{"id":659482,"date":"2025-07-08T17:29:31","date_gmt":"2025-07-08T21:29:31","guid":{"rendered":"https:\/\/www.rochester.edu\/newscenter\/?p=659482"},"modified":"2025-07-08T17:29:31","modified_gmt":"2025-07-08T21:29:31","slug":"hilbert-space-definition-qudits-quantum-mechanics-659482","status":"publish","type":"post","link":"https:\/\/www.rochester.edu\/newscenter\/hilbert-space-definition-qudits-quantum-mechanics-659482\/","title":{"rendered":"Researchers discover more efficient way to route information in quantum computers"},"content":{"rendered":"

Using qudits, Rochester scientists have solved a notoriously difficult problem involving Hilbert space, or the quantum matrix.<\/strong><\/h2>\n

Quantum computers have the potential to revolutionize computing by solving complex problems that stump even today\u2019s fastest machines. Scientists are exploring whether quantum computers could one day help streamline global supply chains, create ultra-secure encryption to protect sensitive data against even the most powerful cyberattacks, or even develop more effective drugs by simulating their behavior at the atomic level.<\/p>\n

But building efficient quantum computers isn\u2019t just about developing faster chips or better hardware. It also requires a deep understanding of quantum mechanics\u2014the strange rules that govern the tiniest building blocks of our universe such as atoms and electrons\u2014and how to effectively move information through quantum systems.<\/p>\n

In a paper published in Physics Review X<\/em><\/a>, a team of physicists\u2014including graduate student Elizabeth Champion and assistant professor Machiel Blok<\/a> from the University of Rochester<\/a>\u2019s Department of Physics and Astronomy<\/a>\u2014outlined a method to address a tricky problem in quantum computing: how to efficiently move information within a multi-level system using quantum units called qudits.<\/p>\n

\u201cEfficiently controlling a qudit processor has been a long-standing challenge,\u201d says Champion, the paper\u2019s first author. \u201cThe methods we developed allow the core operations of a qudit-based quantum computer to be performed in far fewer steps, making full use of the hardware. This can potentially enable quantum computations and simulations that were not possible before.\u201d<\/p>\n

Inside Hilbert space\u2014aka the quantum matrix<\/strong><\/h3>\n

In the 1999 sci-fi movie The Matrix<\/em>, the main character Neo sees the world not as physical objects such as streets and skyscrapers but as a stream of 1s and 0s\u2014the raw data underlying his reality. In quantum physics, there is a similar underlying framework beneath the familiar world of particles and forces. This matrix is called Hilbert space.<\/p>\n

\"Side-by-side
RECONFIGURING THE QUANTUM LANDSCAPE:<\/strong> Qubits (represented by yellow cubes on the left) move information within Hilbert space\u2014but they have their limits. A new method employs \u201cthe largest qudit [represented by blue cubes on the right] and the most efficient method to operate it,\u201d says Blok. This innovation makes the architecture more like a dense, high-rise city\u2014”like connecting all the floors of a high-rise building simultaneously.\u201d (University of Rochester illustration \/ Michael Osadciw)<\/figcaption><\/figure>\n

In classical computers, information lives in specific places on a chip. But in quantum computers, information isn\u2019t tied to a specific location. Instead, it lives in the more abstract world of Hilbert space, a massive mathematical landscape. Here, particles aren\u2019t just tiny dots zipping around but also abstract waves of probability, existing in many locations and states at once. Although Hilbert space is not something you can see or locate in the physical computer chip, it\u2019s where the computational power of quantum computing happens.<\/p>\n

\u201cThe mathematical structure that we use to represent a state of a quantum computer and a calculation is literally a matrix,\u201d Blok says. \u201cThe goal for a quantum computer is to efficiently move information around in that matrix.\u201d<\/p>\n

Beyond bits and qubits<\/strong><\/h3>\n

Moving information through the abstract mathematical landscape of Hilbert space is no small feat. To do this, scientists rely on quantum building blocks called qubits\u2014and, more powerfully, qudits.<\/p>\n

While classical computers transport information using billions of tiny switches called bits, quantum computers typically move information through Hilbert space using qubits\u2014quantum bits that can exist in multiple states at once. In classical systems, each bit is either a \u201c0\u201d (off) or a \u201c1\u201d (on). Qubits, however, are governed by the strange laws of quantum mechanics and can be both \u201c0\u201d and \u201c1\u201d at the same time.<\/p>\n

But even qubits have their limits. Blok likens qubits to \u201cbuilding a sprawling city with too many roads, such as Los Angeles.\u201d His research introduces a fundamentally different approach to moving information within Hilbert space using qudits, which can store more information in a single location. In other words, qudits go beyond \u201c0s\u201d and \u201c1s\u201d and might have three or more states (\u201c0,\u201d \u201c1,\u201d \u201c2,\u201d etc.) in which to encode information. This makes the architecture more like \u201ca dense, high-rise city such as New York,\u201d he says.<\/p>\n

The new method developed by Blok and Champion employs \u201cthe largest qudit and the most efficient method to operate it,\u201d Blok says. The method is inspired by nuclear magnetic resonance, a technique that uses magnetic fields to manipulate a quantum property of particles called \u201cspins.\u201d<\/p>\n

\u201cIt\u2019s like connecting all the floors of a high-rise building simultaneously,\u201d Blok says. \u201cBy tapping into techniques from big-spin physics, we’ve discovered a much more efficient way to route quantum information within each qudit, potentially unlocking faster, more scalable quantum computers with far fewer operational bottlenecks.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"

Using qudits, Rochester scientists have solved a notoriously difficult problem involving Hilbert space, or the quantum matrix.<\/p>\n","protected":false},"author":912,"featured_media":659522,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[116],"tags":[18662,41892,17762,18572,16072],"class_list":["post-659482","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sci-tech","tag-department-of-physics-and-astronomy","tag-machiel-blok","tag-quantum-science","tag-research-finding","tag-school-of-arts-and-sciences"],"acf":[],"yoast_head":"\nResearchers discover more efficient way to route information in quantum computers<\/title>\n<meta name=\"description\" content=\"Using qudits, University of Rochester scientists have solved a notoriously difficult problem involving Hilbert space, or the quantum matrix.\" \/>\n<meta name=\"robots\" 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