The state with reduced entanglement entropy is then represented as a matrix product state, resulting in a high accuracy preparation of the target state. Our method is suitable for NISQ devices and we give rigorous lower bounds on the accuracy of the prepared state in terms of the entanglement entropy. We benchmark our method with 2D normal distribution and Ricker wavelet states with 6--20 qubits.

Figures (7)

• Figure 1: A single truncated MPS disentangling layer followed by a PQC that minimizes entanglement entropy.
• Figure 2: Two-step VDSP method for QSP. MPD stands for matrix product disentangler.
• Figure 3: A PQC with 4 qubits and two layers.
• Figure 4: Scaling of accuracy and infidelity with respect to number of layers for the 2D Ricker wavelet distribution. Left: $n_q = 10$. Right: $n_q = 20$. For VDSP and PQC the number of layers refers to the number of variational layers, while for MPD it refers to the number of MPD layers.
• Figure 5: Hellinger distance between the noisy simulator output and the target distribution as a function of CZ gate infidelity ($1 - F_{\mathrm{CZ}}$) for four state-preparation methods on an 10-qubit 2D Ricker wavelet state. Single-qubit gate fidelity is $F_{1Q} = 0.99999$. Panels correspond to readout error rates $\varepsilon_{\mathrm{ro}} \in \{0.001, 0.005, 0.01\}$.