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 | Huazhong University of Science and Technology, Princeton University |
| Citations | 20 |
| Analysis | Full AI Review Included |
Complete Quantum-State Tomography with a Local Random Field: 6CCVD Technical Analysis
Section titled âComplete Quantum-State Tomography with a Local Random Field: 6CCVD Technical AnalysisâThis document analyzes the requirements and achievements of the research paper âComplete Quantum-State Tomography with a Local Random Fieldâ (arXiv:1909.09980v2) and maps them directly to the advanced material solutions offered by 6ccvd.com.
Executive Summary
Section titled âExecutive SummaryâThe research successfully demonstrates a highly efficient method for complete Quantum-State Tomography (QST) in a solid-state diamond system, leveraging local control and random fields.
- Core Achievement: Reconstruction of highly entangled states in a two-qubit system (NV electron spin coupled to a $^{13}$C nuclear spin) with high fidelity (up to $97.7$%).
- Methodology: QST is achieved by applying a local random microwave field to the electron spin only, eliminating the need for full system access or complex, deterministic pulse design.
- Material Requirement: The experiment relies critically on high-quality Single Crystal Diamond (SCD) hosting Nitrogen-Vacancy (NV) centers and a coupled $^{13}$C nuclear spin, requiring precise isotopic and defect control.
- Controllability Principle: The technique exploits the principle that a fully controllable quantum system, when driven by a random local field, generates sufficient information for complete state reconstruction via a single observable measurement.
- Coherence Validation: The system maintained coherence under microwave drive for the longest experimental evolution time ($2.5$ ”s), confirming the suitability of the solid-state platform for complex quantum control sequences.
- Implication for Scaling: This random-field approach offers a broadly applicable strategy for characterizing and controlling complex, partially-accessible quantum systems, reducing the overhead associated with traditional QST methods.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental section of the paper:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Quantum System | $d=4$ (2 qubits) | N/A | NV electron spin coupled to $^{13}$C nuclear spin |
| Host Material | Diamond (Solid-State Spin System) | N/A | Requires high-purity Single Crystal Diamond (SCD) |
| Zero-Field Splitting ($D/2\pi$) | $2.87$ | GHz | NV-center ground state triplet |
| Applied Magnetic Field ($B$) | $504.7$ | G | Applied along the NV axis |
| Microwave Frequency ($\omega/2\pi$) | $1455.5$ | MHz | Used for electron spin control |
| Control Field Amplitude ($\Omega_{1}/2\pi$) | $7.91$ | MHz | Calibrated via Rabi oscillations |
| Free Induction Coherence Time ($T_{2}^{*}$) | $0.86$ | ”s | Measured via FID experiment |
| Longest Coherent Evolution Time | $> 2.5$ | ”s | Verified under continuous microwave drive |
| Tomography Pulse Length ($\Delta t$) | $0.7$ | ”s | Used for random field generation (15 pulses total) |
| Highly Entangled State Fidelity | $94.9$ | % | Reconstruction fidelity (Concurrence $C \approx 0.91$) |
| Initial State Fidelity ($\rho_{0}$) | $97.7$ | % | Reconstruction fidelity after optical polarization |
| Initialization/Readout Wavelength | $532$ | nm | Green laser pulse |
Key Methodologies
Section titled âKey MethodologiesâThe experimental demonstration utilized advanced quantum control techniques on a solid-state platform:
- System Selection: A two-qubit system was employed, consisting of the electron spin of a Nitrogen-Vacancy (NV) center coupled to a nearby $^{13}$C nuclear spin in diamond.
- Initialization: The system was initialized into the pure state $\vert\uparrow\rangle_{1}\vert\uparrow\rangle_{2}$ via optical ground-state polarization using a $532$ nm laser pulse.
- Control Implementation: The electron spin was driven by a classical control Hamiltonian $H_{c} = \frac{\Omega_{1}}{2}\sigma_{x}^{1}f(t)$, implemented using a microwave field generated by an Arbitrary Waveform Generator (AWG) and delivered via a copper antenna.
- Random Field Generation: The random pulse shapes $f(t)$ were constructed using a truncated Fourier series ($K=10$ components) with uniformly-distributed random variables (amplitudes, frequencies, and phases).
- State Preparation: Non-trivial and highly entangled states were created using either random or numerically optimized microwave preparation pulses (up to $1.8$ ”s duration).
- Tomography Sequence: $d^{2}-1 = 15$ separate random pulses (each $0.7$ ”s long) were applied sequentially to generate an informationally complete measurement record.
- Measurement: The single-qubit observable $M = \sigma_{z}^{1}$ (electronic $m_{s}=0$ population) was measured via state-dependent fluorescence readout.
- Data Processing: Density matrix reconstruction was performed using a least-square minimization technique, utilizing the last 10 data points of every random pulse.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâReplicating and extending this high-fidelity quantum control research requires diamond materials with exceptional purity, precise isotopic control, and integrated engineering featuresâall core specialties of 6CCVD.
| Research Requirement | 6CCVD Solution & Capability | Technical Advantage |
|---|---|---|
| High-Purity Host Material (NV Centers) | Optical Grade Single Crystal Diamond (SCD) | Our SCD substrates feature ultra-low defect densities, minimizing decoherence sources and maximizing the electron spin coherence time ($T_{2}$), critical for implementing long random-field sequences. |
| Isotopic Control ($^{13}$C Nuclear Spin) | Custom Isotopic Purity Diamond | We offer SCD substrates with tailored $^{12}$C enrichment (or depletion) to precisely control the density of coupled $^{13}$C nuclear spins, enabling the creation of scalable, well-isolated quantum registers necessary for advanced quantum simulation. |
| Microwave Control Integration | Custom Metalization Services (Au, Pt, Ti, Cu) | The experiment utilized a copper microwave antenna. 6CCVD provides in-house deposition of thin-film metal stacks (e.g., Ti/Pt/Au or custom Cu layers) directly onto the diamond surface for integrated microwave waveguides and optimized control pulse delivery. |
| Sample Geometry & Access | Custom Dimensions and Polishing | We provide plates/wafers up to $125$ mm (PCD) and offer custom laser cutting services for precise chip dimensions required for integration into microwave and optical setups. |
| Surface Quality for Readout | Ultra-Smooth Polishing ($R_{a} < 1$ nm) | SCD surfaces are polished to $R_{a} < 1$ nm, minimizing optical scatter and maximizing the collection efficiency of the state-dependent fluorescence used for readout. |
| Thickness Requirements | SCD Thickness Control (0.1 ”m to 500 ”m) | Precise control over the SCD layer thickness is available, allowing researchers to optimize the proximity of the NV layer to the surface for enhanced coupling to external fields or integration with nanophotonic structures. |
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house PhD team specializes in optimizing MPCVD growth parameters (nitrogen concentration, isotopic ratio, and crystal orientation) specifically for Random-Field Quantum-State Tomography and solid-state quantum simulation projects. We ensure the material properties meet the stringent requirements for high-fidelity quantum control experiments.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
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.