06 - Current Feasibility and Future Prospects

Introduction

No matter how beautiful a theory is, if experiments are infeasible, it remains a castle in the air. This chapter provides a practical assessment of all experimental schemes proposed in previous chapters:

• Which can be done now?
• Which require technological breakthroughs?
• Which are long-term goals?

We use Technology Readiness Levels (TRL) for quantitative assessment and provide a roadmap with milestones.

Technology Readiness Level Rating System

TRL Definition (NASA Standard)

Our Assessment Criteria

Feasibility:

• ✅ High: Existing technology directly available, $<2$ years
• ⚠️ Medium: Moderate improvements needed, 2-5 years
• ❌ Low: Major breakthroughs required, $>5$ years

Cost:

• $: < $100k USD
• $$: $100k-$1M USD
• $$$: > $1M USD

Impact:

• ⭐⭐⭐: Direct verification of core predictions
• ⭐⭐: Indirect support for theory
• ⭐: Technical demonstration

Feasibility Assessment by Platform

1. Unified Time Scale Measurement

Fabry-Pérot Optical Cavity

TRL: 8-9 (Mature technology)

Feasibility: ✅ High

Cost: $ (University laboratory level)

Impact: ⭐⭐

Assessment:

• ✅ Laser frequency stabilization mature (PDH locking)
• ✅ High finesse cavities commercially available ($\mathcal{F}>10^5$)
• ✅ Phase measurement precision $\sim$ mrad achieved
• ⚠️ Temperature stability requires $<10$ mK (needs ultra-stable cavity)
• ⚠️ Systematic errors (cavity length drift) need real-time calibration

Recommendation:

Immediately feasible, suitable as teaching demonstration and proof of concept.

δ-Ring + AB Flux

TRL: 3-4 (Laboratory principle)

Feasibility: ⚠️ Medium

Cost: $$ (Professional equipment)

Impact: ⭐⭐⭐

Assessment:

• ✅ Cold atom rings have precedents (MIT, NIST)
• ⚠️ Precise AB flux control requires superconducting magnets
• ⚠️ Spectrum measurement requires Bragg spectrometer or time-of-flight
• ❌ Pathological domain avoidance needs fine parameter scanning
• ❌ Finite width corrections need theoretical guidance

Recommendation:

Feasible within 5 years, requires dedicated funding. Priority: High (direct verification of scattering-spectrum equivalence).

2. Spectral Windowing Techniques

PSWF/DPSS Numerical Implementation

TRL: 9 (Mature software)

Feasibility: ✅ High

Cost: $ (Computing resources)

Impact: ⭐⭐

Assessment:

• ✅ Python/MATLAB libraries available (scipy.signal.windows.dpss)
• ✅ Error formulas directly applicable
• ✅ Numerical stability verified
• ⚠️ Large Shannon numbers ($N_0>1000$) require high-precision algorithms

Recommendation:

Deploy immediately as standard tool for all phase-frequency measurements.

Real-Time Windowing Readout

TRL: 5-6 (FPGA prototype)

Feasibility: ⚠️ Medium

Cost: $

Impact: ⭐

Assessment:

• ✅ FPGA can achieve real-time FFT ($\sim$ GHz sampling rate)
• ⚠️ PSWF coefficient precomputation requires large storage (GB level)
• ⚠️ Dynamic window selection requires adaptive algorithms
• ❌ Ultra-high speed ($>10$ GHz) requires custom ASIC

Recommendation:

Feasible within 3 years, targeting FRB baseband processing and quantum measurements.

3. Topological Fingerprint Optical Implementation

π-Step Measurement

TRL: 4-5 (Principle demonstration)

Feasibility: ⚠️ Medium

Cost: $$\ast \ast Impact\ast \ast :⭐⭐⭐\ast \ast Assessment\ast \ast :-✅Fiberringcavitiesmaturetechnology-✅Phasemeasurementprecisionsufficient($< 0.1\pi$)-⚠\stackrel{◯}{R}Delayparameter$\tau$ control requires precise temperature/stress control

• ⚠️ Automated scanning requires programming control
• ❌ Ultrafast delays (fs level) require optical cross-correlation

Recommendation:

3-5 years, requires optical expert team. Priority: High (verify topological quantization).

$\mathbb{Z}_2$ParityFlip\ast \ast TRL\ast \ast :3-4(Proofofconcept)\ast \ast Feasibility\ast \ast :⚠\stackrel{◯}{R}Medium\ast \ast Cost\ast \ast :\$$

Impact: ⭐⭐⭐

Assessment:

• ✅ Sagnac interferometers commercially available
• ⚠️ Dual-ring configuration requires customization
• ⚠️ Precise phase control ($<\lambda /1000$)
• ❌ Critical point localization requires theoretical guidance
• ❌ Topological robustness verification requires large datasets

Recommendation:

5-year攻坚 project. Requires close theory-experiment collaboration.

4. Causal Diamond Quantum Simulation

Cold Atom Optical Lattice

TRL: 5-6 (Laboratory demonstration)

Feasibility: ⚠️ Medium

Cost: $$$

Impact: ⭐⭐⭐

Assessment:

• ✅ Technology mature (multiple laboratories deployed)
• ✅ Entanglement measurement methods known (QFI, MPS)
• ⚠️ Large systems ($>100$ atoms) complex to control
• ⚠️ Long evolution times ($>1$s) limited by decoherence
• ❌ Precise Markovianity verification requires extremely low temperatures ($<\mu$K)

Recommendation:

Retrofit existing facilities, results visible in 2-3 years. Priority: Medium.

Ion Trap Quantum Computer

TRL: 6-7 (Early commercialization)

Feasibility: ✅ High (if device access available)

Cost: $$$ (Rent commercial platform)

Impact: ⭐⭐⭐

Assessment:

• ✅ IonQ, Honeywell provide cloud access
• ✅ High-fidelity gates ($>99%$)
• ✅ Medium scale ($\sim 30$ ions)
• ⚠️ Long queue wait times
• ⚠️ Complex programming (requires quantum algorithm experts)
• ❌ High cost ($\sim $10k$/hour)

Recommendation:

Immediately feasible (if budget available). Suitable for rapid concept verification.

5. FRB Observation Applications

CHIME Data Analysis

TRL: 7-8 (Operational)

Feasibility: ✅ High

Cost: $ (Computing + personnel)

Impact: ⭐⭐

Assessment:

• ✅ Data publicly available (CHIME/FRB Catalog)
• ✅ Processing pipeline documented
• ✅ Community software tools (pulsar, presto)
• ⚠️ Big data processing (TB level) requires HPC
• ⚠️ RFI removal requires experience
• ❌ New physics signal weak, requires stacking $>100$ events

Recommendation:

Complete preliminary analysis within 1 year. Priority: Medium (upper limits rather than detection).

Next-Generation Telescopes

FAST (China):

• Sensitivity: 3× CHIME
• Frequency range: 70 MHz - 3 GHz
• Status: Operational, FRB survey ongoing

SKA (International):

• Sensitivity: 50× CHIME
• Frequency: 50 MHz - 14 GHz
• Status: Phase 1 construction, partial operation expected 2027

Assessment:

• ✅ Hardware performance significantly improved
• ⚠️ Extremely high data rate (PB/day), requires real-time processing
• ⚠️ Complex international cooperation (data sharing policies)

Recommendation:

Prepare software pipeline, deploy within 5 years.

Roadmap: Three-Phase Plan

Phase I (1-3 years): Basic Verification

Goal: Verify core concepts, establish methodology

Milestones:

1. Optical Cavity Three-Path Verification (Chapter 1)

   • Complete Fabry-Pérot cavity measurement
   • Verify $\varphi’/\pi = \rho_{\text{rel}} = \text{tr }Q/2\pi$
   • Publish methodology paper

2. PSWF Error Control Demonstration (Chapter 2)

   • Numerically verify three error formulas
   • Provide minimum Shannon number threshold
   • Open-source software package

3. FRB Data Preliminary Analysis (Chapter 5)

   • Process 10-20 high SNR events
   • Establish windowed upper limit pipeline
   • Provide preliminary $\delta n$ constraints

Budget: $500k (two postdocs + equipment)

Output: 3-5 papers, 1 software package

Phase II (3-7 years): Topology and Quantum Simulation

Goal: Verify topological invariants, implement quantum simulation

Milestones:

1. π-Step Optical Measurement (Chapter 3)

   • Establish fiber ring cavity platform
   • Observe at least 5 $\pi$-steps
   • Verify quantization deviation $<0.1\pi$

2. $\mathbb{Z}_2$ Flip Observation (Chapter 3)

   • Dual-ring Sagnac interferometer
   • Locate critical point $\tau_c$
   • Verify parity robustness

3. Cold Atom Diamond Simulation (Chapter 4)

   • Retrofit existing optical lattice
   • Measure double-layer entanglement $S(E^+), S(E^-)$
   • Verify Markovianity $I(A:C|B)<0.1$

4. δ-Ring Spectrum Measurement (Chapter 1)

   • Build cold atom ring + AB flux
   • Extract ${k_n(\theta)}$
   • Invert $\alpha_{\delta}$, verify identifiability

Budget: $5M (specialized facilities + team)

Output: 8-12 papers, 2-3 PhD degrees

Phase III (7-15 years): Precision Verification and Applications

Goal: Reach theoretical precision limits, explore new physics

Milestones:

1. Ion Trap Precision Measurement

   • Prepare 50+ ion chain entangled states
   • Quantum state tomography precision $>99%$
   • Verify Markovianity to $10^{-3}$ level

2. SKA FRB Survey

   • Process $>10000$ events
   • Statistical precision improved $\times 100$
   • New physics constraint $\delta n < 10^{-22}$

3. Superconducting Quantum Chip

   • Integrate $>100$ qubits
   • Real-time topological fingerprint monitoring
   • Benchmark against classical simulation

Budget: $50M (large facilities)

Output: Theory verification complete or new physics discovered!

Cost-Benefit Analysis

Scientific Benefits

Theory Verification:

• Consistency of unified time scale across $10^{32}$ orders of magnitude
• Experimental confirmation of topological invariants (π-steps, $\mathbb{Z}_2$)
• Deep connection between quantum entanglement and spacetime geometry

New Physics Search:

• Vacuum polarization upper limits $\Rightarrow$ constrain Lorentz violation
• FRB phase anomalies $\Rightarrow$ axions/hidden photons
• Entanglement entropy deviations $\Rightarrow$ quantum gravity corrections

Technology Spillover

Quantum Technology:

• Precise phase measurement $\Rightarrow$ gravitational wave detection, atomic clocks
• PSWF error control $\Rightarrow$ 5G/6G communications
• Quantum simulation $\Rightarrow$ materials design, drug development

Astronomy:

• FRB pipeline $\Rightarrow$ pulsar timing arrays (gravitational waves)
• Windowing analysis $\Rightarrow$ exoplanet search
• Big data processing $\Rightarrow$ SKA science cases

Return on Investment

Phase I ($500k):

• Paper impact factor $\sim 50$ (3 top journals)
• Train 2 postdocs
• ROI: Academic impact >100× (citation count)

Phase II ($5M):

• Paper impact factor $\sim 200$
• Train 3 PhDs
• 2-3 patents (e.g., precision measurement technology)
• ROI: Technology spillover ~10× (civilian applications)

Phase III ($50M):

• Nobel Prize-level discovery? (if successful)
• Industry standard establishment
• ROI: Immeasurable (paradigm shift)

Risk Assessment and Mitigation

Technical Risks

Risk 1: Insufficient coherence time

• Probability: Medium
• Impact: High (quantum simulation failure)
• Mitigation:
  • Develop dynamical decoupling pulse sequences
  • Switch to superconducting platform (longer $T_2$)
  • Lower measurement precision requirements

Risk 2: Systematic errors dominate

• Probability: High
• Impact: Medium (precision limited)
• Mitigation:
  • Multi-platform cross-validation
  • Blind analysis protocols
  • Independent measurement teams

Risk 3: Signal too weak

• Probability: Medium (FRB)
• Impact: Medium (upper limits only)
• Mitigation:
  • Stack more events
  • Wait for next-generation telescopes
  • Switch to other new physics signals

Management Risks

Risk 4: Talent loss

• Probability: Medium
• Impact: High
• Mitigation:
  • Competitive compensation
  • Career development paths
  • International collaboration networks

Risk 5: Funding interruption

• Probability: Low-Medium
• Impact: Extremely high
• Mitigation:
  • Multi-source funding (NSF, DOE, private)
  • Phased deliverables
  • Backup low-cost alternatives

International Cooperation and Resource Integration

Existing Facilities

Directly Available:

• CHIME (Canada): FRB data
• FAST (China): High-sensitivity FRB
• IonQ, Honeywell: Ion trap cloud platforms
• Google, IBM: Superconducting quantum chips

Require Cooperation Agreements:

• University cold atom laboratories (MIT, NIST, MPQ)
• Optical precision measurement centers (JILA, NIST-Boulder)

Recommended Cooperation Models

Data Sharing:

• FRB: Join CHIME/FRB Collaboration
• Quantum simulation: Joint runtime slots

Personnel Exchange:

• Postdoc exchanges (6 months)
• Joint student training

Facility Co-Construction:

• Optical platforms: Laboratory division of labor (π-steps vs $\mathbb{Z}_2$)
• Software development: Open-source collaboration (GitHub organization)

Summary

Immediately Feasible (TRL 7-9)

✅ Optical cavity three-path verification ✅ PSWF software deployment ✅ CHIME data analysis

Time: Within 1 year Cost: $<500k Recommendation: Launch immediately

Medium-Term Goals (TRL 4-6)

⚠️ π-Step measurement ⚠️ Cold atom diamond simulation ⚠️ δ-Ring spectrum measurement

Time: 3-5 years Cost: $2-5M Recommendation: Apply for dedicated funding

Long-Term Vision (TRL 1-3)

❌ $\mathbb{Z}_2$ precision verification ❌ Large-scale quantum simulation ($>100$ qubits) ❌ SKA new physics search

Time: 7-15 years Cost: $10-50M Recommendation: International cooperation big science program

The next chapter (Chapter 7) will summarize all experimental schemes, review key conclusions, and look forward to future theory-experiment interactions.

References

[1] NASA, “Technology Readiness Level Definitions,” https://www.nasa.gov/directorates/heo/scan/engineering/technology/technology_readiness_level

[2] Altman, E., et al., “Quantum Simulators: Architectures and Opportunities,” PRX Quantum 2, 017003 (2021).

[3] Monroe, C., et al., “Programmable quantum simulations of spin systems with trapped ions,” Rev. Mod. Phys. 93, 025001 (2021).

[4] Planck Collaboration, “Planck 2018 results,” A&A 641, A1 (2020).