87 research outputs found
Constructing all qutrit controlled Clifford+T gates in Clifford+T
For a number of useful quantum circuits, qudit constructions have been found
which reduce resource requirements compared to the best known or best possible
qubit construction. However, many of the necessary qutrit gates in these
constructions have never been explicitly and efficiently constructed in a
fault-tolerant manner. We show how to exactly and unitarily construct any
qutrit multiple-controlled Clifford+T unitary using just Clifford+T gates and
without using ancillae. The T-count to do so is polynomial in the number of
controls , scaling as . With our results we can construct
ancilla-free Clifford+T implementations of multiple-controlled T gates as well
as all versions of the qutrit multiple-controlled Toffoli, while the analogous
results for qubits are impossible. As an application of our results, we provide
a procedure to implement any ternary classical reversible function on trits
as an ancilla-free qutrit unitary using T gates.Comment: 14 page
QudCom: Towards Quantum Compilation for Qudit Systems
Qudit-based quantum computation offers unique advantages over qubit-based
systems in terms of noise mitigation capabilities as well as algorithmic
complexity improvements. However, the software ecosystem for multi-state
quantum systems is severely limited. In this paper, we highlight a quantum
workflow for describing and compiling qudit systems. We investigate the design
and implementation of a quantum compiler for qudit systems. We also explore
several key theoretical properties of qudit computing as well as efficient
optimization techniques. Finally, we provide demonstrations using physical
quantum computers as well as simulations of the proposed quantum toolchain
Building Qutrit Diagonal Gates from Phase Gadgets
Phase gadgets have proved to be an indispensable tool for reasoning about
ZX-diagrams, being used in optimisation and simulation of quantum circuits and
the theory of measurement-based quantum computation. In this paper we study
phase gadgets for qutrits. We present the flexsymmetric variant of the original
qutrit ZX-calculus, which allows for rewriting that is closer in spirit to the
original (qubit) ZX-calculus. In this calculus phase gadgets look as you would
expect, but there are non-trivial differences in their properties. We devise
new qutrit-specific tricks to extend the graphical Fourier theory of qubits,
resulting in a translation between the 'additive' phase gadgets and a
'multiplicative' counterpart we dub phase multipliers.
This enables us to generalise the qubit notion of multiple-control to qutrits
in two ways. The first type is controlling on a single tritstring, while the
second type applies the gate a number of times equal to the tritwise
multiplication modulo 3 of the control qutrits.We show how both types of
control can be implemented for any qutrit Z or X phase gate, ancilla-free, and
using only Clifford and phase gates. The first requires a polynomial number of
gates and exponentially small phases, while the second requires an exponential
number of gates, but constant sized phases. This is interesting, because such a
construction is not possible in the qubit setting.
As an application of these results we find a construction for emulating
arbitrary qubit diagonal unitaries, and specifically find an ancilla-free
emulation for the qubit CCZ gate that only requires three single-qutrit
non-Clifford gates, provably lower than the four T gates needed for qubits with
ancilla.Comment: In Proceedings QPL 2022, arXiv:2311.0837
Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
Quantum information processing has witnessed significant advancements through
the application of qubit-based techniques within universal gate sets. Recently,
exploration beyond the qubit paradigm to -dimensional quantum units or
qudits has opened new avenues for improving computational efficiency. This
paper delves into the qudit-based approach, particularly addressing the
challenges presented in the high-fidelity implementation of qudit-based
circuits due to increased complexity. As an innovative approach towards
enhancing qudit circuit fidelity, we explore algebraic relations, such as the
Yang-Baxter-like turnover equation, that may enable circuit compression and
optimization. The paper introduces the turnover relation for the three-qutrit
time propagator and its potential use in reducing circuit depth. We further
investigate whether this relation can be generalized for higher-dimensional
quantum circuits, including a focused study on the one-dimensional spin-1
Heisenberg model. Our work outlines both rigorous and numerically efficient
approaches to potentially achieve this generalization, providing a foundation
for further explorations in the field of qudit-based quantum computing
Asymptotically Improved Grover's Algorithm in any Dimensional Quantum System with Novel Decomposed -qudit Toffoli Gate
As the development of Quantum computers becomes reality, the implementation
of quantum algorithms is accelerating in a great pace. Grover's algorithm in a
binary quantum system is one such quantum algorithm which solves search
problems with numeric speed-ups than the conventional classical computers.
Further, Grover's algorithm is extended to a -ary quantum system for
utilizing the advantage of larger state space. In qudit or -ary quantum
system n-qudit Toffoli gate plays a significant role in the accurate
implementation of Grover's algorithm. In this paper, a generalized -qudit
Toffoli gate has been realized using qudits to attain a logarithmic depth
decomposition without ancilla qudit. Further, the circuit for Grover's
algorithm has been designed for any d-ary quantum system, where d >= 2, with
the proposed -qudit Toffoli gate so as to get optimized depth as compared to
state-of-the-art approaches. This technique for decomposing an n-qudit Toffoli
gate requires access to higher energy levels, making the design susceptible to
leakage error. Therefore, the performance of this decomposition for the unitary
and erasure models of leakage noise has been studied as well
Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits
Multipartite entanglement is one of the core concepts in quantum information
science with broad applications that span from condensed matter physics to
quantum physics foundations tests. Although its most studied and tested forms
encompass two-dimensional systems, current quantum platforms technically allow
the manipulation of additional quantum levels. We report the first experimental
demonstration of a high-dimensional multipartite entangled state in a
superconducting quantum processor. We generate the three-qutrit
Greenberger-Horne-Zeilinger state by designing the necessary pulses to perform
high-dimensional quantum operations. We obtain the fidelity of ,
proving the generation of a genuine three-partite and three-dimensional
entangled state. To this date, only photonic devices have been able to create
and manipulate these high-dimensional states. Our work demonstrates that
another platform, superconducting systems, is ready to exploit high-dimensional
physics phenomena and that a programmable quantum device accessed on the cloud
can be used to design and execute experiments beyond binary quantum
computation.Comment: 6 pages + 6 supplementary information, 3 figures, 1 tabl
Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
Quantum algorithms for unconstrained optimization problems, such as the
Quantum Approximate Optimization Algorithm (QAOA), have been proposed as
interesting near-term algorithms which operate under a hybrid quantum-classical
execution model. Recent work has shown that the QAOA can also be applied to
constrained combinatorial optimization problems by incorporating the problem
constraints within the design of the variational ansatz - often resulting in
quantum circuits containing many multi-controlled gate operations. This paper
investigates potential resource tradeoffs for the QAOA when applied to the
particular constrained optimization problem of Maximum Independent Set. We
consider three variants of the QAOA which make different tradeoffs between the
number of classical parameters, quantum gates, and iterations of classical
optimization. We also study the quantum cost of decomposing the QAOA circuits
on hardware which may support different qubit technologies and native gate
sets, and compare the different algorithms using the gate decomposition score
which combines the fidelity of the gate operations with the efficiency of the
decomposition into a single metric. We find that all three QAOA variants can
attain similar performance but the classical and quantum resource costs may
vary greatly between them.Comment: 17 pages, 8 figures, 5 table
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