On the impact of quantum computing technology on future developments in high-performance scientific computing

1.1 The past: Digital computer revolution

• The digital-computing story runs from early specialized machines to microprocessors that made software-programmable computers available at low cost.The Programma 101 cost $3,200 in 1964; later microprocessors helped bring computer systems-on-a-chip to $20 per device.Source: §1.1 · pp. 2–3

1.2 The present: Quantum computer revolution

• Quantum computing attracts major investment, but industrial interest depends on practical benefits outweighing the costs of hardware, infrastructure, algorithms, and applications.The article also notes its potential to break public-key cryptography, including RSA, through Shor’s algorithm [61].Source: §1 · p. 2, §1.2 · p. 3

1.3 The possible future: Quantum-accelerated computing as a service

• Near-absolute-zero operating temperatures make cloud service a promising access model, while raising questions about the reliability of results sent over potentially decryptable Internet connections.Source: §1.3 · p. 3
• The article sketches large-scale quantum computers as software-programmable devices in a hybrid computing landscape, with quantum-accelerated computing offered as a cloud service.It focuses on developing, simulating, testing, and analyzing device-independent quantum algorithms, while leaving hardware and manual algorithm realization aside.Source: §1.3 · p. 4

2 Scientific Computing

• Scientific computing uses advanced simulations to analyze complex problems across disciplines, from physics and medicine to engineering and the social sciences.The section describes it as a third pillar of scientific research alongside experimental and theoretical science.Source: §2 · p. 4
• The North Sea water-level example proceeds from physical equations through simplified and numerical models to computation, with results checked against measurements.Source: §2 · p. 5
• A million-fold increase in computer power and a million-fold increase in algorithmic efficiency have enabled simulations of more complex phenomena, but approximation results should not be treated as truth.For complicated, new applications, the authors urge care about assumptions, guessed coefficients, approximation and rounding errors, and the absence of realistic error estimates.Source: §2 · p. 5

2.1 Scientific computing from a hardware perspective

• After CPU clock speeds reached the 4 GHz barrier around 2005, HPC shifted from pursuing single-core performance toward parallel systems using multicore CPUs and accelerators.The host offloads computationally expensive, parallelizable code to accelerator devices while coordinating their work.Source: §2.1 · p. 6

ACCELERATORS/CO-PROCESSORS

• Faster chips do not remove the memory wall: moving data between memory layers, compute units, hosts, and accelerators has become a major bottleneck in data-intensive applications.Source: ACCELERATORS/CO-PROCESSORS · p. 7
• FPGAs support dataflow-oriented spatial computing, while computing-in-memory aims to eliminate the central system bus by placing processing units beside storage cells.Source: ACCELERATORS/CO-PROCESSORS · p. 7
• The review’s hardware findings point to parallelism and strategies for overcoming the memory wall, alongside more heterogeneous, massively parallel HPC systems with cloud-enabled end-user access.Source: ACCELERATORS/CO-PROCESSORS · p. 8

2.2 Scientific computing from a software perspective

• Porting scientific codes across parallel architectures can be difficult and costly, with personnel costs sometimes exceeding hardware acquisition costs by orders of magnitude.Source: §2.2 · p. 8
• Device- and vendor-independent standards and middleware seek to support reusable code, but developers still need to respect specific hardware characteristics for good performance.The review also describes CUDA’s optimized libraries and multi-platform accelerator libraries as routes to ready-to-use functionality.Source: §2.2 · pp. 8–9

3 Challenges and strategies for future computing hardware

• The November 2016 Sunway TaihuLight achieved 93 petaflops on Linpack, 74% of its 125.4-petaflop peak, while consuming 15 megawatts.Source: §3 · p. 9
• Scaling conventional technology to exascale could require more than a gigawatt, motivating a reduction in power requirements by at least a factor of 100.Source: §3 · p. 9
• An exascale system with about one billion processing elements could face mean time to interrupts of 35–39 minutes, while current petaflop systems already use only a fraction of theoretical peak performance on cited simulations.Source: §3 · p. 10
• Data movement between processors, memory, and nodes is described as a critical exascale barrier; photonics could reduce interconnect energy consumption by a factor of 100 over electronic technology.CEA and RIKEN are pursuing energy-efficient ARM-based systems, while the U.S. DOE planned two exascale machines by 2023, likely using accelerators.Source: §3 · p. 10
• Quantum parallelism is presented as having potential to contribute to a long-term revolution in scientific computing.Source: §3 · p. 10

4.1 Qubits and quantum circuits

• Reading and writing n-length quantum inputs and outputs imposes a linear-time floor, even if processing in the quantum register takes O(log n).Without global encoding standards, programmers choose encodings; some problems may need reformulation to seek a derived scalar rather than outputting an n-entry solution.Source: §4.1 · p. 11

4.2 Quantum parallelism and no-cloning principle

• An n-qubit register can calculate all 2^n input-state combinations in parallel, but a single run’s final measurement selects randomly, so efficiency gains require techniques that make the desired output highly likely.Source: §4.2 · pp. 11–12
• No-cloning prevents copying quantum registers, so classical domain decomposition that exchanges data between subproblems cannot transfer directly to quantum computers.The section concludes that classical methods relying on concepts forbidden by quantum no-go theorems may require redesign.Source: §4.2 · p. 12

4.3 Reversible computing

• Quantum gates are reversible, and reversible computation could reduce energy dissipation by avoiding bit erasure during computation.Register initialization and storing the computed answer would still require energy, and reversible computing is not yet practical.Source: §4.3 · p. 12

4.4 Application of reversible computing

• If quantum computers make reversible computing practical, reverse-mode debugging and algorithmic differentiation could benefit by reducing the need to store intermediate results.The section identifies algorithmic differentiation as a way to quantify output sensitivity to input changes, including in adjoint-based shape optimization.Source: §4.4 · p. 13
• The section’s conclusions stress that quantum algorithms need programmer-defined input/output encodings and should be designed from scratch rather than simulate classical algorithms.It characterizes their development as relying on linear algebra, stochastics, and complexity theory.Source: §4.4 · p. 13

5.1 Quantum-accelerated linear solvers

• For sparse systems with small κ, quantum estimation of x⊤Mx takes time polynomial in logN, d, and κ versus O(N√κ) classically; writing out x still takes O(N).The comparison applies to a scalar quantity of interest, not retrieval of the complete solution vector.Source: §5.1 · p. 14

5.2 Quantum-accelerated design optimization

• For a positive-definite quadratic approximation near a minimum, quantum optimization uses O(d) queries versus the classical lower bound O(d2); quantum annealing may also address local minima.The query count measures calls to the cost functional, whose evaluations often require numerical simulations.Source: §5.2 · p. 14

5.3 Quantum-accelerated integration and summation

• Quantum integration algorithms offer quadratic speedup over classical ones, with potential for high-dimensional integrals, although research activity in this area has lost impetus.The authors suggest practical quantum computers could renew interest in quantum summation and integration as building blocks for other algorithms.Source: §5.3 · p. 15

5.4 Applications of quantum-accelerated linear solvers

• A preconditioned quantum FEM for electromagnetic-scattering PDEs has polynomial speedup; related linear- and nonlinear-system applications include biology, neuroscience, and network models.In the FEM application, the matrix is constructed algorithmically by numerical integration.Source: §5.4 · p. 15

5.5 Challenges and potential of quantum algorithms

• Meaningful results for the described applications may require thousands or millions of qubits, with up to 90% of quantum resources needed for error correction.The authors suggest efficient data storage and assessing qubit needs at engineering-relevant accuracy as responses to hardware constraints.Source: §5.5 · p. 15
• Quantum error correction remains difficult: repetition codes are ruled out by no-cloning, and measuring intermediate states can destroy superposition needed for continued computation.The passage identifies specialized techniques such as surface codes and notes that invariant checking is harder on quantum computers.Source: §5.5 · p. 16
• Both classical and quantum computing can return only one possible answer rather than an approximate solution, motivating uncertainty quantification of simulation results by default.The proposed ideal is to use increased computing power to quantify error ranges for the same problems, rather than only increasing complexity or size.Source: §5.5 · p. 16
• Formal complexity may not predict practical time-to-solution: even theoretically sub-optimal quantum algorithms could be worthwhile if they offer practical benefits.For HHL, writing out the solution vector would give linear complexity, while overall quantum-versus-classical time-to-solution could still be smaller or larger.Source: §5.5 · p. 16

6 Impact of quantum computing on scientific computing

• Quantum computers are difficult and expensive to build and maintain, requiring special facilities and expertise that may limit access to a small number of institutes.The authors warn this could give those institutes and countries a decisive lead in scientific computing; cloud services are proposed to mitigate the access danger.Source: §6 · p. 17
• Model predictions are meaningful only when their assumptions hold and input data are reliable; quantum-computing errors further complicate interpretation, motivating robust error estimates.The authors also call for new validation methods and argue that results should include robust error estimates.Source: §6 · p. 17
• Quantum computing may increase reliance on complex simulations, but more model parameters do not improve accuracy without reliable measurement data.The authors caution against blind trust in simulation results when assumptions are unmet or input data are unreliable.Source: §6 · p. 17
• Radically different programming models require teaching changes, with greater attention to programming potentially strengthening classical HPC research and hardware-aware algorithm development.The authors say today's supercomputers are fully exploitable by only a small fraction of students and researchers.Source: §6 · p. 17
• Even if quantum computing shifts work toward simulation and away from experiments, carefully designed experiments will remain necessary to validate quantum-algorithm results.Source: §6 · p. 17

7.1 Green aircraft

• Quantum algorithms are being developed to simulate airflow over aircraft wings; the authors project weeks of quantum-computer time versus more than seven years classically.The faster simulations could enhance aircraft modeling and optimization, supporting robust, efficient aircraft with lower noise and CO2 emissions.Source: §7.1 · p. 18

7.2 Optimization in space applications

• D-Wave Two quantum annealing has been used to optimize structures and spacecraft payload packing, while researchers investigate numerical noise and hybrid quantum-classical methods.Other research directions include quantum artificial intelligence, problem decomposition, and hardware embedding.Source: §7.2 · p. 18

7.3 Secure communication technology

• Quantum key distribution is presented as a secure key-exchange approach for a future when quantum computers can break current encryption; DLR experiments transmitted keys from aircraft to ground stations.The experiments show encryption technology can be used with fast-moving objects, and existing optical communications systems can transmit the information.Source: §7.3 · pp. 18–19

7.4 Flood predictions

• A quantum simulator encodes fluid-transport phenomena in a lattice kinetic formalism, implementing lattice Boltzmann streaming and collision with controlled quantum operations.The approach is proposed for controlled platforms such as ion-trap computers or circuit quantum electrodynamics processors, with possible applications including flooding protection.Source: §7.4 · p. 19

7.5 Medicine

• Quantum computing may model molecular interactions at atomic scale, potentially supporting investigation of drug interactions across the human genome's 20,000+ proteins.The authors suggest this could help reduce the time to bring newly designed drugs to patients and inform future drug and cancer-cure design.Source: §7.5 · p. 19

8 Conclusion

• Knowledge transfer could help quantum researchers draw on classical computing's long experience bringing architectures to end users, while classical chip makers may benefit from quantum principles such as reversible computing.The conclusion frames this exchange against classical computing's memory, energy, and instruction-level parallelism walls.Source: §8 · p. 19
• Quantum hardware integrated into conventional HPC systems as task-specific accelerators is presented as the condition under which quantum-enhanced scientific computing has the highest chance of becoming game-changing.The authors say quantum-accelerated cloud services are needed to bring practical computers to industry and academia stakeholders.Source: §8 · p. 20

A Complexity analysis of algorithms

• Reading an n-entry vector requires visiting all n positions, so its read-in complexity remains linear even if two entries are read per operation.The example distinguishes asymptotic complexity from wall-clock time, which could halve in that implementation.Source: A Complexity analysis of algorithms · p. 20

A.1 Bachmann-Landau notation

• Big O notation compares asymptotic growth: f(n) = O(g(n)) when |f(n)| is bounded by a constant multiple of |g(n)| for all sufficiently large n.The appendix illustrates that different constant multiples can still share the same asymptotic class.Source: §A.1 · p. 20

A.2 Polynomial time complexity

• Algorithms with time O(n^k) for constant k are classified as polynomial time; Gaussian elimination solves Ax = b in O(n^3).The appendix gives approximately 2/3 n^3 arithmetic operations for a practical Gaussian-elimination implementation.Source: §A.2 · p. 20

A.3 Exponential time complexity

• Brute-force Sudoku solving is an exponential-time backtracking search that may explore 6.67×10^21 admissible grids in the worst case.Backtracking fills empty positions sequentially and returns to earlier guesses when it reaches a dead end.Source: §A.3 · p. 21

A.4 Sub-exponential time complexity

• Sub-exponential algorithms solve a problem of size n in O(2^(n^ε)) time for every ε > 0.The appendix characterizes this with ε-dependent constants and thresholds bounding the running time for all sufficiently large n.Source: §A.4 · p. 21

A.5 A final word on algorithmic complexity in practice

• For problem sizes near 50, the appendix argues practical complexity analysis may be more useful than asymptotic comparisons alone.In its n = 6 example, Strassen's and Coppersmith-Winograd-based approaches would need hidden constants no larger than 0.9 and 2, respectively, to compete with Gaussian elimination, making both impractical at that size.Source: §A.5 · p. 21

• Qubits can occupy superpositions of zero and one, but standard-basis measurement returns one classical value and destroys that superposition.Source: B Principles of quantum computing · pp. 21–22
• Quantum algorithms use unitary transformations as gates, and the Hadamard gate maps standard basis states into superpositions.Source: B Principles of quantum computing · p. 22
• An n-qubit register holds a superposition of 2^n classical states, while entanglement lets measuring one of two separated qubits reveal the other's state.Source: §B.2 · p. 22, §B.3 · pp. 22–23
• Quantum gates process all 2^n input values simultaneously, a property called quantum parallelism that underlies the expected exponential performance boost.Source: §B.2 · p. 22
• Because a single probabilistic run may yield a mostly random outcome, algorithms need repeated runs and mechanisms to amplify the probability of measuring the desired result.Source: §B.2 · p. 22
• The no-cloning principle forbids copying an arbitrary unknown quantum state, and other no-go theorems complicate adapting classical algorithms to quantum computers.Source: §B.3 · p. 23