From black-hole evaporation to neutron-star interiors, extreme environments and complex dynamics often outpace even the most powerful supercomputers. Enrique Rico Ortega and Sofia Vallecorsa explain how quantum computing will change that.
In 1982 Richard Feynman posed a question that challenged computational limits: can a classical computer simulate a quantum system? His answer: not efficiently. The complexity of the computation increases rapidly, rendering realistic simulations intractable. To understand why, consider the basic units of classical and quantum information.
A classical bit can exist in one of two states: |0> or |1>. A quantum bit, or qubit, exists in a superposition α|0> + β|1>, where α and β are complex amplitudes with real and imaginary parts. This superposition is the core feature that distinguishes quantum bits and classical bits. While a classical bit is either |0> or |1>, a quantum bit can be a blend of both at once. This is what gives quantum computers their immense parallelism – and also their fragility.
The difference becomes profound with scale. Two classical bits have four possible states, and are always in just one of them at a time. Two qubits simultaneously encode a complex-valued superposition of all four states.
Resources scale exponentially. N classical bits encode N boolean values, but N qubits encode 2N complex amplitudes. Simulating 50 qubits with double-precision real numbers for each part of the complex amplitudes would require more than a petabyte of memory, beyond the reach of even the largest supercomputers.
Direct mimicry
Feynman proposed a different approach to quantum simulation. If a classical computer struggles, why not use one quantum system to emulate the behaviour of another? This was the conceptual birth of the quantum simulator: a device that harnesses quantum mechanics to solve quantum problems. For decades, this visionary idea remained in the realm of theory, awaiting the technological breakthroughs that are now rapidly bringing it to life. Today, progress in quantum hardware is driving two main approaches: analog and digital quantum simulation, in direct analogy to the history of classical computing.

In analog quantum simulators, the physical parameters of the simulator directly correspond to the parameters of the quantum system being studied. Think of it like a wind tunnel for aeroplanes: you are not calculating air resistance on a computer but directly observing how air flows over a model.
A striking example of an analog quantum simulator traps excited Rydberg atoms in precise configurations using highly focused laser beams known as “optical tweezers”. Rydberg atoms have one electron excited to an energy level far from the nucleus, giving them an exaggerated electric dipole moment that leads to tunable long-range dipole–dipole interactions – an ideal setup for simulating particle interactions in quantum field theories (see “Optical tweezers” figure).
The positions of the Rydberg atoms discretise the space inhabited by the quantum fields being modelled. At each point in the lattice, the local quantum degrees of freedom of the simulated fields are embodied by the internal states of the atoms. Dipole–dipole interactions simulate the dynamics of the quantum fields. This technique has been used to observe phenomena such as string breaking, where the force between particles pulls so strongly that the vacuum spontaneously creates new particle–antiparticle pairs. Such quantum simulations model processes that are notoriously difficult to calculate from first principles using classical computers (see “A philosophical dimension” panel).
Universal quantum computation
Digital quantum simulators operate much like classical digital computers, though using quantum rather than classical logic gates. While classical logic manipulates classical bits, quantum logic manipulates qubits. Because quantum logic gates obey the Schrödinger equation, they preserve information and are reversible, whereas most classical gates, such as “AND” and “OR”, are irreversible. Many quantum gates have no classical equivalent, because they manipulate phase, superposition or entanglement – a uniquely quantum phenomenon in which two or more qubits share a combined state. In an entangled system, the state of each qubit cannot be described independently of the others, even if they are far apart: the global description of the quantum state is more than the combination of the local information at every site.
A philosophical dimension
The discretisation of space by quantum simulators echoes the rise of lattice QCD in the 1970s and 1980s. Confronted with the non-perturbative nature of the strong interaction, Kenneth Wilson introduced a method to discretise spacetime, enabling numerical solutions to quantum chromodynamics beyond the reach of perturbation theory. Simulations on classical supercomputers have since deepened our understanding of quark confinement and hadron masses, catalysed advances in high-performance computing, and inspired international collaborations. It has become an indispensable tool in particle physics (see “Fermilab’s final word on muon g-2”).
In classical lattice QCD, the discretisation of spacetime is just a computational trick – a means to an end. But in quantum simulators this discretisation becomes physical. The simulator is a quantum system governed by the same fundamental laws as the target theory.
This raises a philosophical question: are we merely modelling the target theory or are we, in a limited but genuine sense, realising it? If an array of neutral atoms faithfully mimics the dynamical behaviour of a specific gauge theory, is it “just” a simulation, or is it another manifestation of that theory’s fundamental truth? Feynman’s original proposal was, in a sense, about using nature to compute itself. Quantum simulators bring this abstract notion into concrete laboratory reality.
By applying sequences of quantum logic gates, a digital quantum computer can model the time evolution of any target quantum system. This makes them flexible and scalable in pursuit of universal quantum computation – logic able to run any algorithm allowed by the laws of quantum mechanics, given enough qubits and sufficient time. Universal quantum computing requires only a small subset of the many quantum logic gates that can be conceived, for example Hadamard, T and CNOT. The Hadamard gate creates a superposition: |0> → (|0> + |1>) / √2. The T gate applies a 45° phase rotation: |1> → eiπ/4|1>. And the CNOT gate entangles qubits by flipping a target qubit if a control qubit is |1>. These three suffice to prepare any quantum state from a trivial reference state: |ψ> = U1 U2 U3 … UN |0000…000>.

To bring frontier physics problems within the scope of current quantum computing resources, the distinction between analog and digital quantum simulations is often blurred. The complexity of simulations can be reduced by combining digital gate sequences with analog quantum hardware that aligns with the interaction patterns relevant to the target problem. This is feasible as quantum logic gates usually rely on native interactions similar to those used in analog simulations. Rydberg atoms are a common choice. Alongside them, two other technologies are becoming increasingly dominant in digital quantum simulation: trapped ions and superconducting qubit arrays.
Trapped ions offer the greatest control. Individual charged ions can be suspended in free space using electromagnetic fields. Lasers manipulate their quantum states, inducing interactions between them. Trapped-ion systems are renowned for their high fidelity (meaning operations are accurate) and long coherence times (meaning they maintain their quantum properties for longer), making them excellent candidates for quantum simulation (see “Trapped ions” figure).
Superconducting qubit arrays promise the greatest scalability. These tiny superconducting circuit materials act as qubits when cooled to extremely low temperatures and manipulated with microwave pulses. This technology is at the forefront of efforts to build quantum simulators and digital quantum computers for universal quantum computation (see “Superconducting qubits” figure).
The noisy intermediate-scale quantum era
Despite rapid progress, these technologies are at an early stage of development and face three main limitations.
The first problem is that qubits are fragile. Interactions with their environment quickly compromise their superposition and entanglement, making computations unreliable. Preventing “decoherence” is one of the main engineering challenges in quantum technology today.
The second challenge is that quantum logic gates have low fidelity. Over a long sequence of operations, errors accumulate, corrupting the result.
Finally, quantum simulators currently have a very limited number of qubits – typically only a few hundred. This is far fewer than what is needed for high-energy physics (HEP) problems.

This situation is known as the noisy “intermediate-scale” quantum era: we are no longer doing proof-of-principle experiments with a few tens of qubits, but neither can we control thousands of them. These limitations mean that current digital simulations are often restricted to “toy” models, such as QED simplified to have just one spatial and one time dimension. Even with these constraints, small-scale devices have successfully reproduced non-perturbative aspects of the theories in real time and have verified the preservation of fundamental physical principles such as gauge invariance, the symmetry that underpins the fundamental forces of the Standard Model.
Quantum simulators may chart a similar path to classical lattice QCD, but with even greater reach. Lattice QCD struggles with real-time evolution and finite-density physics due to the infamous “sign problem”, wherein quantum interference between classically computed amplitudes causes exponentially worsening signal-to-noise ratios. This renders some of the most interesting problems unsolvable on classical machines.
Quantum simulators do not suffer from the sign problem because they evolve naturally in real-time, just like the physical systems they emulate. This promises to open new frontiers such as the simulation of early-universe dynamics, black-hole evaporation and the dense interiors of neutron stars.
Quantum simulators will powerfully augment traditional theoretical and computational methods, offering profound insights when Feynman diagrams become intractable, when dealing with real-time dynamics and when the sign problem renders classical simulations exponentially difficult. Just as the lattice revolution required decades of concerted community effort to reach its full potential, so will the quantum revolution, but the fruits will again transform the field. As the aphorism attributed to Mark Twain goes: history never repeats itself, but it often rhymes.
Quantum information
One of the most exciting and productive developments in recent years is the unexpected, yet profound, convergence between HEP and quantum information science (QIS). For a long time these fields evolved independently. HEP explored the universe’s smallest constituents and grandest structures, while QIS focused on harnessing quantum mechanics for computation and communication. One of the pioneers in studying the interface between these fields was John Bell, a theoretical physicist at CERN.
Just as the lattice revolution needed decades of concerted community effort to reach its full potential, so will the quantum revolution
HEP and QIS are now deeply intertwined. As quantum simulators advance, there is a growing demand for theoretical tools that combine the rigour of quantum field theory with the concepts of QIS. For example, tensor networks were developed in condensed-matter physics to represent highly entangled quantum states, and have now found surprising applications in lattice gauge theories and “holographic dualities” between quantum gravity and quantum field theory. Another example is quantum error correction – a vital QIS technique to protect fragile quantum information from noise, and now a major focus for quantum simulation in HEP.
This cross-disciplinary synthesis is not just conceptual; it is becoming institutional. Initiatives like the US Department of Energy’s Quantum Information Science Enabled Discovery (QuantISED) programme, CERN’s Quantum Technology Initiative (QTI) and Europe’s Quantum Flagship are making substantial investments in collaborative research. Quantum algorithms will become indispensable for theoretical problems just as quantum sensors are becoming indispensable to experimental observation (see “Sensing at quantum limits”).
The result is the emergence of a new breed of scientist: one equally fluent in the fundamental equations of particle physics and the practicalities of quantum hardware. These “hybrid” scientists are building the theoretical and computational scaffolding for a future where quantum simulation is a standard, indispensable tool in HEP.
Further reading
M C Bañuls et al. 2020 Eur. Phys. J. D 74 165.
Y Alexeev et al. 2021 PRX Quantum 2 017001.
C W Bauer et al. 2023 PRX Quantum 4 027001.
A Di Meglio et al. 2024 PRX Quantum 5 037001.
T A Cochran et al. 2025 Nature 642 315.
D González-Cuadra et al. 2025 Nature 642 321.