## Imperfections Lower the Simulation Cost of Quantum Computers – Physics

Posted: November 28, 2020 at 4:58 pm

Jordi Tura

November 23, 2020• Physics 13, 183

Classical computers can efficiently simulate the behavior of quantum computers if the quantum computer is imperfect enough.

With a few quantum bits, an ideal quantum computer can process vast amounts of information in a coordinated way, making it significantly more powerful than a classical counterpart. This predicted power increase will be great for users but is bad for physicists trying to simulate on a classical computer how an ideal quantum computer will behave. Now, a trio of researchers has shown that they can substantially reduce the resources needed to do these simulations if the quantum computer is imperfect [1]. The arXiv version of the trios paper is one of the most Scited papers of 2020 and the result generated quite a stir when it first appeared back in FebruaryI overheard it being enthusiastically discussed at the Quantum Optics Conference in Obergurgl, Austria, at the end of that month, back when we could still attend conferences in person.

In 2019, Google claimed to have achieved the quantum computing milestone known as quantum advantage, publishing results showing that their quantum computer Sycamore had performed a calculation that was essentially impossible for a classical one [2]. More specifically, Google claimed that they had completed a three-minute quantum computationwhich involved generating random numbers with Sycamores 53 qubitsthat would take thousands of years on a state-of-the-art classical supercomputer, such as IBMs Summit. IBM quickly countered the claim, arguing that more efficient memory storage would reduce the task time on a classical computer to a couple of days [3]. The claims and counterclaims sparked an industry clash and an intense debate among supporters in the two camps.

Resolving the disparity between these estimates is one of the goals of the new work by Yiqing Zhou, of the University of Illinois at UrbanaChampaign, and her two colleagues [1]. In their study, they focused on algorithms for classically replicating imperfect quantum computers, which are also known as NISQ (noisy intermediate-scale quantum) devices [4]. Todays state-of-the-art quantum computersincluding Sycamoreare NISQ devices. The algorithms the team used are based on so-called tensor network methods, specifically matrix product states (MPS), which are good for simulating noise and so are naturally suited for studying NISQ devices. MPS methods approximate low-entangled quantum states with simpler structures, so they provide a data-compression-like protocol that can make it less computationally expensive to classically simulate imperfect quantum computers (see Viewpoint: Pushing Tensor Networks to the Limit).

Zhou and colleagues first consider a random 1D quantum circuit made of neighboring, interleaved two-qubit gates and single-qubit random unitary operations. The two-qubit gates are either Controlled-NOT gates or Controlled-Z (CZ) gates, which create entanglement. They ran their algorithm for NISQ circuits containing different numbers of qubits, N, and different depths, Da parameter that relates to the number of gates the circuit executes (Fig. 1). They also varied a parameter in the MPS algorithm. is the so-called bond dimension of the MPS and essentially controls how well the MPS capture entanglement between qubits.

The trio demonstrate that they can exactly simulate any imperfect quantum circuit if D and N are small enough and is set to a value within reach of a classical computer. They can do that because shallow quantum circuits can only create a small amount of entanglement, which is fully captured by a moderate . However, as D increases, the team finds that cannot capture all the entanglement. That means that they cannot exactly simulate the system, and errors start to accumulate. The team describes this mismatch between the quantum circuit and their classical simulations using a parameter that they call the two-qubit gate fidelity fn. They find that the fidelity of their simulations slowly drops, bottoming out at an asymptotic value f as D increases. This qualitative behavior persists for different values of N and . Also, while their algorithm does not explicitly account for all the error and decoherence mechanisms in real quantum computers, they show that it does produce quantum states of the same quality (perfection) as the experimental ones.

In light of Googles quantum advantage claims, Zhou and colleagues also apply their algorithm to 2D quantum systemsSycamore is built on a 2D chip. MPS are specifically designed for use in 1D systems, but the team uses well-known techniques to extend their algorithm to small 2D ones. They use their algorithm to simulate an N=54, D=20 circuit, roughly matching the parameters of Sycamore (Sycamore has 54 qubits but one is unusable because of a defect). They replace Googles more entangling iSWAP gates with less entangling CZ gates, which allow them to classically simulate the system up to the same fidelity as reported in Ref. [2] with a single laptop. The simulation cost should increase quadratically for iSWAP-gate circuits, and although the team proposes a method for performing such simulations, they have not yet carried them out because of the large computational cost it entails.

How do these results relate to the quantum advantage claims by Google? As they stand, they do not weaken or refute claimswith just a few more qubits, and an increase in D or f, the next generation of NISQ devices will certainly be much harder to simulate. The results also indicate that the teams algorithm only works if the quantum computer is sufficiently imperfectif it is almost perfect, their algorithm provides no speed up advantage. Finally, the results provide numerical insight into the values of N, D, f, and for which random quantum circuits are confined to a tiny corner of the exponentially large Hilbert space. These values give insight into how to quantify the capabilities of a quantum computer to generate entanglement as a function of f, for example.

So, whats next? One natural question is, Can the approach here be transferred to efficiently simulate other aspects of quantum computing, such as quantum error correction? The circuits the trio considered are essentially random, whereas quantum error correction circuits are more ordered by design [5]. That means that updates to the new algorithm are needed to study such systems. Despite this limitation, the future looks promising for the efficient simulation of imperfect quantum devices [6, 7].

Jordi Tura is an assistant professor at the Lorentz Institute of the University of Leiden, Netherlands. He also leads the institutes Applied Quantum Algorithms group. Tura obtained his B.Sc. degrees in mathematics and telecommunications and his M.Sc. in applied mathematics from the Polytechnic University of Catalonia, Spain. His Ph.D. was awarded by the Institute of Photonic Sciences, Spain. During his postdoctoral stay at the Max Planck Institute of Quantum Optics in Germany, Tura started working in the field of quantum information processing for near-term quantum devices.

A nanopatterned magnetic structure features an unprecedently strong coupling between lattice vibrations and quantized spin waves, which could lead to novel ways of manipulating quantum information. Read More

Go here to see the original:

Imperfections Lower the Simulation Cost of Quantum Computers - Physics

- Cambridge named as world-leading centre of quantum computing research - Varsity Online - February 5th, 2021
- Quantum Computing Market 2018 Size, Application,Revenue, Types, Trends in Future, Scope to 2030 | D-Wave Systems Inc., QX Branch Co., IBM Co., Google... - February 5th, 2021
- Quantum computing breakthrough uses cryogenics to scale machines to thousands of times their current size - The Independent - February 3rd, 2021
- Quantum Computing Market worth $1,765 million by 2026 - Exclusive Report by MarketsandMarkets - PRNewswire - February 3rd, 2021
- IBM's Goldeneye: Behind the scenes at the world's largest dilution refrigerator - ZDNet - February 3rd, 2021
- Establishing a Women Inclusive Future in Quantum Computing - Analytics Insight - February 3rd, 2021
- The risk of giving in to quantum progress - ComputerWeekly.com - February 3rd, 2021
- Quantum Computing 101 -What it is, how is it different and why it matters - The Jerusalem Post - February 3rd, 2021
- Here's Why Quantum Computing Will Not Break Cryptocurrencies - Forbes - December 24th, 2020
- Global Quantum Computing Market Predicted to Garner $667.3 Million by 2027, Growing at 30.0% CAGR from 2020 to 2027 - [193 pages] Informative Report... - December 24th, 2020
- Quantum Computer Completed A 2.5-Billion-Year Task In 200 Seconds - Intelligent Living - December 24th, 2020
- University collaboration gives Scotland the edge in global quantum computing race - HeraldScotland - December 24th, 2020
- Scaling the heights of quantum computing to deliver real results - Chinadaily.com.cn - China Daily - December 24th, 2020
- Bitcoin is quantum computing resistant regardless of rising fears among investors - FXStreet - December 24th, 2020
- This Incredible Particle Only Arises in Two Dimensions - Popular Mechanics - December 24th, 2020
- Two Years into the Government's National Quantum Initiative - Nextgov - December 24th, 2020
- Atos Delivers Its First GPU-Accelerated Quantum Learning Machine to the Irish Centre for High-End Computing - HPCwire - December 24th, 2020
- With Next Cryo, a startup that's really cooling its jets - Innovate Long Island - Innovate Long Island - December 24th, 2020
- Chip-Based Photon Source Is 100X More Efficient than Previous, Bringing Quantum Integration Within Reach - HPCwire - December 24th, 2020
- Quantum computing - Wikipedia - December 17th, 2020
- What is quantum computing? - December 17th, 2020
- Explainer: What is a quantum computer? | MIT Technology Review - December 17th, 2020
- Eight leading quantum computing companies in 2020 | ZDNet - December 17th, 2020
- Wall Streets latest shiny new thing: quantum computing - The Economist - December 17th, 2020
- Quantum computing: Strings of ultracold atoms reveal the surprising behavior of quantum particles - ZDNet - December 17th, 2020
- Anyon Systems to Deliver a Quantum Computer to the Canadian Department of National Defense - GlobeNewswire - December 17th, 2020
- Chinese quantum computer may be the most powerful ever seen - Siliconrepublic.com - December 17th, 2020
- 'Magic' angle graphene and the creation of unexpected topological quantum states - Princeton University - December 17th, 2020
- This breakthrough could unlock the true power of quantum - Wired.co.uk - December 17th, 2020
- ASC20-21 Student Supercomputer Challenge Kickoff: Quantum Computing Simulations, AI Language Exam and Pulsar Searching with FAST - Business Wire - November 28th, 2020
- Quantum Computing Market : Analysis and In-depth Study on Size Trends, and Regional Forecast - Cheshire Media - November 28th, 2020
- Global Quantum Computing Market 2020 Recovering From Covid-19 Outbreak | Know About Brand Players: D-Wave Systems, 1QB Information Technologies,... - November 28th, 2020
- Is the blockchain vulnerable to hacking by quantum computers? - Moneyweb.co.za - November 28th, 2020
- Here's Why the Quantum World Is Just So Strange - Walter Bradley Center for Natural and Artificial Intelligence - November 28th, 2020
- Cracking the Secrets of an Emerging Branch of Physics: Exotic Properties to Power Real-World Applications - SciTechDaily - November 28th, 2020
- Quantum Computing Market Detailed Analysis of Current and Future Industry Figures 2020-2026 | Leading Players StationQ- Microsoft, Google, 1QB... - November 16th, 2020
- Quantum Computing in the CloudCan It Live Up to the Hype? - Electronic Design - November 16th, 2020
- Supply Chain: The Quantum Computing Conundrum | Logistics - Supply Chain Digital - The Procurement & Supply Chain Platform - November 16th, 2020
- CCNY & partners in quantum algorithm breakthrough | The City College of New York - The City College of New York News - November 16th, 2020
- Hybrid cloud and quantum computing to shape IT: IBM chief - Nikkei Asian Review - November 16th, 2020
- NTTs Kazuhiro Gomi says Bio Digital Twin, quantum computing the next-gen tech - Backend News - November 16th, 2020
- A Scoville Heat Scale For Measuring The Progress Of Emerging Technologies In 2021 - Forbes - November 16th, 2020
- How quantum computing could drive the future auto industry - TechHQ - September 17th, 2020
- Spin-Based Quantum Computing Breakthrough: Physicists Achieve Tunable Spin Wave Excitation - SciTechDaily - September 17th, 2020
- 2025 will be the year of Quantum on the desktop - Fudzilla - September 17th, 2020
- Putting the Quantum in Security - Optics & Photonics News - September 17th, 2020
- NTT Research and University of Notre Dame Collaborate to Explore Continuous-Time Analog Computing - Quantaneo, the Quantum Computing Source - September 17th, 2020
- Assistant Professor in Computer Science job with Indiana University | 286449 - The Chronicle of Higher Education - September 17th, 2020
- EU leaders to ask European Commission to name areas of strategic weakness - Reuters - September 17th, 2020
- We Just Found Another Obstacle For Quantum Computers to Overcome - And It's Everywhere - ScienceAlert - September 2nd, 2020
- Quantum Computing Market Is Booming Worldwide | D-Wave Systems, 1QB Information Technologies, QxBranch LLC and more - The Daily Chronicle - September 2nd, 2020
- Tufts Joins Major Effort to Build the Next Generation of Quantum Computers - Tufts Now - September 2nd, 2020
- The Quantum Dream: Are We There Yet? - Toolbox - September 2nd, 2020
- Bipartisan Bill Calls for Government-Led Studies Into Emerging Tech Impacts - Nextgov - September 2nd, 2020
- Two Pune Research Institutes Are Building India's First Optical Atomic Clocks - The Wire Science - September 2nd, 2020
- Vitalik Buterin highlights major threats to Bitcoin BTC and Ethereum ETH - Digital Market News - September 2nd, 2020
- What Is Quantum Supremacy And Quantum Computing? (And How Excited Should We Be?) - Forbes - August 23rd, 2020
- Has the world's most powerful computer arrived? - The National - August 23rd, 2020
- Will Quantum Computers Really Destroy Bitcoin? A Look at the Future of Crypto, According to Quantum Physicist Anastasia Marchenkova - The Daily Hodl - August 23rd, 2020
- This Week's Awesome Tech Stories From Around the Web (Through August 22) - Singularity Hub - August 23rd, 2020
- A Meta-Theory of Physics Could Explain Life, the Universe, Computation, and More - Gizmodo - August 23rd, 2020
- This Twist on Schrdinger's Cat Paradox Has Major Implications for Quantum Theory - Scientific American - August 23rd, 2020
- Scientists Have Shown There's No 'Butterfly Effect' in the Quantum World - VICE - August 23rd, 2020
- Quantum Information Processing Market 2020 | Know the Latest COVID19 Impact Analysis And Strategies of Key Players: 1QB Information Technologies,... - August 23rd, 2020
- Doctor Strange might want to trade his Time Stone for time crystals that are doing some otherworldly things - SYFY WIRE - August 23rd, 2020
- Trump betting millions to lay the groundwork for quantum internet in the US - CNBC - April 28th, 2020
- Announcing the IBM Quantum Challenge - Quantaneo, the Quantum Computing Source - April 28th, 2020
- Wiring the Quantum Computer of the Future: Researchers from Japan and Australia propose a novel 2D design - QS WOW News - April 28th, 2020
- Muquans and Pasqal partner to advance quantum computing - Quantaneo, the Quantum Computing Source - April 28th, 2020
- Deltec Bank, Bahamas - Quantum Computing Will bring Efficiency and Effectiveness and Cost Saving in Baking Sector - marketscreener.com - April 28th, 2020
- New way of developing topological superconductivity discovered - Chemie.de - April 28th, 2020
- Hot Qubits Could Deliver a Quantum Computing Breakthrough - Popular Mechanics - April 19th, 2020
- Quantum Computing With Particles Of Light: A $215 Million Gamble - Forbes - April 19th, 2020
- Quantum computing heats up down under as researchers reckon they know how to cut costs and improve stability - The Register - April 19th, 2020
- The future of quantum computing in the cloud - TechTarget - April 19th, 2020
- World coronavirus Dispatch: Quantum Computing Market Recent Trends and Developments, Challenges and Opportunities, key drivers and Restraints over the... - April 19th, 2020
- Quantum Computing Market 2020 Break Down by Top Companies, Applications, Challenges, Opportunities and Forecast 2026 Cole Reports - Cole of Duty - April 19th, 2020
- Science of Star Trek - The UCSB Current - April 19th, 2020
- Defense budget cuts following the pandemic will be hard to swallow | TheHill - The Hill - April 19th, 2020
- Pentagon wants commercial, space-based quantum sensors within 2 years - The Sociable - April 19th, 2020