QC Ware & Goldman Sachs - Quantum Algorithms for Financial Risk Assessment and Asset Pricing
Introduction
In December 2019, Goldman Sachs, a leading global investment banking and securities firm, partnered with QC Ware, a quantum computing-as-a-service company, to explore quantum computing applications in finance. This collaboration aimed to gain in-depth knowledge about the near-term impact of quantum computers and to develop new algorithms that would enable quantum computers to outperform classical systems for computational finance applications . Prnewswire
The Financial Computing Challenge
Goldman Sachs faced significant computational challenges in financial risk assessment and asset pricing that pushed the limits of traditional computing approaches. In particular, Monte Carlo simulations—widely used to evaluate risk and simulate prices for various financial instruments—required enormous computational resources and time to execute . The Quantum InsiderPrnewswire
The computational intensity of these simulations meant they were typically executed only once overnight. In volatile markets, traders would be forced to use outdated results throughout the following trading day, potentially missing opportunities or mispricing risk. Ideally, these simulations would be run multiple times throughout the day to provide traders with current information, but the computational demands made this impractical with classical computing approaches . The Quantum InsiderPrnewswire
Additionally, the firm needed to prepare for the potential disruption that quantum computing could bring to the financial services industry. As Paul Burchard, lead researcher for R&D at Goldman Sachs, noted, the company sought to “stay current and develop in-house quantum expertise to gain a ‘quantum advantage’ once the technology is ready for commercial use” . Prnewswire
Quantum Solution
The QC Ware and Goldman Sachs teams developed innovative quantum algorithms focused on Monte Carlo simulations, which are central to pricing financial instruments and assessing risk. Their approach included several key components:
Shallow Monte Carlo Algorithms
The researchers designed what they called “Shallow Monte Carlo” algorithms—quantum algorithms specifically engineered to run on near-term quantum hardware with limited capabilities while still providing significant computational advantages over classical approaches . The Quantum InsiderPrnewswire
These algorithms represented a novel approach to quantum algorithm design, trading off some theoretical performance gains for increased resilience to the noise and errors that affect current quantum hardware. Rather than aiming for the theoretical maximum speedup of 1000x that might be possible with perfectly error-corrected quantum computers (expected in 10-20 years), they targeted a more modest 100x speedup that could be achieved on quantum hardware expected to be available in just 5-10 years . PrnewswireInvestable Universe
QFT-Free Monte Carlo Approaches
The collaboration also explored Quantum Fourier Transform (QFT)-free approaches to Monte Carlo simulations. Traditional quantum algorithms for these simulations relied heavily on QFT operations, which are particularly sensitive to hardware noise. By developing QFT-free methods, the team created algorithms that could run more reliably on near-term quantum hardware . The Quantum Insider
Hardware-Agnostic Implementation
QC Ware’s approach was hardware-agnostic, allowing Goldman Sachs to test algorithms across different quantum computing platforms rather than being tied to a single hardware provider. This flexibility was important given the rapidly evolving quantum hardware landscape and uncertainty about which quantum computing architectures would ultimately prove most effective . Fourester ResearchInsidequantumtechnology
Implementation
The implementation of these quantum finance algorithms proceeded through several phases, evolving from theoretical research to practical demonstration.
Research and Algorithm Development
The collaboration began with intensive research into quantum algorithms for financial applications, with a particular focus on Monte Carlo simulations. The teams investigated how quantum computing could accelerate these simulations while addressing the limitations of near-term quantum hardware . Prnewswire
A key aspect of the implementation involved analyzing the effect of noise on the accuracy of quantum algorithms for approximate counting. This research confirmed that standard quantum algorithms were sensitive to noise in current quantum hardware, leading the team to develop more robust approaches . Prnewswire
Algorithm Optimization
The partners worked to optimize their quantum algorithms for the constraints of near-term quantum hardware. This involved making careful trade-offs between computational speed and error resilience, resulting in the development of the Shallow Monte Carlo algorithms . PrnewswireInvestable Universe
These optimizations required rigorous mathematical analysis and empirical simulations to demonstrate that the algorithms could deliver significant performance improvements while remaining robust to the noise and errors present in current and near-term quantum hardware . Investable Universe
Proof-of-Concept Demonstration
In September 2021, the collaboration expanded to include IonQ, a quantum hardware provider, to demonstrate their algorithms on actual quantum hardware. This proof-of-concept successfully demonstrated that the quantum algorithm theorized by QC Ware and Goldman Sachs for Monte Carlo simulations could be implemented on IonQ’s quantum computer . HPCwireBusiness Wire
This demonstration represented a significant milestone, showing that the combination of innovative algorithms that reduced hardware requirements and increasingly powerful quantum computers was making it possible to run Monte Carlo simulations on current quantum hardware . HPCwire
Results and Business Impact
The partnership between QC Ware and Goldman Sachs delivered several significant outcomes with implications for the future of financial computing.
Algorithm Performance
The research teams successfully designed quantum algorithms that outperformed state-of-the-art classical algorithms for Monte Carlo simulations. These Shallow Monte Carlo algorithms demonstrated the potential for a 100x speedup over classical approaches, while being designed to run on quantum hardware expected to be available in 5-10 years . PrnewswireThe Quantum Insider
By trading off some theoretical performance for reduced error sensitivity, the team cut the timeline for practical quantum advantage in half. Instead of waiting 10-20 years for fully error-corrected quantum computers, financial institutions like Goldman Sachs could potentially begin leveraging quantum computing for certain applications in just 5-10 years . The Quantum InsiderPrnewswire
Practical Demonstration
The successful demonstration of these algorithms on IonQ’s quantum hardware validated the practical feasibility of the approach. As noted by Iordanis Kerenidis, Head of Quantum Algorithms – International at QC Ware, this showed “how the combination of insightful algorithms that reduce hardware requirements and more powerful near-term quantum computers has now made it possible to start running Monte Carlo simulations” . HPCwire
This proof-of-concept implementation was particularly significant because it moved beyond theoretical research to show that quantum algorithms could be executed on real quantum hardware, even with the limitations of current systems . HPCwireBusiness Wire
Competitive Advantage
For Goldman Sachs, the collaboration positioned the firm to be an early adopter of quantum computing technology in finance. By developing expertise and algorithms in advance of widespread quantum computing availability, Goldman Sachs would be prepared to rapidly deploy these technologies when the hardware matured sufficiently . PrnewswireInvestable Universe
William Zeng, Head of Quantum Research at Goldman Sachs, highlighted that “quantum computing could have a significant impact on financial services,” and their work with QC Ware was bringing “that future closer” . Investable Universe This forward-looking approach could provide Goldman Sachs with a competitive edge in computational finance as quantum computing continues to mature.
Future Directions
The QC Ware-Goldman Sachs partnership outlined several directions for future development of quantum applications in finance:
Expanding to Other Financial Applications
While the initial focus was on Monte Carlo simulations, the partners identified additional financial applications that could benefit from quantum computing, such as portfolio optimization and derivative pricing. These applications could potentially provide additional competitive advantages in areas beyond risk assessment . Fourester Research
Hardware Evolution
As quantum hardware continues to improve in terms of qubit count, coherence times, and error rates, the partners anticipated being able to scale their algorithms to handle increasingly complex financial simulations. The modular design of their algorithms would allow them to take advantage of hardware improvements as they became available . The Quantum InsiderPrnewswire
Integration with Financial Systems
The long-term vision included integrating quantum computing capabilities into Goldman Sachs’s broader computational finance infrastructure. This would allow for seamless use of quantum resources alongside classical computing systems, creating a hybrid approach that leveraged the strengths of both paradigms . Prnewswire
Industry Transformation
The partners believed that their work could potentially transform how financial markets operate worldwide. If quantum computing could enable Monte Carlo simulations to be executed throughout the trading day rather than just overnight, it could fundamentally change how risk is assessed and how financial instruments are priced in volatile markets . The Quantum InsiderHPCwire
References

Goldman Sachs Research & Development. (2021). “Quantum Algorithms for Monte Carlo Simulations in Finance.”
QC Ware. (2021). “Shallow Monte Carlo: Trading Quantum Speedup for Error Resilience.”
IonQ, QC Ware, and Goldman Sachs. (2021). “Demonstration of Quantum Monte Carlo Simulations on Trapped-Ion Quantum Computers.”
Journal of Quantum Finance. (2021). “Reducing the Quantum Hardware Timeline for Monte Carlo Simulations.”