Quantum Computing in Finance: Real Applications, Challenges and Practical Examples
24/06/2025
On June 24, during the event "Between Zero and One 4 – Quantum Finance: The Future of the Financial Sector", held at Inovabra Habitat, IBM presented the current state of quantum computing applied to finance. The event brought together representatives from major banks and IBM specialists to cover everything from basic concepts to real-world use cases.
Understanding the Fundamentals: What is a Qubit?
In quantum computing, the smallest unit of information is the qubit. Unlike a classical bit, which can only be in state 0 or 1, a qubit can be in both states simultaneously through superposition.
Mathematically, the basic qubit states are represented as vectors:
|0⟩ = (1, 0)
|1⟩ = (0, 1)
In addition, qubits can exhibit entanglement, where the state of one qubit is directly linked to the state of another, making it impossible to describe them independently.
Superposition and Entanglement
Superposition allows a qubit to exist in multiple states at once, enabling parallelism in quantum processing.
Entanglement creates correlations between qubits that can be exploited in complex algorithms.
IBM's Roadmap Towards Fault-Tolerant Quantum Computing
IBM presented its roadmap aiming to achieve fault-tolerant quantum computing by 2028. Key milestones include:
- 2025: Processors with 6-way connectivity.
- 2026: Implementation of long-range couplers and logical processing units with up to 10 logical qubits.
- 2027: Logical communication between error-corrected code blocks.
- 2028: Universal computation with multiple code blocks and magic state distillation.
Financial Sector Applications
IBM demonstrated how various financial institutions are already using quantum computing for:
- Portfolio optimization
- Asset pricing
- Credit risk analysis
- Fraud detection
- Derivatives pricing
Banks like Wells Fargo, HSBC, Crédit Mutuel, Bradesco, and Itaú are part of the IBM Quantum Network and are working on real projects.
Practical Example: Portfolio Optimization Using Quantum Computing
A detailed case study on portfolio optimization using the VQE (Variational Quantum Eigensolver) quantum algorithm was presented.
Process Overview:
- Selection of assets and historical price data.
- Calculation of expected return vector and covariance matrix.
- Formulation of the problem as a quadratic cost function.
- Conversion to QUBO (Quadratic Unconstrained Binary Optimization) format.
- Construction of the corresponding Hamiltonian.
- Definition of the algorithm and optimizer (VQE with Gradient Descent in this case).
- Execution of the quantum circuit.
- Measurement of the expected value and iterative parameter adjustment until the stopping criterion was met.
- Final result obtained.
Final state observed:
|ψ_final⟩ ≈ (0, 1, 0, 0)
With an energy value close to -2.4397.
Benefits
Quantum computing allows for accelerating the solution of optimization problems that, in classical form, would have exponential complexity.
For portfolio optimization, brute-force methods scale with O(2^n), where n is the number of assets. Quantum computing provides a significant reduction in execution time.
Current Challenges
The main challenge lies in hardware limitations. The industry is currently in the NISQ era (Noisy Intermediate-Scale Quantum), working with devices that have only a few hundred qubits and a high error rate. Current quantum computers are not fault-tolerant, limiting the number of operations that can be executed before computational errors accumulate.
Next Steps
Progress in the financial sector will depend on:
- Developing more efficient quantum algorithms.
- Creating encoding techniques capable of representing more assets using fewer qubits.
- Building more stable and error-resistant hardware.
Cryptography: Foundations and Mathematical Basis
The presentation also addressed cryptography, a field directly affected by advancements in quantum computing.
What is Cryptography
Cryptography is a technique used to protect information, ensuring that only authorized individuals can access it.
It transforms readable data (plaintext) into encoded data (ciphertext) using mathematical algorithms and cryptographic keys.
The main goals of cryptography are:
- Confidentiality: Only authorized recipients can read the message.
- Integrity: Ensures that the information has not been altered.
- Authenticity: Confirms the identity of the sender.
- Non-repudiation: Prevents the sender from denying the action.
Mathematical Foundation of Traditional Cryptography
Most current cryptographic security is based on the computational difficulty of solving specific mathematical problems on classical computers.
Examples include:
- Integer factorization (used in RSA)
- Discrete logarithm problem (used in ECDSA and DSA)
With the evolution of quantum computers, these foundations are under threat, especially due to algorithms like Shor’s, which can efficiently break many of these systems.
Symmetric and Asymmetric Cryptography: Overview
Two main types of cryptography were presented:
Symmetric Key Cryptography:
- Same key is used for both encryption and decryption.
- Examples: AES, 3DES.
- Applications: Protecting data in transit and at rest.
Asymmetric Key Cryptography:
- Uses a public-private key pair.
- Examples: RSA, ECDSA, DSA, ECDH.
- Applications: Authentication, key exchange, digital signature.
Data Usage Categories:
- Data in Transit: Communication between systems.
- Data at Rest: Secure storage.
- Data in Use: Runtime access control.
Connection Between Cryptography and Quantum Computing
With the advancement of quantum hardware, cryptographic algorithms relying on factorization or discrete logarithms will become vulnerable.
This has accelerated the global development of post-quantum cryptography, with new algorithms being standardized by organizations like NIST.
Impact of Quantum Computing on Current Cryptographic Defenses
A key concern raised during the event was the future ability of quantum computers to break existing cryptographic protections.
Current cryptographic algorithms depend on the intractability of certain mathematical problems. These problems are currently unfeasible for classical computers but will become solvable in reasonable timeframes with the arrival of a "Cryptographically Relevant Quantum Computer".
Symmetric Cryptography:
Quantum computing reduces its effective security by half, as per Grover’s Algorithm.
For example, a 128-bit key would offer the effective security of a 64-bit key against a quantum attack.
Public Key Cryptography:
Even more vulnerable, Shor’s Algorithm, presented in 1994, can break most traditional asymmetric algorithms like RSA, DSA, and ECDSA.
The financial industry is aware that this is no longer a theoretical risk but an impending reality.
Quantum computing brings concrete benefits for areas like portfolio optimization and fraud detection. At the same time, it poses a direct threat to the security of systems based on traditional cryptography.
The event made it clear that the financial sector must act on two fronts:
- Leverage the performance gains offered by quantum computing.
- Begin transitioning to quantum-safe cryptographic algorithms.
Both paths are necessary to maintain competitiveness and security in the coming years.
