arXiv:quant-ph/0110100 · Fortschritte der Physik

Error Sensitivity of a Quantum Simulator I: a First Example

G. Strini

Published Mar 1, 2002• 19 citations

Abstract

As the first useful Quantum Computers presumably will be quantum simulators, here the minimum number of qubits necessary for the solution of Schrödinger's equation in simple test problems is evaluated. From the present preliminary results it appears that it is possible to realize a useful quantum simulator with a register of only 10-15 qubits. The intrinsic sensitivity to some errors appears to be moderate without the need of error correcting methods. At present there is at least some indication that the amplitude errors are more dangerous than phase and decoherence errors. So corrections limited to amplitude errors may be very useful.

DOI: 10.1002/1521-3978(200203)50:2<171::aid-prop171>3.0.co;2-b

Related papers

Quantum simulation of the single-particle Schrödinger equation

Giuliano Benenti, G. Strini

The nature of a quantum computer is described in the concrete context of a quantum simulator of the single-particle Schrödinger equation. We show that a register of 6–10 qubits is sufficient to realize a useful quantum simulator capable of efficiently solving standard quantum mechanical problems.

arXiv:0709.1704American Journal of PhysicsJun 10, 200896 citations

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

Ying Li, Simon C. Benjamin

Quantum computers will need to be tolerant to errors introduced by noise, but current proposals estimate that the number of qubits required for error correction will be many orders of magnitude larger than the number needed for useful computation. A new proposal uses a classical-quantum hybrid scheme to implement simple error-tolerant quantum processors with relatively few resources.

arXiv:1611.09301Physical Review XJun 29, 2017687 citations

Efficient fault-tolerant quantum computing

Andrew M. Steane

Abstract Quantum computing1—the processing of information according to the fundamental laws of physics—offers a means to solve efficiently a small but significant set of classically intractable problems. Quantum computers are based on the controlled manipulation of entangled quantum states, which are extremely sensitive to noise and imprecision; active correction of errors must therefore be implemented without causing loss of coherence. Quantum error-correction theory2, 3, 4, 5, 6, 7, 8, 9 has made great progress in this regard, by predicting error-correcting ‘codeword’ quantum states. But the coding is inefficient and requires many quantum bits10, 11, 12, which results in physically unwieldy fault-tolerant quantum circuits10, 11, 12, 13, 14, 15, 16, 17, 18. Here I report a general technique for circumventing the trade-off between the achieved noise tolerance and the scale-up in computer size that is required to realize the error correction. I adapt the recovery operation (the process by which noise is suppressed through error detection and correction) to simultaneously correct errors and perform a useful measurement that drives the computation. The result is that a quantum computer need be only an order of magnitude larger than the logic device contained within it. For example, the physical scale-up factor10, 11 required to factorize a thousand-digit number is reduced from 1, 500 to 22, while preserving the original tolerated gate error rate (10−5) and memory noise per bit (10−7). The difficulty of realizing a useful quantum computer is therefore significantly reduced.

Sep 18, 1998124 citations

5-qubit quantum error correction in a charge qubit quantum computer

Dave Touchette, Haleemur Ali, Michael Hilke

We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. The quantum register is a multi charge-qubit system in a semiconductor environment, where the main sources of noise are phase decoherence and relaxation. We evaluate the decay of the density matrix for this multi-qubit system and perform regular quantum error corrections. The performance of the error correction in this realistic system is found to yield an improvement of the fidelity. The fidelity can be maintained arbitrarily close to one by sufficiently increasing the frequency of error correction. This opens the door for arbitrarily long quantum computations.

arXiv:1010.3242Oct 15, 20103 citations

What Limits the Simulation of Quantum Computers?

Yiqing Zhou, E. Miles Stoudenmire, Xavier Waintal

An ultimate goal of quantum computing is to perform calculations beyond the reach of any classical computer.It is therefore imperative that useful quantum computers be very difficult to simulate classically, otherwise classical computers could be used for the applications envisioned for the quantum ones.Perfect quantum computers are unarguably exponentially difficult to simulate: the classical resources required grow exponentially with the number of qubits N or the depth D of the circuit.This difficulty has triggered recent experiments on deep, random circuits that aim to demonstrate that quantum devices may already perform tasks beyond the reach of classical computing.These real quantum computing devices, however, suffer from many sources of decoherence and imprecision which limit the degree of entanglement that can actually be reached to a fraction of its theoretical maximum.They are characterized by an exponentially decaying fidelity F ∼ ð1 -ϵÞ ND with an error rate ϵ per operation as small as ≈1% for current devices with several dozen qubits or even smaller for smaller devices.In this work, we provide new insight on the computing capabilities of real quantum computers by demonstrating that they can be simulated at a tiny fraction of the cost that would be needed for a perfect quantum computer.Our algorithms compress the representations of quantum wave functions using matrix product states, which are able to capture states with low to moderate entanglement very accurately.This compression introduces a finite error rate ϵ so that the algorithms closely mimic the behavior of real quantum computing devices.The computing time of our algorithm increases only linearly with N and D in sharp contrast with exact simulation algorithms.We illustrate our algorithms with simulations of random circuits for qubits connected in both one-and twodimensional lattices.We find that ϵ can be decreased at a polynomial cost in computing power down to a minimum error ϵ ∞ .Getting below ϵ ∞ requires computing resources that increase exponentially with ϵ ∞ =ϵ.For a two-dimensional array of N ¼ 54 qubits and a circuit with control-Z gates, error rates better than state-of-the-art devices can be obtained on a laptop in a few hours.For more complex gates such as a SWAP gate followed by a controlled rotation, the error rate increases by a factor 3 for similar computing time.Our results suggest that, despite the high fidelity reached by quantum devices, only a tiny fraction ð∼10 -8 Þ of the system Hilbert space is actually being exploited.

arXiv:2002.07730Physical Review XNov 23, 2020254 citations

Virheenvähennysmenetelmiä digitaalisen kvanttisimulaation näkökulmasta

Aino Suomi

Quantum technology is a rapidly growing field; in the near future, quantum computers may be able to solve computationally complex problems that currently cannot be realistically solved by a classical computer. Digital quantum simulation is one such potential applications. Simulating the behavior of quantum mechanical systems, such as molecules, with a quantum computer is possible in polynomial time. Running the same computation with a classical computer would take an amount of time exponentially scaling with the size of the problem. Being able to obtain error free results of such simulations on a quantum computer could make it possible to obtain more accurate information on, for example, the effects of drugs or the chemical properties of materials. However, at this point quantum computing is in the Noisy intermediate-scale quantum (NISQ) era. The technology in this current era is defined by sensitivity of systems to noise and a limited amount of computing power. Noise can be defined as any unwanted signal, which can cause errors in the calculation results. As of 2026, the size of quantum processors available is from 50 qubits to 1121 qubits. Due to the limited number of physical qubits available, it is not possible to achieve fault tolerance by programming data into error-corrected logical qubits. The use of error mitigation methods, which aim to minimize the impact of error in the computational results, is a promising option to error correction due to no lower limits for the QPU size. The thesis was to conducted as a literature review on the use of different methods to mitigate noise-induced error in the results of digital quantum simulation implented on NISQ-era quantum computers. The methods considered in this thesis are zeronoise extrapolation (ZNE), Clifford data regression (CDR) and probabilistic error cancellation (PEC). The effectiveness of error mitigation methods is examined on the basis of various indicators, such as accuracy compared to theoretical results, and resource requirements by reviewing articles or conference publications on the digital quantum simulation of spin Hamiltonian dynamics. Based on the results of the study, it is possible to conclude that the error mitigation methods examined in the thesis successfully reduced effects of noise from the results of the simulations. On the other hand, there is a trade-off between the use of resources and accuracy: higher accuracy increases the overhead of using mitigation with a certain rate depending on the method. However, the use of error reduction methods is 4 still preferable due to the benefits they provide in obtaining usable results. The best results are obtained by tailoring the selection of methods based on the application and the type of error to be mitigated.

Jun 18, 20260 citations