Implement QBit data type for bit-transposed Float64 vector storage

[Copilot]

Changelog entry

Add QBit library for storing Float64 vectors in bit-transposed format, enabling efficient vector similarity search operations.

Changelog category

• New feature

Description for reviewers

Implements QBit data structure in ydb/library/qbit/ that stores List<Float64> vectors by transposing bits across elements. Instead of element-wise storage, data is organized into 64 bit planes where each plane contains one bit position from all vector elements.

Core Implementation (327 lines)

• TQBit class with bit transposition algorithms
• MSB-to-LSB ordering for progressive precision
• Binary serialization format with dimension/row headers
• O(dimension) add/get operations

API

TQBit qbit(128);                      // 128-dimensional vectors
qbit.AddVector(vec);                  // Add Float64 vector
auto retrieved = qbit.GetVector(0);   // Retrieve by index
TString data = qbit.Serialize();      // Binary persistence
qbit.Deserialize(data);               // Load from binary

Use Cases

• Approximate nearest neighbor: read first N bit planes for N-bit precision (8× I/O reduction for 8-bit first pass)
• Progressive refinement: start low precision, refine gradually
• Per-plane compression: exploit bit-level patterns
• SIMD operations: sequential bit access

Verification

• 15 unit tests covering API, edge cases, serialization
• Standalone Python verification confirms bit-exact preservation
• Handles IEEE 754 special values (±0, ±inf, NaN)

Based on ClickHouse QBit implementation.

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Original prompt

Implement QBit data type to store float64 vectors (in case of YDB it's List) transposed by bits. As reference QBit from https://github.com/ClickHouse/ClickHouse should be used

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