Quantinuum’s recent announcement about its breakthrough on topological qubits garnered headlines across both the specialist scientific media as well as those more broadly interested in the advances that will make quantum computing useful more quickly than anticipated. However, hidden in the details was a reference to a technology that is as rare as it is valuable. The fact is that the topological qubit that was generated could only have been done via Quantinuum’s H-Series quantum processors due to their various qualities and functions of which measurement and ‘feed-forward’ is critical.

As we know, great advances are often built on the back of little-known utilities - functions and tools that rarely get mentioned. These are sometimes technological constructs that might seem simple on the surface, but which are difficult (in the case of feed-forward make that “very difficult” to create), and without which critical advances would remain merely theoretical.

As detailed in two manuscripts that have been uploaded onto the pre-print repository, arXiv, Quantinuum researchers and their collaborators successfully demonstrated, for the first time, a large-scale implementation of a long-standing theory in quantum information science; namely the use of measurement and feed-forward (see below for a detailed explanation of what this means) to efficiently generate long-range entangled states.

The two experiments, conducted with research partners at the California Institute of Technology, Harvard University, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used Quantinuum’s trapped ion quantum computers, Powered by Honeywell, to show how feed-forward enables success by dramatically reducing the resources required to produce highly-entangled quantum states and topologically ordered phases, one of the most exciting areas of research in modern physics.

Feed-forward uses selective measurements during the execution of a quantum circuit and adapts future operations depending on those measurement results. To be successful in running an adaptive quantum circuit, several challenging requirements must be met: (1) a select group of qubits must be measured in the middle of a circuit with high fidelity, and without accidentally measuring other qubits, and (2) the measurement results must be sent to a classical computer and quickly processed to create instructions to be fed-forward to the quantum computer on the fly - all of which must be done fast enough to prevent the active qubits from decohering.

Once these requirements are met, the feed-forward capabilities let quantum computers create long-range entangled states which are emerging as central to various branches of modern physics such as quantum error correction codes and the study of spin liquids in condensed matter. It is also the essential component of topological order and could enable the simulation of quantum systems beyond the reach of classical computation.

In the paper “Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer”, Quantinuum, working with colleagues from the California Institute of Technology and Harvard University use feed-forward to explore topologically ordered phases of matter. 

Separately, a different team of scientists from Quantinuum, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used feed-forward to explore adaptive quantum circuits in “Experimental Demonstration of the Advantage of Adaptive Quantum Circuits”. 

Two of Quantinuum’s physicists who worked on both experiments, Henrik Dreyer and Michael Foss-Feig, offered some observations on the work.

“While it has been clear to theorists that feed-forward would be a useful primitive, doing it with low errors has turned out to be very challenging. The H-Series systems have made it possible to use this primitive efficiently,” said Henrik, managing director and scientific lead at Quantinuum’s office in Munich, Germany.

Michael, who is based at Quantinuum’s world-leading quantum computing laboratory outside of Denver, Colorado, also described feed-forward and adaptive quantum circuits as a jump toward meaningful simulations.

“This capability speeds up the timeline for new scientific discoveries,” he said.

These successful experiments proved that feed-forward operations reduce the quantum resources required for certain algorithms and are a valuable building block for more advanced research.

"I am really excited by the opportunities opened up by this demonstration: using wave-function collapse is a very powerful tool for preparing very exotic entangled states further down the road, where there are no good scalable alternatives," said Dr. Ruben Verresen, a physicist at Harvard University and a co-author of the topological order paper.

The authors note that “the primary technical challenge in implementing adaptive circuits is the requirement to perform partial measurements of a subset of qubits in the middle of a quantum circuit with minimal cross-talk on unmeasured qubits, return those results to a classical computer for processing, and then condition future operations on the results of that processing in real time.”

The paper describes how quantum hardware has now reached a state where adaptive quantum circuits are possible and can outperform unitary circuits. The experiment detailed in the paper “firmly establishes that given access to the same amount of quantum computational resources with respect to available gates and circuit depth, adaptive quantum circuits can perform tasks that are impossible for quantum circuits without feedback.”

Henrik and Michael noted that the adaptive circuit research provides concrete evidence not only that feed-forward works, but that it now works well enough to achieve tasks that would not be possible without it.

“We were trying to find a metric by which somebody can look at our data produced by a shallow adaptive circuit, and convince themselves it could not have been produced with a unitary circuit of the same depth,” Michael said. The metric proposed in the adaptive circuits paper achieved exactly that.

A good match: Trapped ion architecture and feed-forward 

Demonstrating this technique required significant performance from the H1-1. 

“It's a huge challenge to implement this in a way that works well,” Michael said. 

Quantinuum’s H-Series has the capabilities that are crucial to this work: high fidelity gates, low state preparation and measurement (SPAM) error, low memory error, the ability to perform mid-circuit measurement, and all-to-all connectivity.

The feed-forward theory has been well-known for years but challenging to execute in practice, and as the paper states:

“While individual elements of this triad have been demonstrated in the context of error correction and topological order, combining all of these ingredients into one experimental platform has proven elusive since the inception of this idea more than a decade ago. Here, we demonstrate for the first time the deterministic, high-fidelity preparation of long-range entangled quantum states using a protocol with constant depth, using Quantinuum’s H-Series programmable Ytterbium ion trap quantum computer.”

The authors also note that “the all-to-all connectivity of the device was vital for the implementation of the periodic two-dimensional geometry and the conditional dynamics.”

In summary – these papers showcase state-of-the-art demonstrations of what can be done with quantum computers today but are only a preview of what will be done tomorrow.

Quantinuum has unveiled our new optics and electromechanical engineering laboratory space at our largest operating site, in Broomfield Colorado.

Not only is the new space more than twice as big as the space we occupy today, but it will also house a clean, quiet, temperature controlled, state-of-the-art laboratory that befits the excellence of the work we do here.

Our hardware engineering and teams are focused on optimizing, customizing, and miniaturizing the components that power the H-Series quantum computers, demanding that our teams blur the boundaries between discrete disciplines, such as bulk optics and micro photonics, or embedded software and control electronics. Getting the handover right between different deeply skilled experts requires proximity and an intimate understanding of how one workflow blends into the other.

This is why this new lab space will make such a powerful contribution to our hardware success: because it is built around the needs of deeply connected, multidisciplinary teams, entirely focused on our goal of designing and building the first truly useful, breakaway quantum computer.

Six things you need to know about Quantinuum’s new lab

1. State-of-the-Art Facility: Our new lab, with its state-of-the-art design and facilities, creates an environment for collaboration that will spur advances in the fields of optics, photonics, electromechanical engineering, and others.
   
   
2. Expansive and Efficient Space: The lab is not only going to be much larger than what we have today, it is also highly functional, with high ceilings and cloud superstructures over optics benches for better movement and workflow, which will afford our teams greater flexibility and access to every angle of the technology they are creating.
   
   
3. Advancing Micro and Nano Optics: As we aim to reduce our beam delivery size, we're drawing together the work of different teams, creating a dynamic environment where optics transitions into photonics, yielding new potential in terms of size, scale and performance. The location of certain teams will enable such cross-disciplinary workflows.
   
   
4. Custom Fabrication Capabilities: The new optics lab, together with our highly capable chip and trap fabrication capabilities, is designed to enable generational transitions from off-the-shelf, multipurpose optical components to fabricating more compact and fit-for-purpose devices: Think of moving from Functionality on a Table, through Functionality on a Chip, to Functionality on a Trap.
   
   
5. Greater Collaboration and Integration: The new laboratory layout improves the way some teams are co-located, with an eye always toward helping to enhance collaboration. For example, the new engineering space was designed to facilitate close cooperation between the electronics and software teams who design our control systems, as well as the mechanical teams who package the hardware and the test teams who validate it.  Such proximity between disciplines supports faster decision-making and more efficient resolution of interdisciplinary challenges, leading to a virtuous circle of accelerated design and development, faster innovation, and better quantum computers.
   
   
6. Ready for Future Expansion: As we prepare for the next stage of the journey towards fault-tolerant quantum computing, where demand for quantum compute will scale exponentially everywhere, this new laboratory space is fit for the future as well as meeting the demands of today.

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Quantinuum’s new H2-1 quantum computer proves that trapped-ion architecture, which is well-known for achieving outstanding qubit quality and gate fidelity, is also built for scale – and Quantinuum’s benchmarking team has the data to prove it. 

The bottom line: the new System Model H2 surpasses the H1 in complexity and qubit capacity while maintaining all the capabilities and fidelities of the previous generation – an astounding accomplishment when developing successive generations of quantum systems.

The newest entry in the H-Series is starting off with 32 qubits whereas H1 started with 10. H1 underwent several upgrades, ultimately reaching a 20-qubit capacity, and H2 is poised to pick up the torch and run with it. Staying true to the ultimate goal of increasing performance, H2 does not simply increase the qubit count but has already achieved a higher Quantum Volume than any other quantum computer ever built: 2¹⁶ or 65,536. 

Most importantly for the growing number of industrials and academic research institutions using the H-Series, benchmarking data shows that none of these hardware changes reduced the high-performance levels achieved by the System Model H1. That’s a key challenge in scaling quantum computers – preserving performance while adding qubits. The error rate on the fully connected circuits is comparable to the H1, even with a significant increase in qubits. Indeed, H2 exceeds H1 in multiple performance metrics: single-qubit gate error, two-qubit gate error, measurement cross talk and SPAM. 

Key to the engineering advances made in the second-generation H-Series quantum computer are reductions in the physical resources required per qubit. To get the most out of the quantum charge-coupled device (QCCD) architecture, which the H-Series is built on, the hardware team at Quantinuum introduced a series of component innovations, to eliminate some performance limitations of the first generation in areas such as ion-loading, voltage sources, and delivering high-precision radio signals to control and manipulate ions.

The research paper, “A Race Track Trapped-Ion Quantum Processor,” details all of these engineering advances, and exactly what impacts they have on the computing performance of the machine. The paper includes results from component and system-level benchmarking tests that document the new machine’s capabilities at launch. These benchmarking metrics, combined with the company’s advances in topological qubits, represent a new phase of quantum computing.

Advancing Beyond Classical Simulation

‍In addition to the expanded capabilities, the new design provides operational efficiencies and a clear growth path.

At launch, H2’s operations can still be emulated classically. However, Quantinuum released H2 at a small percentage of its full capacity. This new machine has the ability to upgrade to more qubits and gate zones, pushing it past the level where classical computers can hope to keep up.

Increased Efficiency in New Trap Design

This new generation quantum processor represents the first major trap upgrade in the H-Series. One of the most significant changes is the new oval (or racetrack) shape of the ion trap itself, which allows for a more efficient use of space and electrical control signals. 

One key engineering challenge presented by this new design was the ability to route signals beneath the top metal layer of the trap. The hardware team addressed this by using radiofrequency (RF) tunnels. These tunnels allow inner and outer voltage electrodes to be implemented without being directly connected on the top surface of the trap, which is the key to making truly two-dimensional traps that will greatly increase the computational speed of these machines. 

The new trap also features voltage “broadcasting,” which saves control signals by tying multiple DC electrodes within the trap to the same external signal. This is accomplished in “conveyor belt” regions on each side of the trap where ions are stored, improving electrode control efficiency by requiring only three voltage signals for 20 wells on each side of the trap.

The other significant component of H2 is the Magneto Optical Trap (MOT) which replaces the effusive atomic oven that H1 used. The MOT reduces the startup time for H2 by cooling the neutral atoms before shooting them at the trap, which will be crucial for very large machines that use large numbers of qubits. 

Industry-leading Results from 15 Benchmarking Tests

Quantinuum has always valued transparency and supported its performance claims with publicly available data. 

To quantify the impact of these hardware and design improvements, Quantinuum ran 15 tests that measured component operations, overall system performance and application performance. The complete results from the tests are included in the new research paper. 

The hardware team ran four system-level benchmark tests that included more complex, multi-qubit circuits to give a broader picture of overall performance. These tests were:

• Mirror benchmarking: A scalable way to benchmark arbitrary quantum circuits.
• Quantum volume: A popular system-level test with a well-established construction that is comparable across gate-based quantum computers.
• Random circuit sampling: A computational task of sampling the output distributions of random quantum circuits.
• Entanglement certification in Greenberger-Horne-Zeilinger (GHZ) states: A demanding test of qubit coherence that is widely measured and reported across a variety of quantum hardware.

H2 showed state-of-the-art performance on each of these system-level tests, but the results of the GHZ test were particularly impressive. The verification of the globally entangled GHZ state requires a relatively high fidelity, which becomes harder and harder to achieve with larger numbers of qubits. 

With H2’s 32 qubits and precision control of the environment in the ion trap, Quantinuum researchers were able to achieve an entangled state of 32 qubits with a fidelity of 82.0(7)%, setting a new world record.

In addition to the system level tests, the Quantinuum hardware team ran these component benchmark tests:

• SPAM experiment
• Single-qubit gate randomized benchmarking
• Two-qubit gate randomized benchmarking
• Two-qubit SU gate randomized benchmarking RB
• Two-qubit parameterized gate randomized benchmarking
• Measurement/reset crosstalk benchmarking 
• Interleaved transport randomized benchmarking
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The paper includes results from those tests as well as results from these application benchmarks:

• Hamiltonian simulation
• Quantum Approximate Optimization Algorithm 
• Error correction: repetition code
• Holographic quantum dynamics simulation 

For more than two decades, there has been a general consensus among physicists pursuing the development of universal, fault-tolerant quantum computers that non-Abelian topological states would offer a promising path to success, if the states could ever be created.

These states host exotic quasi-particles—called anyons—that allow the storage of quantum information in their internal states which can only be changed by "braiding" them around each other in spacetime. Small perturbations in the trajectory of these braids would then leave the topology of the braid unchanged, making this paradigm inherently robust. It is as if they are ‘deaf’ to the noise of a system.

The problem however, is that non-Abelian anyons have never yet been detected, much less controlled. 

Until now.

Now, Quantinuum scientists, in collaboration with researchers from Harvard University and Caltech, have turned years of theory regarding topological states into reality, using the unique capabilities of the new H2 trapped-ion processor to create and control non-Abelian anyons. Using a shallow adaptive circuit on the H2, the research team prepared a non-Abelian quantum state on 27 qubits with a fidelity per site exceeding 98.4%.

This demonstration hinges on crucial advances in theory and experiment. On the theory side, Dr. Ruben Verresen, Prof. Ashvin Vishwanath (Harvard) and Dr. Nathanan Tantivasadakarn (Caltech) have shown how to use mid-circuit measurement to significantly simplify the route towards this kind of non-Abelian state. On the experimental side, the increased qubit capacity of the H2 system allows for sufficient complexity to create collective non-Abelian particles, while keeping the extremely low gate and mid-circuit measurement errors of previous generations.

The achievement has set the stage for an accelerated path to fault-tolerant quantum computing while also paving the way for new fields of research within condensed matter physics and high-energy physics.

The paper documenting the research, "Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor," is posted in Nature. This research was one of several papers published at the launch of H2, the next generation in Quantinuum's H-Series quantum computer, Powered by Honeywell.  

Advancing the Hardware Roadmap

Quantinuum has been advancing this area of research in “stealth mode” for some considerable time.  

Ilyas Khan, Quantinuum’s Chief Product Officer said "I recall vividly discussing topological quantum computing with Henrik 7 years ago during a long hot summer when devices such as our H2 processor were hard to even dream about. This research represents a milestone that benefits the industry as a whole and yet again demonstrates our ability to not only be world leaders today but also long into the future.”

"Topological order is our best shot at creating a quantum computer with very low error rates," Henrik said. "We need to be able to operate on the system while keeping it protected from the environment," he said. "Topological order can offer that protection. This research demonstrates that the more exotic kind of topological state, the non-Abelian kind, can be created with today's devices on-demand and with high fidelity. One of next steps will be to demonstrate stability by repetitive error-correction, utilizing the same ingredients used to prepare the state in the first place."

According to Tony Uttley, President and COO of Quantinuum, this advance represents a breakaway moment for Quantinuum.  

"We've reached a point with our technology that we can build a quantum computer on top of a quantum computer," Tony said. "These non-Abelian topological qubits can layer on top of physical qubits without changing how our quantum computer operates. That accomplishment will accelerate our work on the path to fault-tolerant quantum computing."

In a meaningful advance in an important area of industrial and real-world relevance, Quantinuum researchers have demonstrated a quantum algorithm capable of solving complex combinatorial optimization problems while making the most of available quantum resources. 

Results on the new H2 quantum computer evidenced a remarkable ability to solve combinatorial optimization problems with as few quantum resources as those employed by just one layer of the quantum approximate optimization algorithm (QAOA), the current and traditional workhorse of quantum heuristic algorithms. 

Optimization problems are common in industry in contexts such as route planning, scheduling, cost optimization and logistics. However, as the number of variables increases and optimization problems grow larger and more complex, finding satisfactory solutions using classical algorithms becomes increasingly difficult. 

Recent research suggests that certain quantum algorithms might be capable of solving combinatorial optimization problems better than classical algorithms. The realization of such quantum algorithms can therefore potentially increase the efficiency of industrial processes. 

However, the effectiveness of these algorithms on near-term quantum devices and even on future generations of more capable quantum computers presents a technical challenge: quantum resources will need to be reduced as much as possible in order to protect the quantum algorithm from the unavoidable effects of quantum noise.

Sebastian Leontica and Dr. David Amaro, a senior research scientist at Quantinuum, explain their advances in a new paper, “Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits” published on arXiv. This is one of several papers published at the launch of Quantinuum’s H2, that highlight the unparalleled power of the newest generation of the H-Series, Powered by Honeywell. 

“We should strive to use as few quantum resources as possible no matter how good a quantum computer we are operating on, which means using the smallest possible number of qubits that fit within the problem size and a circuit that is as shallow as possible,” Dr. Amaro said. “Our algorithm uses the fewest possible resources and still achieves good performance.”

The researchers use a parameterized instantaneous quantum polynomial (IQP) circuit of the same depth as the 1-layer QAOA to incorporate corrections that would otherwise require multiple layers. Another differentiating feature of the algorithm is that the parameters in the IQP circuit can be efficiently trained on a classical computer, avoiding some training issues of other algorithms like QAOA. Critically, the circuit takes full advantage of, and benefits from features available on Quantinuum’s devices, including parameterized two-qubit gates, all-to-all connectivity, and high-fidelity operations. 

“Our numerical simulations and experiments on the new H2 quantum computer at small scale indicate that this heuristic algorithm, compared to 1-layer QAOA, is expected to amplify the probability of sampling good or even optimal solutions of large optimization problems,” Dr. Amaro said. “We now want to understand how the solution quality and runtime of our algorithm compares to the best classical algorithms.”

This algorithm will be useful for current quantum computers as well as larger machines farther along the Quantinuum hardware roadmap. 

How the Experiment Worked

The goal of this project was to provide a quantum heuristic algorithm for combinatorial optimization that returns better solutions for optimization problems and uses fewer quantum resources than state of the art quantum heuristics. The researchers used a fully connected parameterized IQP, warm-started from 1-layer QAOA. For a problem with n binary variables the circuit contained up to n(n-1)/2 two-qubit gates and the researchers employed only 2^0.32n shots. 

The algorithm showed improved performance on the Sherrington-Kirkpatrick (SK) optimization problem compared to the 1-layer QAOA. Numerical simulations showed an average speed up of 2^0.31n compared to 2^0.5n when looking for the optimal solution. 

Experimental results on our new H2 quantum computer and emulator confirmed that the new optimization algorithm outperforms 1-layer QAOA and reliably solves complex optimization problems. The optimal solution was found for 136 out of 312 instances, four of which were for the maximum size of 32 qubits. A 30-qubit instance was solved optimally on the H2 device, which means, remarkably, that at least one of the 776 shots measured after performing 432 two-qubit gates corresponds to the unique optimal solution in the huge set of 2³⁰ > 10⁹ candidate solutions. 

These results indicate that the algorithm, in combination with H2 hardware, is capable of solving hard optimization problems using minimal quantum resources in the presence of real hardware noise.

Quantinuum researchers expect that these promising results at small scale will encourage the further study of new quantum heuristic algorithms at the relevant scale for real-world optimization problems, which requires a better understanding of their performance under realistic conditions.

Speedup of IQP over QAOA

Numerical simulations of 256 SK random instances for each problem size from 4 to 29 qubits. Graph A shows the probability of sampling the optimal solution in the IQP circuit, for which the average is 2^-0.31n. Graph B shows the enhancement factor compared to 1-layer QAOA, for which the average is 2^0.23n. These results indicate that Quantinuum’s algorithm has significantly better runtime than 1-layer QAOA.

When thinking about changes in phases of matter, the first images that come to mind might be ice melting or water boiling. The critical point in these processes is located at the boundary between the two phases – the transition from solid to liquid or from liquid to gas. 

Phase transitions like these get right to the heart of how large material systems behave and are at the frontier of research in condensed matter physics for their ability to provide insights into emergent phenomena like magnetism and topological order. In classical systems, phase transitions are generally driven by thermal fluctuations and occur at finite temperature. On the contrary, quantum systems can exhibit phase transitions even at zero temperatures; the residual fluctuations that control such phase transitions at zero temperature are due to entanglement and are entirely quantum in origin.  

Quantinuum researchers recently used the H1-1 quantum computer to computationally model a group of highly correlated quantum particles at a quantum critical point — on the border of a transition between a paramagnetic state (a state of magnetism characterized by a weak attraction) to a ferromagnetic one (characterized by a strong attraction).

Simulating such a transition on a classical computer is possible using tensor network methods, though it is difficult. However, generalizations of such physics to more complicated systems can pose serious problems to classical tensor network techniques, even when deployed on the most powerful supercomputers.  On a quantum computer, on the other hand, such generalizations will likely only require modest increases in the number and quality of available qubits.

In a technical paper submitted to the arXiv, Probing critical states of matter on a digital quantum computer, the Quantinuum team demonstrated how the powerful components and high fidelity of the H-Series digital quantum computers could be harnessed to tackle a 128-site condensed matter physics problem, combining a quantum tensor network method with qubit reuse to make highly productive use of the 20-qubit H1-1 quantum computer.

Reza Haghshenas, Senior Advanced Physicist, and the lead author the paper said, “This is the kind of problem that appeals to condensed-matter physicists working with quantum computers, who are looking forward to revealing exotic aspects of strongly correlated systems that are still unknown to the classical realm. Digital quantum computers have the potential to become a versatile tool for working scientists, particularly in fields like condensed matter and particle physics, and may open entirely new directions in fundamental research.”

The role of quantum tensor networks

Tensor networks are mathematical frameworks whose structure enables them to represent and manipulate quantum states in an efficient manner. Originally associated with the mathematics of quantum mechanics, tensor network methods now crop up in many places, from machine learning to natural language processing, or indeed any model with a large number of interacting, high-dimensional mathematical objects. 

The Quantinuum team described using a tensor network method--the multi-scale entanglement renormalization ansatz (MERA)--to produce accurate estimates for the decay of ferromagnetic correlations and the ground state energy of the system. MERA is particularly well-suited to studying scale invariant quantum states, such as ground states at continuous quantum phase transitions, where each layer in the mathematical model captures entanglement at different scales of distance. 

“By calculating the critical state properties with MERA on a digital quantum computer like the H-Series, we have shown that research teams can program the connectivity and system interactions into the problem,” said Dave Hayes, Lead of the U.S. quantum theory team at Quantinuum and one of the paper’s authors. “So, it can, in principle, go out and simulate any system that you can dream of.”

Simulating a highly entangled quantum spin model

In this experiment, the researchers wanted to accurately calculate the ground state of the quantum system in its critical state. This quantum system is composed of many tiny quantum magnets interacting with one another and pointing in different directions, known as a quantum spin model. In the paramagnetic phase, tiny, individual magnets in the material are randomly oriented, and only correlated with each other over small length-scales. In the ferromagnetic phase, these individual atomic magnetic moments align spontaneously over macroscopic length scales due to strong magnetic interactions. 

In the computational model, the quantum magnets were initially arranged in one dimension, along a line. To describe the critical point in this quantum magnetism problem, particles in the line needed to be entangled with one another in a complex way, making this as a very challenging problem for a classical computer to solve in high dimensional and non-equilibrium systems. 

“That's as hard as it gets for these systems,” Dave explained. “So that's where we want to look for quantum advantage – because we want the problem to be as hard as possible on the classical computer, and then have a quantum computer solve it.”

To improve the results, the team used two error mitigation techniques, symmetry-based error heralding, which is made possible by the MERA structure, and zero-noise extrapolation, a method originally developed by researchers at IBM. The first involved enforcing local symmetry in the model so that errors affecting the symmetry of the state could be detected. The second strategy, zero-noise extrapolation, involves adding noise to the qubits to measure the impact it has, and then using those results to extrapolate the results that would be expected under conditions with less noise than was present in the experiment.

Future applications

The Quantinuum team describes this sort of problem as a stepping-stone, which allows the researchers to explore quantum tensor network methods on today’s devices and compare them either to simulations or analytical results produced using classical computers. It is a chance to learn how to tackle a problem really well before quantum computers scale up in the future and begin to offer solutions that are not possible to achieve on classical computers. 

“Potentially, our biggest applications over the next couple of years will include studying solid-state systems, physics systems, many-body systems, and modeling them,” said Jenni Strabley, Senior Director of Offering Management at Quantinuum.

The team now looks forward to future work, exploring more complex MERA generalizations to compute the states of 2D and 3D many-body and condensed matter systems on a digital quantum computer – quantum states that are much more difficult to calculate classically. 

The H-Series allows researchers to simulate a much broader range of systems than analog devices as well as to incorporate quantum error mitigation strategies, as demonstrated in the experiment. Plus, Quantinuum’s System Model H2 quantum computer, which was launched earlier this year, should scale this type of simulation beyond what is possible using classical computers.