DeepAI AI Chat
Log In Sign Up

K-sparse Pure State Tomography with Phase Estimation

by   Burhan Gulbahar, et al.

Quantum state tomography (QST) for reconstructing pure states requires exponentially increasing resources and measurements with the number of qubits by using state-of-the-art quantum compressive sensing (CS) methods. In this article, QST reconstruction for any pure state composed of the superposition of K different computational basis states of n qubits in a specific measurement set-up, i.e., denoted as K-sparse, is achieved without any initial knowledge and with quantum polynomial-time complexity of resources based on the assumption of the existence of polynomial size quantum circuits for implementing exponentially large powers of a specially designed unitary operator. The algorithm includes 𝒪(2 / | c_k|^2) repetitions of conventional phase estimation algorithm depending on the probability | c_k|^2 of the least possible basis state in the superposition and 𝒪(d K (log K)^c) measurement settings with conventional quantum CS algorithms independent from the number of qubits while dependent on K for constant c and d. Quantum phase estimation algorithm is exploited based on the favorable eigenstructure of the designed operator to represent any pure state as a superposition of eigenvectors. Linear optical set-up is presented for realizing the special unitary operator which includes beam splitters and phase shifters where propagation paths of single photon are tracked with which-path-detectors. Quantum circuit implementation is provided by using only CNOT, phase shifter and - π / 2 rotation gates around X-axis in Bloch sphere, i.e., R_X(- π / 2), allowing to be realized in NISQ devices. Open problems are discussed regarding the existence of the unitary operator and its practical circuit implementation.


page 1

page 2

page 3

page 4


SWAP Test for an Arbitrary Number of Quantum States

We develop a recursive algorithm to generalize the quantum SWAP test for...

Fast and robust quantum state tomography from few basis measurements

Quantum state tomography is a powerful, but resource-intensive, general ...

Efficient Approximate Quantum State Tomography with Basis Dependent Neural-Networks

We use a meta-learning neural-network approach to predict measurement ou...

(Pseudo) Random Quantum States with Binary Phase

We prove a quantum information-theoretic conjecture due to Ji, Liu and S...

Semi-device-dependent blind quantum tomography

Extracting tomographic information about quantum states is a crucial tas...

Fermionic tomography and learning

Shadow tomography via classical shadows is a state-of-the-art approach f...

Adaptive Quantum State Tomography with Neural Networks

Quantum State Tomography is the task of determining an unknown quantum s...