Quantum States, superposition
Perhaps you’ve heard of quantum computing and the seemingly sci-fi nature of how it works. It’s generating interest in many industries with some exciting discoveries and applications. But with all the hype around it, it can be tough to determine what quantum computers can do today. In this article we’ll explore why quantum computing is increasingly relevant to Moody’s.
In 2019, Google claimed to have achieved quantum supremacy when they stated that their Sycamore quantum computer took roughly three minutes to perform a task that would take thousands of years for a supercomputer. This was a fantastic achievement that showed the potential of quantum computing. Even though we are in the early stages of the technology and fault-tolerant quantum computers are still far away in the future, recent work on applications suggests some industries might benefit from quantum computing even in the short term.
The finance industry will probably be one of the first to benefit from quantum computing. Finance has many use cases that require large amounts of live data and complex computational tasks like stock prediction, portfolio optimization, and derivative pricing to name a few. The methods that are used to tackle these problems take a lot of time and space in today’s classical computers. However, some of these can be adapted to quantum computing and will potentially be solved effectively even in near-term quantum devices, providing an advantage vs the classical approach.
With so many amazing possibilities in the quantum revolution, you might be wondering how quantum computing makes possible to find a more efficient solution to some problems. It’s not magic, although it does feel like. In quantum computing, the basic unit of information is the qubit or quantum bit. Whereas classical bits represent information in the form of ‘0’ or ‘1’, quantum states can be ‘0’, ‘1’ or a combination of ‘0’ and ‘1’. This special property of qubits that allows them to represent information as a mixture of both states is called superposition. Thanks to superposition, N qubits can represent 2N states simultaneously, for that a classical computer would need 2N classical bits. 300 qubits can represent more states than there are atoms in the universe, a “true quantum leap” indeed [2].
Bit vs Qubit
Quantum states are represented as vectors in a so-called “Hilbert Space”. These vectors are denoted by using Dirac’s bra-ket notation |Ψ>. The qubit shown below is in a state of superposition between ‘0’ and ‘1’ (basis states) with some probability amplitude α and β that satisfy |α|2 + |β|2= 1. Now what happens when this state is measured? If you do not measure the state, you are in a bizarre quantum world where you can manipulate the quantum state but when you measure the state, it collapses to one of the basis states, it will collapse to ‘0’ with probability |α|2 or to ‘1’ with probability |β|2.
Quantum States, superposition
Entanglement
Now that we know what qubit states look like, how do we perform operations on them? Similar to classical bit states, qubit states can be changed by using quantum gates. However, one of the most interesting properties of qubits is ‘entanglement’. A pair of qubits are said to be entangled when the qubits are in such a state that the action on one qubit impacts the state of the other qubit, even if they are far away
from each other. As depicted in the above picture, you can see the quantum entangled state in the bottom right corner and the corresponding circuit [4], that is, the set of gates we need to apply to the qubits to get the resulting state, in the top left corner. Another important property is interference, we can manipulate qubit states in such a way that the states which contain the information we need have their probability amplitudes amplified whereas those that we are not interested in, have their probability amplitudes cancelled out.
Quantum algorithms leverage superposition, entanglement, and interference to solve some problems in a more efficient way.
TOTAL IMPACT OVER
3+ YEARS
TOTAL IMPACT OVER
20+ YEARS
AVERAGE YEARLY BUDGET FROM MOST FORTUNE 500 COMPANIES
From NISQ to error-corrected quantum computers.
Adapted from Rigetti
Quantum computing is a new paradigm in computing, but there are many open challenges to work on. Creating and maintaining the state of a qubit is not an easy task. Even a small change in the environment can make a qubit unstable, quantum chips based in superconducting qubits, widely used today, are kept in a dilution fridge of almost absolute zero temperature. Some research groups and companies are working on building qubits that can be scaled and maintained at room temperature – including technologies with laser trapped ions or diamonds. Moreover, today’s quantum computers do not have error correction and they contain noise, we refer to them as Noisy Intermediate Scale Quantum (NISQ) quantum computers.
Current quantum algorithms are run in NISQ devices employing error mitigation techniques. The quantum computers that we have today are composed of a few hundred qubits and therefore the size of the problems they can handle is still moderate. But it is not just about the number of qubits. There is more than one metric needed to measure quantum computing performance. According to IBM Research the key three metrics are scale (number of qubits), quality (Quantum Volume) and speed (Circuit Layer Operations Per Second, CLOPS) [3].
Now the biggest question is, how will quantum disrupt the financial industry? Who will benefit from this and how? Although the power of quantum computing is still beginning to show and there are many open questions, major financial institutions such as JPMorgan Chase & Co, Goldman Sachs, HSBC or Barclays have been working for some years to understand how to harness quantum computing. At Moody’s, we announced this year the creation of our Quantum Computing unit and released a set of Frequently Asked Questions on why we are investing on this.
As mentioned earlier, finance is believed to be one of the first sectors to benefit from quantum computing. Some use cases have the potential to be solved by quantum algorithms designed for near- term quantum computers. Also, when large-scale robust quantum computers become a reality, other quantum algorithms will speed up many computations used in finance. Quantum computing researchers are working on developing quantum algorithms that solve relevant problems more efficiently and building robust quantum hardware. Financial institutions need to understand what benefits quantum computing can bring them:
With improved optimization and decision-making techniques to advance current finance methods and to serve customers better, finance organizations investing in quantum computing at an early stage stand to gain a significant competitive advantage.
Not only will these organizations get a competitive edge, but there are other advantages of being among the first movers too (based on a BCG report).
According to the same report by BCG, it is predicted that quantum computing will create a total impact of $500M in the coming 3+ years and $70B in the coming 20+ years. Right now, the average yearly budget for most Fortune500 companies is $1 million. In 2019, a strategist at Bank of America said quantum computing will be the smartphone of 2020’s and in 2020, a Goldman Sachs researcher pointed out quantum computing as a critical technology [2]. McKinsey also estimates a $3100M industry by 2028 with a 30,8% compound annual growth rate (CAGR).
This is just the tip of the iceberg! At Moody’s, we’re implementing the phenomenal characteristics that quantum physics embeds in computation, and we stand to use that effect to improve current processes in finance. The cases above are some of the examples of cases that will eventually disrupt the financial services industry but surely there will be more.
The road is long but full of discoveries and innovations, and we are here to help you get ready! Join Moody’s in our Quantum Journey by following our group research or participating in our user study groups. Contact us for more information.
References
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