arXiv subjects

Andrew Cross

Publications and source records attributed to Andrew Cross.

8 recordsLinked to original sources

arXiv2025

Theory and Architecture of Syndrome-Resolved Logical Gates

We introduce a general framework for weak transversal gates, namely syndrome-resolved implementation of logical unitaries realized by local physical unitaries, and demonstrate its wide impact in three applications: partial fault-tolerant architecture, short-depth state preparation, and magic state distillation. Our theoretical contribution is to prove a sufficient condition for a general Calderbank-Shor-Steane code to admit weak transversal gates, and to present an efficient algorithm to determine the physical multiqubit Pauli rotations. To demonstrate the practicality of weak transversal gates in the near future, we propose a partially fault-tolerant Clifford+$\phi$ architecture that implements in-place Pauli rotations via a repeat-until-success strategy. Numerical simulations indicate that a rotation of 0.001 attains a logical error of $9.6\times10^{-5}$ on a surface code with $d=7$ at a physical error rate of $p=10^{-4}$, while avoiding the spacetime overheads of magic state factories, small angle synthesis, and routing. Resource estimates on surface and [[144,12,12]] bivariate bicycle codes for a Trotter-like circuit with $N=108$ logical qubits indicate runtime reductions of factors of 778 and 45, respectively, relative to the conventional method, due to the natural parallelism of rotation gates. Looking further ahead, we consider state-preparation tasks allowing postselection. We show that weak transversal gadgets prepare high-level equatorial magic states with a substantially improved cost-accuracy tradeoff, achieving up to a $10^3$-fold reduction in spacetime cost for a magic state at the 11th level of the Clifford hierarchy. Furthermore, we integrate weak transversal gates into magic state distillation pipelines, reducing the logical error rate of level-2 distillation of the $\sqrt{T}$ state by up to a factor of 94 with a small increase in spacetime cost.

quant-ph↗

arXiv2025

Small Binary Stabilizer Subsystem Codes

We establish a database consisting of a representative of every binary quantum stabilizer code under local Clifford permutation equivalence for $n\leq 9$.

quant-ph↗

arXiv2022

Quantum Locally Testable Code with Constant Soundness

In this paper, we present two constructions of quantum locally testable codes (QLTC) with constant soundness. In the first approach, we introduce an operation called check product, and show how this operation gives rise to QLTCs of constant soundness, constant rate, and distance scaling with locality. In the second approach, we consider hypergraph product of a quantum code and a classical repetition code, and observe a special case in which the soundness of component codes is preserved. This insight leads us to construct QLTCs of constant soundness, scalable rate and distance, and constant average locality. Our work marks a step towards constructing QLTCs of high soundness and distance, which would give a different construction to the No Low-Energy Trivial States (NLTS) theorem.

cs.IT↗

arXiv2017

Quantum optimization using variational algorithms on near-term quantum devices

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.

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arXiv2016

Demonstration of weight-four parity measurements in the surface code architecture

We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the parities of four data qubit states in either the $X$- or the $Z$-basis. Given the connectivity of the lattice, we perform full characterization of the static $Z$-interactions within the set of five qubits, as well as dynamical $Z$-interactions brought along by single- and two-qubit microwave drives. The parity measurements are significantly improved by modifying the microwave two-qubit gates to dynamically remove non-ideal $Z$ errors.

quant-ph↗

arXiv2015

Doubled Color Codes

We show how to perform a fault-tolerant universal quantum computation in 2D architectures using only transversal unitary operators and local syndrome measurements. Our approach is based on a doubled version of the 2D color code. It enables a transversal implementation of all logical gates in the Clifford+T basis using the gauge fixing method proposed recently by Paetznick and Reichardt. The gauge fixing requires six-qubit parity measurements for Pauli operators supported on faces of the honeycomb lattice with two qubits per site. Doubled color codes are promising candidates for the experimental demonstration of logical gates since they do not require state distillation. Secondly, we propose a Maximum Likelihood algorithm for the error correction and gauge fixing tasks that enables a numerical simulation of logical circuits in the Clifford+T basis. The algorithm can be used in the online regime such that a new error syndrome is revealed at each time step. We estimate the average number of logical gates that can be implemented reliably for the smallest doubled color code and a toy noise model that includes depolarizing memory errors and syndrome measurement errors.

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arXiv2007

Codeword Stabilized Quantum Codes

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.

quant-ph↗

arXiv2007

Transversality versus Universality for Additive Quantum Codes

Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise between corresponding qubits in each code block, thus allowing error propagation to be carefully limited. If any quantum operation could be implemented using a set of such gates, the set would be {\em universal}; codes with such a universal, transversal gate set have been widely desired for efficient fault-tolerant quantum computation. We study the structure of GF(4)-additive quantum codes and prove that no universal set of transversal logic operations exists for these codes. This result strongly supports the idea that additional primitive operations, based for example on quantum teleportation, are necessary to achieve universal fault-tolerant computation on additive codes.

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