Logic Gates and Magic State Distillation – IBM Paper Details Path Forward

By John Russell

January 22, 2024

Implementing error correction and mitigation are perhaps the chief goals today for the quantum computing community. IBM has a new Nature paper (Encoding a magic state with beyond break-even fidelity) demonstrating the use of dynamic circuits to better implement magic state distillation.

IBM posted a blog on the latest work, noting that the experiment opens a new area of research — using dynamic circuits to prepare magic states. It also “sets us on the path” to solving one of the most important challenges in quantum computing — running high-fidelity logical gates on error-corrected qubits.

Excerpt from the blog:

“Two decades ago, researchers Sergey Bravyi and Alexei Kitaev, now at IBM and the California Institute of Technology respectively, published a paper titled “Universal quantum computation with ideal Clifford gates and noisy ancillas.” In this paper, Bravyi and Kitaev proved that we can access the full power of quantum computers using just four tools. The first is the ability to control a quantum state. The second is a set of easy-to-run gates called Clifford gates like X, Y, Z, H, SWAP, and CNOT. The third is the ability to measure our qubit values. And the fourth is most important: the ability to prepare certain error-prone states beyond what Clifford gates can access. Their method found that for certain states, they could apply a sequence of Clifford operations to distill these error-prone states into “magic states” that they can use for computation. The Clifford gates, plus the distilled magic states, allow you to run any quantum computation.

“In our new paper, we demonstrated a new procedure to encode magic states onto four qubits of the 27-qubit IBM Falcon processor on the ibm_peekskill system. Our scheme focused on starting with better states prior to the distillation process. Then, to prepare the magic states, we employed some of the important dynamic circuit techniques we introduced last year. We perform mid-circuit measurement and feed the value forward in the circuit, steering the state closer to the required magic state. By exploiting dynamical circuits we were able to improve yield — the number of magic states produced over time — than what would otherwise be possible if we did not have access to these possible if we did not have access to these capabilities. Basically, we can create more magic states and less junk.”

The IBM researchers cite progress on magic states using trapped ion architectures (IonQ,  Institute for Experimental Physics, University of Innsbruck) and suggest their new approach can reduce the cost (qubit redundancy) needed. IBM, of course, uses superconducting qubits.

In their paper, the IBM researchers write:

“We distill magic states to complete a universal set of fault-tolerant logic gates that is needed for large-scale quantum computing with low-density parity-check code architectures. High-fidelity magic states are produced by processing noisy input magic states with fault-tolerant distillation circuits; experimental progress in preparing input magic states using trapped-ion architectures is described in refs. It is expected that a considerable number of the qubits of a quantum computer will be occupied performing magic-state distillation schemes and, as such, it is valuable to find ways of reducing its cost. One way to reduce the cost is to improve the fidelity of input states, such that magic states can be distilled with less resource-intensive circuits.

“Here we propose and implement an error-suppressed encoding circuit to prepare a state that is input to magic-state distillation using a heavy-hexagonal lattice of superconducting qubits. Our circuit prepares an input magic state, which we call a CZ state, encoded on a four-qubit error-detecting code. We explain how our encoded magic state can be used in large-scale quantum-computing architectures in the section ‘Using CZ states in large-scale quantum-computing architectures’. Our circuit is capable of detecting any single error during state preparation, as such, the infidelity of the encoded state is suppressed as Ó (ε2), where ε is the probability that a circuit element experiences an error. By contrast, a standard encoding circuit prepares an input state with infidelity Ó (ε). Furthermore, we can improve the yield of the prepared magic states with the error-suppressed circuit using adaptive circuits that are conditioned in real time on the outcomes of mid-circuit measurements. We propose several tomographical experiments to interrogate the preparation of the magic state, including a complete set of fault-tolerant projective logical Pauli measurements that can also tolerate the occurrence of a single error during readout.”

The researchers say they’ve shown experimental progress has reached a point at which “we can make prototype gadgets that can affect the resource cost of large-scale quantum computers” and that the prototype can be used together with magic-state distillation. “It will be interesting to continue to design, develop and test new gadgets with real hardware that will improve the performance of the key subroutines needed for fault-tolerant quantum computing.”

Link to blog, https://research.ibm.com/blog/quantum-magic-states#-fn-1

Link to IBM paper, https://www.nature.com/articles/s41586-023-06846-3

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