Physical p‐bit Hardware Prototype

The goal is to build a small hardware p-bit computer containing at least 8 independent natural physical p-bits, where stochastic behavior is generated by real electronic noise rather than a software PRNG, and connect it to a PC over USB. The design is simple enough to be built at home as a proof-of-concept using readily available components, with device-to-device variations compensated through software calibration using MCU (microcontroller), such as an ESP32 or RP2350.

Natural p-bits

Each p-bit uses a physical electronic noise source followed by amplification and a comparator. A controllable bias voltage changes the probability of the output being 0 or 1:

$$ P(m_i=1)=f(V_i) $$

A microcontroller controls the bias voltages through a multi-channel DAC and reads the digital p-bit outputs.

Calibration

Real p-bits will not be identical. Each channel may have a different offset, gain and noise distribution.

During calibration, the controller sweeps the bias of each p-bit and measures its output probability:

$$ V \rightarrow P(1) $$

The resulting probability curve is stored as a calibration table. During operation, a requested p-bit probability or p-kit bias is converted back into the voltage required by that particular physical p-bit.

Calibration also measures:

• zero-bias probability, ideally near 50%;
• temporal autocorrelation;
• cross-correlation between different p-bits;
• drift with time and temperature.

This allows imperfect discrete noise devices to behave approximately like calibrated p-bits and provides a small physical hardware backend for IBM p-kit.

Visual schematics

Schematic 1

+------------------------------------------------------------------+
|                    USB / CONTROL SECTION                         |
|                                                                  |
|  USB-C                                                           |
|  +-----+                                                         |
|  | USB |----+                                                    |
|  +-----+    |                                                    |
|             v                                                    |
|       +-------------+        +-------------+   +-------------+   |
|       | MCU / USB   |------->| 8-ch DAC    |<--| 2.5V REF    |   |
|       | RP2040 etc. |  SPI   |             |   |             |   |
|       +-------------+        +-------------+   +-------------+   |
|             ^                     | | | | | | | |                |
|             |                     | | | | | | | |                |
|             | digital inputs      | | | | | | | | bias voltages  |
|             |                     v v v v v v v v                |
|             |                    B0 B1 B2 B3 B4 B5 B6 B7         |
|             |                                                    |
|             +------------- from p-bit outputs -- Q0 ... Q7 ------+
|                                                                  |
+------------------------------------------------------------------+

Schematic 2

+---------------------------------------------------+
|              PHYSICAL P-BIT SECTION               |
|                                                   |
|              +------------------+                 |
|              |     [P-BIT 0]    |                 |
|              |                  |                 |
|              | Noise source     |                 |
|              |      ↓           |                 |
|              | Amplifier        |                 |
|              |      ↓           |                 |
| VBIAS0 ----->| Comparator       |                 |
|              |      ↓           |                 |
|              |      Q0          |                 |
|              +------------------+                 |
|                                                   |
|                     .                             |
|                     .                             |
|                     .                             |
|                                                   |
|              +------------------+                 |
|              |     [P-BIT 7]    |                 |
|              |                  |                 |
|              | Noise source     |                 |
|              |      ↓           |                 |
|              | Amplifier        |                 |
|              |      ↓           |                 |
| VBIAS7 ----->| Comparator       |                 |
|              |      ↓           |                 |
|              |      Q7          |                 |
|              +------------------+                 |
|                                                   |
| Q0 ... Q7 ---------------------------> MCU inputs |
+---------------------------------------------------+

VBIAS0 … VBIAS7 are analog voltages generated by the DAC. Each VBIAS controls the probability of its corresponding p-bit output being 0 or 1.

MCU Responsibilities

For the basic 8-p-bit board, the MCU has about 5 main jobs:

1. Communicate with the PC over USB
2. Set VBIAS0 ... VBIAS7 through the DAC
3. Read Q0 ... Q7 digital p-bit outputs
4. Calibrate each p-bit by sweeping VBIAS and measuring P(1)
5. Apply the calibration so a requested probability or bias is converted to the correct DAC voltage

Later:

6. Run the p-kit update loop locall by computing

   [ I_i = h_i + \sum_j J_{ij} m_j ]

   then set the corresponding bias voltages, sample the physical p-bits, and repeat.

Next ideas

• we can combine these 8 physical p-bits with 56 p-bits emulated on the MCU and study how the circuit’s performance changes compared to a fully emulated implementation