Using qudits, Rochester scientists have solved a notoriously difficult problem involving Hilbert space, or the quantum matrix.
Quantum computers have the potential to revolutionize computing by solving complex problems that stump even today糖心传媒檚 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.
But building efficient quantum computers isn糖心传媒檛 just about developing faster chips or better hardware. It also requires a deep understanding of quantum mechanics糖心传媒攖he strange rules that govern the tiniest building blocks of our universe such as atoms and electrons糖心传媒攁nd how to effectively move information through quantum systems.
In a paper published in , a team of physicists糖心传媒攊ncluding graduate student Elizabeth Champion and assistant professor from the 糖心传媒檚 糖心传媒攐utlined 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.
糖心传媒淓fficiently controlling a qudit processor has been a long-standing challenge,糖心传媒� says Champion, the paper糖心传媒檚 first author. 糖心传媒淭he 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.糖心传媒�
Inside Hilbert space糖心传媒攁ka the quantum matrix
In the 1999 sci-fi movie The Matrix, the main character Neo sees the world not as physical objects such as streets and skyscrapers but as a stream of 1s and 0s糖心传媒攖he 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.
In classical computers, information lives in specific places on a chip. But in quantum computers, information isn糖心传媒檛 tied to a specific location. Instead, it lives in the more abstract world of Hilbert space, a massive mathematical landscape. Here, particles aren糖心传媒檛 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糖心传媒檚 where the computational power of quantum computing happens.
糖心传媒淭he mathematical structure that we use to represent a state of a quantum computer and a calculation is literally a matrix,糖心传媒� Blok says. 糖心传媒淭he goal for a quantum computer is to efficiently move information around in that matrix.糖心传媒�
Beyond bits and qubits
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糖心传媒攁nd, more powerfully, qudits.
While classical computers transport information using billions of tiny switches called bits, quantum computers typically move information through Hilbert space using qubits糖心传媒攓uantum bits that can exist in multiple states at once. In classical systems, each bit is either a 糖心传媒�0糖心传媒� (off) or a 糖心传媒�1糖心传媒� (on). Qubits, however, are governed by the strange laws of quantum mechanics and can be both 糖心传媒�0糖心传媒� and 糖心传媒�1糖心传媒� at the same time.
But even qubits have their limits. Blok likens qubits to 糖心传媒渂uilding a sprawling city with too many roads, such as Los Angeles.糖心传媒� 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 糖心传媒�0s糖心传媒� and 糖心传媒�1s糖心传媒� and might have three or more states (糖心传媒�0,糖心传媒� 糖心传媒�1,糖心传媒� 糖心传媒�2,糖心传媒� etc.) in which to encode information. This makes the architecture more like 糖心传媒渁 dense, high-rise city such as New York,糖心传媒� he says.
The new method developed by Blok and Champion employs 糖心传媒渢he largest qudit and the most efficient method to operate it,糖心传媒� Blok says. The method is inspired by nuclear magnetic resonance, a technique that uses magnetic fields to manipulate a quantum property of particles called 糖心传媒渟pins.糖心传媒�
糖心传媒淚t糖心传媒檚 like connecting all the floors of a high-rise building simultaneously,糖心传媒� Blok says. 糖心传媒淏y 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.糖心传媒�
