Random circuit sampling
Algorithms and benchmarks / Sampling and quantum advantage tests
Runs randomly chosen circuits and samples their output bit strings, a task designed to be hard for classical computers; it was used for the first claims of quantum advantage and is also a benchmark (cross-entropy benchmarking).
- Era
- Noisy intermediate-scale (NISQ)
- Problem class
- Sampling and quantum advantage tests
- Speedup
- Believed exponential for exact simulation; the achievable classical cost depends on fidelity and keeps falling with new tensor-network methods.
How it works
Layers of random single-qubit gates and fixed two-qubit gates are applied; the measured bit strings are compared with ideal probabilities computed classically for small or simplified cases, giving a fidelity estimate.
Typical use cases
- Demonstrating and benchmarking quantum processors.
Related pages
Resource estimates
No resource estimate with stated assumptions was verified for this family in this release.
Demonstrations
- 2024: A 67-qubit experiment with 32 cycles, which the authors place beyond the capabilities of existing classical supercomputers even accounting for noise. (A. Morvan et al. 2024)
- 2022: A classical method sampled one million bit strings from the 53-qubit, 20-cycle Sycamore circuits at a fidelity of about 0.0037 in about 15 hours on 512 GPUs. (F. Pan et al. 2022)
Hardware platforms that fit
- Superconducting qubits: Run on the 53-qubit Sycamore superconducting processor (Arute et al. 2019; Pan et al. 2022) and with 67 qubits (Morvan et al. 2024).
What you need to run it
- Classical simulation
- Up to about 48 qubits with state vectors on the largest supercomputers (De Raedt et al. 2019); tensor networks reach further at low fidelity, at large GPU cost (Pan et al. 2022).
- Noisy hardware (NISQ)
- Fifty or more qubits with high-fidelity two-qubit gates on a 2D grid; the boundary moves as classical methods improve.
- Fault-tolerant machine
- Not applicable for this family.
- Annealer or analogue simulator
- Not applicable for this family.
Calculate the memory of a simulation
Where to run it in Europe
Superconducting qubits
- VLQ (Czechia; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones VLQ
- Euro-Q-Exa (Germany; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Euro-Q-Exa
- EuroQCS-Spain (Spain; Inaugurated, per the EuroHPC JU): Superconducting annealing; analogue quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones EuroQCS-Spain
- Quantum Inspire (Netherlands; In operation, per the source): Online platform with superconducting transmon QPUs, a neutral-atom emulator and simulators; a Spin-2+ electron spin QPU is listed as archived. Access: Quantum Inspire registration.
- LRZ Quantum Integration Centre (QIC) (Germany; In operation, per the source): Superconducting systems from IQM (54 qubits, up to 150 in future), a 20-qubit AQT ion-trap system, and a neutral-atom system being developed by planqc (MAQCS project). Access: LRZ quantum computing consulting.
- Finnish Quantum-Computing Infrastructure (FiQCI) (Finland; In operation, per the source): Hybrid HPC and quantum computing platform: VTT Q50 (53 qubits) and Aalto Q20 (20 qubits), superconducting systems made by IQM, used through the LUMI supercomputer environment. Access: FiQCI calls for academic projects.
- Quantum Spain quantum computer at BSC-CNS (Spain; In operation, per the source): Superconducting; digital quantum computer with a 35-qubit processor, integrated into the MareNostrum 5 supercomputer. Access: Spanish Supercomputing Network (RES) quantum access. Deployment milestones Quantum Spain quantum computer at BSC-CNS
The full infrastructure catalogue · The infrastructure deployment tracker
Software
European tools in the software directory
Other open-source frameworks
- qsim (Google Quantum AI (United States); non-European)
- Cirq (Google Quantum AI (United States); non-European)
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- Advantage claims have been narrowed or overturned by better classical algorithms (Pan et al. 2022).
- The output has no direct application.
In the Quantum Algorithm Zoo
No matching Zoo entry was found on 23 October 2026; the Zoo lists algorithms with a proven or conjectured speedup, not this family.
Index: the Quantum Algorithm Zoo by Stephen P. Jordan, last updated 2026-09-10, checked 2026-10-23. The portal links to it and copies no description from it. Browse the full Quantum Algorithm Zoo (external site)
Named in European procurements
None of the procurement documents read for this release names it.
Sources
- S. Boixo et al. (2018). Characterizing Quantum Supremacy in Near-Term Devices. Nature Physics 14, 595 (2018); arXiv:1608.00263. Read: abstract page, retrieved 2026-10-23.
- F. Arute et al. (2019). Quantum supremacy using a programmable superconducting processor. Nature 574, 505 (2019); supplementary information on arXiv:1910.11333. Read: arXiv page of the supplementary information, retrieved 2026-10-23.
- A. Morvan et al. (2024). Phase transition in Random Circuit Sampling. Nature 634, 328 (2024); arXiv:2304.11119. Read: abstract page, retrieved 2026-10-23.
- F. Pan, K. Chen, P. Zhang (2022). Solving the sampling problem of the Sycamore quantum circuits. Phys. Rev. Lett. 129, 090502 (2022); arXiv:2111.03011. Read: abstract page, retrieved 2026-10-23.
- H. De Raedt et al. (2019). Massively parallel quantum computer simulator, eleven years later. Computer Physics Communications (2019), DOI 10.1016/j.cpc.2018.11.005; arXiv:1805.04708. Read: abstract page, retrieved 2026-10-23.