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https://github.com/runeape-sats/qmoney

QMoney: A Peer-to-Peer Quantum Money System v0.0.1
https://github.com/runeape-sats/qmoney

bitcoin quantum-computing

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QMoney: A Peer-to-Peer Quantum Money System v0.0.1

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# QMoney: A Peer-to-Peer Quantum Money System



v0.0.1 draft



## Abstract

QMoney introduces a novel quantum money system that combines the unforgeable nature of quantum states with a peer-to-peer (P2P) transaction framework inspired by Bitcoin. Using a 2-qubit quantum bill, QMoney leverages the **no-cloning theorem** to ensure that currency cannot be counterfeited, while a decentralized network of nodes verifies and transfers ownership without a central mint or bank. This white paper details the preparation, verification, and P2P exchange of quantum bills, illustrated through a toy example using photon polarization and polarizers. By merging quantum security with Bitcoin’s P2P philosophy, QMoney offers a vision for a trustless, quantum-secure digital currency.



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## 1. Introduction

Traditional currencies and even modern cryptocurrencies like Bitcoin face challenges in achieving absolute unforgeability. Physical money can be replicated with advanced techniques, while Bitcoin, though secure against double-spending via its blockchain, relies on computational assumptions vulnerable to quantum attacks (e.g., Shor’s algorithm breaking ECDSA). Quantum money, first proposed by Stephen Wiesner in 1969, encodes currency in quantum states—such as superpositions of qubits—that cannot be perfectly copied due to the **no-cloning theorem**, offering a physics-based solution to counterfeiting.



**QMoney** extends this concept into a **peer-to-peer quantum money system**, integrating Bitcoin’s decentralized ethos. In Bitcoin, a P2P network of nodes validates transactions without a central authority, using a public ledger (the blockchain) to track ownership. QMoney adapts this model: instead of a mint and bank, users and nodes in a network collectively issue, verify, and transfer 2-qubit quantum bills. This white paper presents a minimal 2-qubit scheme to illustrate QMoney’s core mechanisms—quantum state preparation, decentralized verification, and P2P exchange—while providing a practical example with photon polarization. As of March 2025, quantum hardware remains experimental, but QMoney lays a theoretical foundation for a future where quantum and P2P technologies converge.



---



## 2. Theoretical Background

### 2.1 The No-Cloning Theorem

The **no-cloning theorem**, established by Wootters and Zurek in 1982, underpins QMoney’s security. It asserts that no unitary operation can duplicate an unknown quantum state |ψ⟩ = α|0⟩ + β|1⟩ into |ψ⟩ ⊗ |ψ⟩. Attempts to copy—e.g., by measuring and reconstructing—collapse the state, losing superposition information (e.g., |+⟩ becomes |0⟩ or |1⟩). In QMoney, this ensures that quantum bills cannot be forged, as any duplication attempt introduces detectable errors, a feature Bitcoin lacks, relying instead on cryptographic hardness.



### 2.2 Qubits and Measurement Bases

A **qubit**, unlike Bitcoin’s classical bits, exists in a superposition within a two-dimensional Hilbert space:

- |0⟩: e.g., horizontal polarization;

- |1⟩: e.g., vertical polarization;

- |+⟩ = (|0⟩ + |1⟩)/√2 or |-⟩ = (|0⟩ - |1⟩)/√2, superpositions akin to diagonal polarizations.



Measurement occurs in bases:

- **Standard basis**: |0⟩, |1⟩;

- **Hadamard basis**: |+⟩, |-⟩, accessed via the Hadamard gate H = (1/√2) * [1 1; 1 -1].



QMoney uses these bases to encode bills, with verification performed by P2P nodes rather than a central authority, mirroring Bitcoin’s distributed validation.



### 2.3 Bitcoin’s Peer-to-Peer Model

Bitcoin operates on a P2P network where nodes—computers running the Bitcoin protocol—validate transactions using a proof-of-work consensus mechanism. Transactions are broadcast to the network, recorded on a blockchain, and verified without intermediaries. QMoney adopts this P2P structure, replacing Bitcoin’s digital signatures with quantum state measurements, aiming for a decentralized quantum currency resilient to both classical and quantum threats.



---



## 3. QMoney: 2-Qubit Peer-to-Peer Quantum Money Scheme

### 3.1 State Preparation

In QMoney, a 2-qubit quantum bill is created by any user (a “minter”) in the P2P network:

1. **Random Basis Selection**: For each qubit, choose:

   - 0 (standard basis: |0⟩, |1⟩), 50% probability;

   - 1 (Hadamard basis: |+⟩, |-⟩), 50% probability.

2. **Random Bit Value**: 0 or 1, 50% probability.

3. **State Preparation**:

   - Basis 0, bit 0: |0⟩;

   - Basis 0, bit 1: |1⟩;

   - Basis 1, bit 0: |+⟩;

   - Basis 1, bit 1: |-⟩.



The minter broadcasts the quantum state (e.g., |0⟩ ⊗ |-⟩) and a classical “serial number” (basis and bit pairs, e.g., “0:0, 1:1”) encrypted with their quantum-resistant public key. Unlike Bitcoin’s mining, issuance is lightweight, requiring only quantum state generation.



### 3.2 Verification

Verification is decentralized, performed by P2P nodes:

- **Serial Number Decryption**: Nodes decrypt the serial number using the minter’s public key.

- **Measurement**:

  - Basis 0: Measure in the standard basis.

  - Basis 1: Apply a Hadamard gate, then measure in the standard basis.

- **Consensus**: Nodes broadcast measurement results. If the majority match the serial number’s bit values (e.g., 0 for Qubit 0, 1 for Qubit 1), the bill is valid. This mirrors Bitcoin’s consensus but uses quantum measurements instead of hash validation.



### 3.3 Peer-to-Peer Transfer

To spend a bill, the owner transfers the quantum state to a recipient via a quantum channel (e.g., optical fiber) and broadcasts a transaction to the P2P network, akin to Bitcoin’s transaction propagation. Nodes re-verify the state, updating a quantum-aware blockchain—a ledger recording ownership transitions without storing the fragile quantum states themselves. Double-spending is prevented by network consensus: once spent, the original state is measured (destroyed), and only the new owner’s state is valid.



### 3.4 Security

QMoney’s security combines quantum and P2P strengths:

- **No-Cloning**: Prevents state duplication.

- **Basis Secrecy**: Encrypted serial numbers hide bases from adversaries.

- **P2P Consensus**: Decentralized verification thwarts centralized attacks, unlike traditional quantum money’s reliance on a bank.



---



## 4. Simulating QMoney with Polarizers

### 4.1 Setup

We simulate a QMoney bill using photon polarization:

- |0⟩: Horizontal (H);

- |1⟩: Vertical (V);

- |+⟩: Diagonal (D);

- |-⟩: Anti-diagonal (A).

- **Hadamard Simulation**: Half-wave plate (HWP) at 22.5°.



Nodes use polarizers and HWPs to verify states in a P2P setting.



### 4.2 Example QMoney Bill

A user prepares:

- **Qubit 0**: Basis 0, bit 0 → |0⟩ (H);

- **Qubit 1**: Basis 1, bit 1 → |-⟩ (A).



State: |0⟩ ⊗ |-⟩ (H ⊗ A). Serial number (“0:0, 1:1”) is encrypted and broadcast.



### 4.3 Verification Process

Nodes in the P2P network:

- **Qubit 0**: Measure with H polarizer → Passes, yields |0⟩.

- **Qubit 1**: Apply HWP (A → V), measure with V polarizer → Passes, yields |1⟩.



Results (‘10’) are broadcast; majority consensus confirms validity.



### 4.4 Simulating a Counterfeiting Attempt

An adversary measures in the standard basis:

- Qubit 0 (H): H → |0⟩;

- Qubit 1 (A): H or V (50% each), e.g., V.



Prepares H ⊗ V copies. Nodes verify:

- Qubit 0: Passes;

- Qubit 1: HWP (V → A), V polarizer → 50% pass rate.



Copies fail consensus 50% of the time, detected by the network.



---



## 5. Security Analysis

QMoney’s dual-layer security includes:

- **Quantum Protection**: No-cloning ensures unforgeability.

- **P2P Resilience**: Decentralized nodes prevent single-point failures, unlike Bitcoin’s reliance on computational puzzles vulnerable to quantum speedup.

- **Error Detection**: Wrong-basis measurements yield inconsistent results across nodes.



For two qubits, counterfeiting success drops to 25% with one Hadamard-basis qubit; more qubits amplify this exponentially.



---



## 6. Challenges and Limitations

- **Scalability**: Two qubits are insufficient for robust security; 100+ qubits would resist quantum attacks like Grover’s algorithm.

- **Noise**: Decoherence in quantum channels (e.g., fiber optics) risks false rejections.

- **Infrastructure**: Quantum hardware and networks (e.g., quantum repeaters) are nascent in 2025.

- **Blockchain Integration**: A quantum-aware ledger must handle state destruction and P2P verification efficiently.



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## 7. Conclusion

QMoney fuses quantum unforgeability with Bitcoin’s P2P framework, offering a trustless, quantum-secure currency. This 2-qubit model, demonstrated with polarizers, showcases its potential. Future work could scale QMoney with advanced quantum networks and ledgers, heralding a new era of decentralized finance.



---

## 8. Citations

- Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System. Retrieved from https://bitcoin.org/bitcoin.pdf

(The original Bitcoin white paper introducing the P2P transaction framework and blockchain, which QMoney adapts for its decentralized verification.)

- Wiesner, S. (1983). Conjugate coding. SIGACT News, 15(1), 78–88.

(Originally written in 1969, published later; introduces quantum money using quantum states, foundational to QMoney’s unforgeability.)

- Wootters, W. K., & Zurek, W. H. (1982). A single quantum cannot be cloned. Nature, 299(5886), 802–803.

(Establishes the no-cloning theorem, the core security principle preventing counterfeiting in QMoney.)

- Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.

(A standard reference for quantum mechanics concepts like qubits, superposition, and the Hadamard gate, used in QMoney’s 2-qubit scheme.)

- Shor, P. W. (1997). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5), 1484–1509.

(Describes Shor’s algorithm, highlighting Bitcoin’s vulnerability to quantum attacks, motivating QMoney’s quantum-resistant design.)

- Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC '96), 212–219.

(Introduces Grover’s algorithm, relevant to QMoney’s scalability challenges with larger qubit counts.)



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