Advances In Association Algorithms Make Small, Noisy Quantum Computing Systems Possible

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Current noisy, intermediate scale quantum computers have between 50 and 100 qubits, lose their \"quantumness\" quickly, and lack error correction, which requires more qubits. Since the late 1990s, however, theoreticians have been developing algorithms designed to run on an idealized large, error-correcting, fault tolerant quantum computer.

\"Quantum computers have the promise to outperform classical computers for certain tasks, but on currently available quantum hardware they can't run long algorithms. They have too much noise as they interact with environment, which corrupts the information being processed,\" said Marco Cerezo, a physicist specializing in quantum computing, quantum machine learning, and quantum information at Los Alamos and a lead author of the paper. \"With variational quantum algorithms, we get the best of both worlds. We can harness the power of quantum computers for tasks that classical computers can't do easily, then use classical computers to complement the computational power of quantum devices.\"

The basic unit of information in quantum computing is the qubit, similar to the bit in traditional digital electronics. Unlike a classical bit, a qubit can exist in a superposition of its two \"basis\" states, which loosely means that it is in both states simultaneously. When measuring a qubit, the result is a probabilistic output of a classical bit. If a quantum computer manipulates the qubit in a particular way, wave interference effects can amplify the desired measurement results. The design of quantum algorithms involves creating procedures that allow a quantum computer to perform calculations efficiently.

The threshold theorem shows how increasing the number of qubits can mitigate errors,[33] yet fully fault-tolerant quantum computing remains \"a rather distant dream\".[34]According to some researchers, noisy intermediate-scale quantum (NISQ) machines may have specialized uses in the near future, but noise in quantum gates limits their reliability.[34]In recent years, investment in quantum computing research has increased in the public and private sectors.[35][36]As one consulting firm summarized,[37]

The most well-known example of a problem that allows for a polynomial quantum speedup is unstructured search, which involves finding a marked item out of a list of n {\\displaystyle n} items in a database. This can be solved by Grover's algorithm using O ( n ) {\\displaystyle O({\\sqrt {n}})} queries to the database, quadratically fewer than the Ω ( n ) {\\displaystyle \\Omega (n)} queries required for classical algorithms. In this case, the advantage is not only provable but also optimal: it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups.

For problems with all these properties, the running time of Grover's algorithm on a quantum computer scales as the square root of the number of inputs (or elements in the database), as opposed to the linear scaling of classical algorithms. A general class of problems to which Grover's algorithm can be applied[62] is Boolean satisfiability problem, where the database through which the algorithm iterates is that of all possible answers. An example and possible application of this is a password cracker that attempts to guess a password. Breaking symmetric ciphers with this algorithm is of interest to government agencies.[63]

Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically, quantum simulation may be an important application of quantum computing.[64] Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a collider.[65]

Deep generative chemistry models emerge as powerful tools to expedite drug discovery. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome in the future by quantum computers. Quantum computers are naturally good for solving complex quantum many-body problems[74] and thus may be instrumental in applications involving quantum chemistry. Therefore, one can expect that quantum-enhanced generative models[75] including quantum GANs[76] may eventually be developed into ultimate generative chemistry algorithms.

Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between L and L2, where L is the number of digits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 104 bits without error correction.[86] With error correction, the figure would rise to about 107 bits. Computation time is about L2 or about 107 steps and at 1 MHz, about 10 seconds. However, other careful estimates[87][88] lower the qubit count to 3 million for factorizing 2,048-bit integer in 5 months on a trapped-ion quantum computer.

Despite the scientific and engineering challenges facing the development of quantum computers, considerable progress is being made toward applying the technology to commercial applications. In this article, we discuss the solutions that some companies are already building using quantum hardware. Framing these as examples of combinatorics problems, we illustrate their application in four industry verticals: cybersecurity, materials and pharmaceuticals, banking and finance, and advanced manufacturing. While quantum computers are not yet available at the scale needed to solve all of these combinatorics problems, we identify three types of near-term opportunities resulting from advances in quantum computing: quantum-safe encryption, material and drug discovery, and quantum-inspired algorithms.

However, it is unclear whether a similar phenomenon will play out in quantum, particularly since many different models and architectures are still being explored. Current quantum devices are small and noisy, while the holy grail for the technology is to achieve large, highly-controlled, coherent, analog or digital quantum computers.Footnote 5 In short, a computer where the rate of component failure is sufficiently low to deliver uninterrupted service. Even for the most complex combinatorics problems, it could be that quantum-inspired classical computers ultimately dominate, or that one or several quantum computer designs ultimately dominate, or that some kind of hybrid approach yields a market leader. For now, however, we know that quantum algorithms have inspired useful innovations in software for classical computers that have generated commercial opportunities.Footnote 6

The promise of quantum computers lies in their potential to drastically reduce the time it takes to solve these sorts of problems by utilizing algorithms that make use of quantum effects. Not all combinatorics problems require quantum computers. There are combinatorics problems that are comparatively easy for humans as well as classical computers and sufficiently large and coherent quantum computers to solve (i.e., trying every sequence of 22, 23, and 24 combinations). There are combinatorics problems that are challenging for humans to solve, but easy for classical computers as well as for sufficiently large and coherent quantum computers to solve (i.e., trying every combination on a gym lock). Notably there is no benefit to having a quantum computer solve either of these sorts of problems, because we can work through these problems with our existing classical computers, and these classical computers suffer comparatively fewer shortcomings compared to quantum computers.

Combinatorics challenges are common in banking and finance, from arbitrage to credit scoring to derivatives development. One way banks and other financial institutions deal with these problems is to constrain them in order to make them more tractable. In other words, banks simplify the problems to reduce the set of possible solutions. Constraining the set of possible solutions means that sometimes the best solution is never found. There is a potential for quantum computers to shed insights into larger problems where constraints are relaxed and where more outcomes are possible.

With the preceding as a backdrop, one might assume that banks would like to incorporate as many different factors as possible when credit scoring. However, a paper by quantum computing software company 1Qbit highlights a cost to using a large number of factors: verifying the accuracy of the information.Footnote 37 After all, without robust verification, borrowers may omit key information or outright lie. Therefore, lenders might be willing to sacrifice prediction accuracy for a reduced cost of verifying the accuracy of a loan application. Using data from lending decisions and relevant customer characteristics, the paper demonstrates the combinatorics challenges of determining which information to collect in order to generate accurate predictions without spending too much on verifying the accuracy of the data. These are combinatorics problems because every possible grouping of customer characteristics needs to be assessed. So, if there are one hundred possible borrower characteristics, factors 1, 3, and 15 need to be compared to factors 2, 9, 22, 51, and 85 and so on. Importantly, the number of possible combinations to assess increases exponentially with every additional factor. 59ce067264

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