Scalable estimation of pure multi-qubit states

Abstract

We introduce an inductive $n$-qubit pure-state estimation method. This is based on projective measurements on states of $2n+1$ separable bases or $2$ entangled bases plus the computational basis. Thus, the total number of measurement bases scales as $O(n)$ and $O(1)$, respectively. Thereby, the proposed method exhibits a very favorable scaling in the number of qubits when compared to other estimation methods. Monte Carlo numerical experiments show that the method can achieve a high estimation fidelity. For instance, an average fidelity of $0.88$ on the Hilbert space of $10$ qubits is achieved with $21$ separable bases. The use of separable bases makes our estimation method particularly well suited for applications in noisy intermediate-scale quantum computers, where entangling gates are much less accurate than local gates. We experimentally demonstrate the proposed method in one of IBM's quantum processors by estimating 4-qubit Greenberger-Horne-Zeilinger states with a fidelity close to $0.875$ via separable bases. Other $10$-qubit separable and entangled states achieve an estimation fidelity in the order of $0.85$ and $0.7$, respectively.

10 pages, 3 figures

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Scalable multi-particle entanglement of trapped ions
• Robust randomized benchmarking of quantum processes
• Efficient quantum state tomography
• Quantum circuits with many photons on a programmable nanophotonic chip
• Computing with spin qubits at the surface code error threshold
• Fast universal quantum control above the fault-tolerance threshold in silicon
• Direct Fidelity Estimation from Few Pauli Measurements
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Entanglement Certification $-$ From Theory to Experiment
• Precision tomography of a three-qubit donor quantum processor in silicon
• Permutationally invariant quantum tomography
• Experimental characterization of qutrits using SIC-POVMs
• Wigner tomography of two qubit states and quantum cryptography
• Optimal quantum state reconstruction for cold trapped ions
• Mutually unbiased bases: tomography of spin states and star-product scheme
• Measurement of spatial qubits

Cited by in corpus (9)

• Parallel tomography of quantum non-demolition measurements in multi-qubit devices
• Complete physical characterization of QND measurements via tomography
• Detecting entanglement of unknown states by violating the Clauser-Horne-Shimony-Holt inequality
• Disti-Mator: an entanglement distillation-based state estimator
• Minimal orthonormal bases for pure quantum state estimation
• Cyclic measurements and simplified quantum state tomography
• Matrix-Completion Quantum State Tomography
• K-sparse Pure State Tomography with Phase Estimation
• Ptychographic estimation of pure multiqubit states in a quantum device