Complete Quantum-State Tomography with a Local Random Field
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-01-10 |
| Journal | Physical Review Letters |
| Authors | Pengcheng Yang, Min Yu, Ralf Betzholz, Christian Arenz, Jianming Cai |
| Institutions | Princeton University, Huazhong University of Science and Technology |
| Citations | 20 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThe research demonstrates a novel, highly efficient method for complete Quantum-State Tomography (QST) in complex, partially accessible multiqubit systems using a local random control field.
- Core Innovation: Complete QST is achieved by randomly driving and measuring only a single accessible qubit, provided the total system is fully controllable by that local field.
- System Demonstrated: A two-qubit solid-state spin system consisting of a Nitrogen-Vacancy (NV) center electron spin coupled to a nearby Carbon-13 (13C) nuclear spin in diamond.
- Efficiency Advantage: The method eliminates the need for computationally expensive optimal control algorithms or tailored classical fields required by deterministic QST, and avoids the necessity of full system access required by standard randomized protocols.
- Mechanism: A random control pulse âshakesâ the total system, generating a statistically independent, informationally complete set of observables when measured locally over a sufficient duration.
- Key Achievement: High-fidelity reconstruction (94.9% to 97.7%) of highly entangled electron-nuclear spin states, accessing the nuclear spin state indirectly via the electron spin measurement.
- Generality: The principle is broadly applicable to any fully controllable quantum system where access is limited to only a subset of components.
Technical Specifications
Section titled âTechnical SpecificationsâThe experiment utilized a solid-state NV center in diamond operating under specific magnetic and microwave conditions.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Quantum System Size | 2 | Qubits (d=4) | NV electron spin coupled to 13C nuclear spin. |
| Zero-Field Splitting (D/2Ï) | 2.87 | GHz | NV ground-state manifold. |
| Applied Magnetic Field (B) | 504.7 | G | Used to lift the ms = ±1 degeneracy. |
| Microwave Frequency (w/2Ï) | 1455.5 | MHz | Used for driving the electron spin. |
| Control Field Amplitude (Ω1/2Ï) | 7.91 | MHz | Calibrated Rabi oscillation frequency (f(t)=1). |
| Longitudinal Hyperfine Coupling (Azz/2Ï) | 11.832 ± 0.005 | MHz | Electron-nuclear spin interaction. |
| Random Pulse Duration (Ît) | 0.7 | ”s | Length of individual random pulses used for tomography. |
| Number of Tomography Pulses | 15 | Pulses | Required to generate d2 - 1 linearly independent measurements. |
| Electron Spin Coherence Time (T2*) | 0.86 | ”s | Coherence time under Free Induction Decay (FID). |
| Achieved Fidelity (Entangled State) | 94.9 | % | Reconstruction fidelity for the highly entangled state (Concurrence C = 0.91). |
Key Methodologies
Section titled âKey MethodologiesâThe experimental procedure combined optical initialization, microwave control using an Arbitrary Waveform Generator (AWG), and fluorescence readout.
- System Initialization: The NV center electron spin and the intrinsic nitrogen nuclear spin were polarized into the initial pure state (Ï0 = |ââ©1|ââ©2) using a 532 nm green laser pulse (optical ground-state polarization).
- State Preparation: Target states (including highly entangled states) were created by applying a preparation microwave pulse, generated by the AWG, to the electron spin.
- Random Field Generation: The control field f(t) was designed using a truncated Fourier series (K=10 components) with uniformly distributed random amplitudes, frequencies (0 to 4 MHz), and phases (0 to 2Ï).
- Tomography Sequence: A set of 15 separate random pulses, each 0.7 ”s in duration, were applied sequentially to the electron spin to generate the necessary informationally complete measurement record.
- Local Measurement: The expectation value of the electronic ms=0 state population (represented by the observable M = Ï1z) was measured via state-dependent fluorescence readout.
- Data Acquisition and Reconstruction: The measurement record consisted of the last 10 data points from the expectation measurement of each of the 15 random pulses. The density operator was reconstructed from this noisy data using a least-square minimization technique, subject to physical constraints (positivity and unit trace).
Commercial Applications
Section titled âCommercial ApplicationsâThis random-field tomography technique is highly relevant for the engineering and benchmarking of emerging quantum technologies, particularly those based on solid-state spin systems.
- Quantum Computing and Simulation: Provides a robust, model-independent method for characterizing the full quantum state of multiqubit processors (like those based on NV centers or trapped ions) where direct access to all qubits is impractical.
- Quantum Sensing: Enables the characterization of complex spin environments (e.g., distant nuclear spin baths) coupled to a local sensor qubit, crucial for optimizing NV-center based magnetometers and gyroscopes.
- Quantum Control Engineering: The underlying principle suggests that a quantum computer/simulator can potentially be fully operated (controlled and read out) based solely on classical measurement data and local random driving, without requiring detailed prior knowledge of the physical hardware model.
- Solid-State Quantum Devices: Applicable to the development and quality control of solid-state devices utilizing coupled spin states, such as those based on silicon carbide (SiC) defects or quantum dots.
View Original Abstract
Single-qubit measurements are typically insufficient for inferring arbitrary quantum states of a multiqubit system. We show that, if the system can be fully controlled by driving a single qubit, then utilizing a local random pulse is almost always sufficient for complete quantum-state tomography. Experimental demonstrations of this principle are presented using a nitrogen-vacancy (NV) center in diamond coupled to a nuclear spin, which is not directly accessible. We report the reconstruction of a highly entangled state between the electron and nuclear spin with fidelity above 95% by randomly driving and measuring the NV-center electron spin only. Beyond quantum-state tomography, we outline how this principle can be leveraged to characterize and control quantum processes in cases where the system model is not known.