A little bit more than magic: The secret to quantum computing may lie in negativity
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| ARTHUR C. CLARKE |
Quantum computers hold great promise for applications from drug discovery to cybersecurity. Yet figuring out what would give quantum computers their edge over everyday, “classical,” computers is a subtle problem. A new theoretical study led by researchers at the Cavendish Laboratory shows that quantum computers are harder to make powerful than previously assumed, while offering the clearest picture yet of what actually makes them work.
The research, published in Physical Review Letters, helps identify the precise quantum states that are genuinely useful for quantum computation. It also increases the set of quantum calculations known to be easy for classical computers to compute, meaning quantum devices face a higher bar to demonstrate an advantage.
At the heart of quantum computing is a kind of “magic”. Quantum computers typically work with quantum bits, or qubits: particles such as electrons or atoms that can exist in two states at once. To run algorithms that outperform any classical computer, those qubits must be prepared in special starting configurations known as ‘magic states’. These states act as the computational fuel: without them, a quantum computer is no better than a conventional machine.
But the new research expands scientists’ understanding that not all magic states are equal. Many states that appear ‘magic’ and were previously assumed to be useful turn out to offer no quantum advantage.
By identifying this class of useless magic states, the team redraws the boundary between calculations that need a quantum computer and those that can still be handled classically.
“We’re showing that magic is necessary but not sufficient to unlock quantum computer’s full power,” said Dr David Arvidsson-Shukur, from the Hitachi Laboratory at the Cavendish Laboratory. “If a quantum state is not magic, you can’t get a quantum advantage. But having magic alone doesn’t guarantee you have one either. The picture is more nuanced and much more interesting than that.”
To identify which quantum states have what the team classifies as “useful” magic, and which have the ‘useless’ kind, the researchers turned to a mathematical framework developed in Cambridge in 1945 by Paul Dirac, the physicist behind the relativistic quantum equation that predicted antimatter. Working at St John’s College, Dirac independently established a distribution similar to one introduced a decade earlier by MIT’s John Kirkwood, and extended the idea by building the mathematical framework in which to use it. This became known as the Kirkwood-Dirac distribution.
The framework involves a concept that sounds paradoxical: negative probabilities, which the team used to phrase the task of quantum computation. And just as Dirac once argued that a negative solution to an equation should be taken seriously (a theory that eventually led to the discovery of anti-matter), the team shows that the appearance of negative values in the Kirkwood-Dirac distribution is a meaningful signal. When that distribution stays entirely positive (or zero) throughout a computation for a given input quantum state, a classical computer can simulate the quantum computation with ease. When it goes negative, classical simulation becomes exponentially harder and a genuine quantum advantage may exist.
“We’re essentially bringing a new ingredient to the magic mix: the Kirkwood-Dirac negativity,” said J.J. Thio, lead author of the study and PhD student in Prof Crispin Barnes’ group at the Cavendish Laboratory and St John’s College, the same as Dirac’s. “The idea builds on probabilities—for example, the odds of obtaining a heads-up upon flipping a coin – but coming with a twist: they may be negative. And those negative “probabilities” are needed for the quantum computer to outperform its classical counterpart as well.
“That distribution provides a stricter, more precise framework for mapping which quantum states can be efficiently simulated by classical computers.”
To demonstrate their theory, Thio worked with fellow student Rishi Goel to complete a classical simulation programme that runs on a standard laptop, performing computations previously thought to require a quantum computer. The result is a direct demonstration that the classical frontier is larger than we previously thought.
These findings matter because billions of pounds are being invested in quantum computing by governments and private companies worldwide. Yet there is still genuine scientific uncertainty about when quantum computers will outperform classical machines on tasks of practical value.
By pushing the boundary of what classical computers can do, the Cambridge team is helping establish a clearer, more rigorous threshold for what would constitute a true quantum advantage. “Without this kind of foundational work, we will never know whether a quantum device has achieved something genuinely beyond classical reach,” said Arvidsson-Shukur.
The team hopes the results will guide both the design of quantum software and the production of magic states, which remains one of the major engineering challenges in building large-scale quantum computers.
“The better we can identify these useful magic states, the better we can produce and apply them,” said Dr Nicole Yunger Halpern, a Fellow of the Joint Center for Quantum Information and Computer Science (Maryland, USA). “Some of us have conjectured for years that Kirkwood–Dirac negativity can assist with this goal, and I’m delighted that the group has finally answered affirmatively.”
This new work brings the field a step closer to a complete understanding of what gives quantum computers their potential. A question that, despite decades of research, remains open.
Quantum simulators get error bars
University of Innsbruck
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Researchers have developed a method for determining the accuracy of quantum simulations. The new method not only reconstructs the dynamics of a quantum system from experimental data, but can also quantify the uncertainty of the predictions derived from it. The verification method was demonstrated in Innsbruck, Austria, on an ion-trap quantum computer with up to 51 qubits in this quantum lab at IQOQI Innsbruck.
view moreCredit: Markus R. Knabl/IQOQI Innsbruck
In the coming years, increasingly larger and more powerful quantum systems are expected to tackle problems that are difficult or impossible to solve using conventional computers. However, the more powerful quantum simulations become, the more difficult it is to independently verify their results. Where classical simulation is still feasible, results can be cross-checked against it directly; beyond that regime, other methods are needed.
Researchers led by Tristan Kraft of the Technical University of Munich and Peter Zoller of the University of Innsbruck and the Institute for Quantum Optics and Quantum Information at the Austrian Academy of Sciences, together with Barbara Kraus of the Technical University of Munich, have now demonstrated how a quantum simulator can be experimentally characterized and how the uncertainties that arise in the process can be translated into quantitative error limits for its results. The approach was demonstrated by a team led by Manoj Joshi and Christian Roos using an ion-trap quantum simulator containing up to 51 ions.
Not only the result, but also its accuracy
Quantum simulators are physical systems that can be used to replicate the behavior of other quantum systems. Their potential lies in the ability to study complex many-particle systems, the calculation of which quickly reaches its limits with classical computers. “But no real experiment is perfect,” says Tristan Kraft. “Interactions may turn out differently than expected, the system is influenced by its environment, and measurements are also subject to uncertainties.”
The researchers have now developed an approach that uses experimental data to learn how the quantum simulator actually behaves. “From this data, we determine the relevant interactions as well as key influences from fluctuations and noise. We then calculate how the uncertainties in this model affect the simulation results,” explains Tristan Kraft. “The quantum simulator thus provides not just a single value, but a result with error margins that quantify its accuracy.”
The new method was first tested on a system of ten ions, whose dynamics can still be calculated using a conventional computer. The resulting models and error bounds were compared with independent measurements. The researchers then applied the method to a chain of 51 ions and demonstrated that the approach can also be applied to significantly larger systems.
Error limits also for 2D quantum simulation
The researchers will now apply this approach to two-dimensional quantum systems. “This is particularly important because classical calculations for such systems become significantly more difficult as the number of particles increases,” explains quantum computing pioneer Peter Zoller. “This also makes independent verification of the results increasingly complex, making the question of experimentally determined error limits all the more important.”
The researchers are working to adapt the approach to the latest generation of two-dimensional quantum simulators. These systems offer greater precision and allow for the study of larger numbers of particles. In the long term, this approach could also open up a way to quantitatively measure quantum advantages. “After all, when a classical computer and a quantum simulator tackle the same problem, it’s not just a matter of which one delivers a result faster. What’s also crucial is which one can solve the problem with a smaller, verifiable margin of error,” says Peter Zoller. In the future, quantum simulation could be measured not only by the size of a system or the speed at which a calculation is performed, but also by which problems can be solved with verifiable accuracy.
The new approach was published in the journal Physical Review X and the researchers received funding from the Austrian Science Fund (FWF), the German Ministry of Research, Technology and Space, the European Union, and BMW among others.
Publication: Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning. Tristan Kraft, Manoj K. Joshi, William Lam, Tobias Olsacher, Florian Kranzl, Johannes Franke, Lata Kh Joshi, Rainer Blatt, Augusto Smerzi, Daniel Stilck França, Benoît Vermersch, Barbara Kraus, Christian F. Roos und Peter Zoller. Phys. Rev. X 16, 031037. DOI: 10.1103/s96t-n8tx
Journal
Physical Review X
Method of Research
Experimental study
Article Title
Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning
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