Classical Half-Adder using Trapped-ion Quantum Bits Towards Energy-efficient Computation Sagar Silva Pratapsi1 2 aPatrick H. Huber3aPatrick Barthel3Sougato Bose4Christof Wunderlich3aand

2025-04-29 0 0 688.8KB 10 页 10玖币

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Classical Half-Adder using Trapped-ion Quantum Bits:

Towards Energy-eﬃcient Computation

Sagar Silva Pratapsi,1, 2, a) Patrick H. Huber,3, a) Patrick Barthel,3Sougato Bose,4Christof Wunderlich,3, a) and

Yasser Omar1, 5, 6, a)

1)Instituto Superior Técnico, University of Lisbon, Lisbon 1049-001, Portugal.

2)Instituto de Telecomunicações, Lisbon 1049-001, Portugal.

3)Department of Physics, School of Science and Technology, University of Siegen, 57068 Siegen,

Germany

4)Department of Physics and Astronomy, University College London, London WC1E 6BT,

5)Physics of Information and Quantum Technologies group, Center of Physics and Engineering of Advanced Materials (CeFEMA),

Lisbon 1049-001, Portugal

6)PQI – Portuguese Quantum Institute, Lisbon 1600-531, Portugal

(*Electronic mail: contact.yasser@pqi.pt)

(*Electronic mail: Christof.Wunderlich@uni-siegen.de)

(*Electronic mail: p.huber@physik.uni-siegen.de)

(*Electronic mail: spratapsi@tecnico.ulisboa.pt)

(Dated: 5 April 2024)

Reversible computation has been proposed as a future paradigm for energy efﬁcient computation, but so far few imple-

mentations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known

to be reversible. In this work, we provide a proof-of-principle of classical logical gates running on quantum tech-

nologies. In particular, we propose, and realise experimentally, Toffoli and Half-Adder circuits suitable for classical

computation, using radiofrequency-controlled 171Yb+ions in a macroscopic linear Paul-trap as qubits. We analyse the

energy required to operate the logic gates, both theoretically and experimentally, with a focus on the control energy.

We identify bottlenecks and possible improvements in future platforms for energetically-efﬁcient computation, e.g.,

trap chips with integrated antennas and cavity QED. Our experimentally veriﬁed energetic model also ﬁlls a gap in the

literature of the energetics of quantum information, and outlines the path for its detailed study, as well as its potential

applications to classical computing.

Computational tasks are responsible for a non-negligible

part of the world’s energy consumption. It is estimated that

computationally-intensive data-centres represent 1% of the

global energy budget1. So far, increases in energy efﬁciency

have been able to offset the growing demand for computation:

peak-usage energy efﬁciency has doubled every 1.5 years dur-

ing the 1960–2000 period, while since the 2000s this ﬁgure

is closer to 2.6 years1,2. However, processor efﬁciency gains

cannot continue to grow forever. There is a fundamental limi-

tation of the current paradigm of non-reversible computation,

known as Landauer’s principle3, where each irreversible bit

operation dissipates kBTln2 of heat.

Reversible computation may thus become an important

computation paradigm in the future. Reversible systems

may also avoid the heat costs of contemporary CMOS pro-

cessors, such as capacitor charging, switching and current

leakage4,5, which are ultimately responsible for the typical

40% energy cost for cooling in data centres6; they may also

protect against external attacks such as power usage anal-

ysis. It is, then, worthwhile to investigate how energy-

efﬁcient reversible platforms can become. Some propos-

als for reversible computing platforms have been billiard-

ball models7,8, adiabatic circuits9–13, nano-machines14–18, su-

a)Corresponding author.

perconducting devices19–21, quantum-dot cellular automata22,

and others (see23 for a review of reversible computation).

But, so far, experimental realisations of reversible compu-

tation are lacking in practice. Quantum mechanical sys-

tems, which evolve unitarily, are also reversible by nature,

and are thus an attractive candidate for energetically efﬁcient

computation24,25. Although quantum platforms are limited by

coherence time, we can reset the coherence for classical com-

putations by measuring in the computational basis in-between

logical operations. We may also exploit super-selection rules

to protect classical information, as was proposed recently in

a quantum dot platform26. Can we then build energy efﬁcient

circuits for universal reversible computation using quantum

computing platforms?

In this work, we explore an implementation of reversible

computation using quantum technologies, by realising a clas-

sical Half-Adder circuit—an important building block for

arithmetic operations27—using quantum states of trapped

ions. To do so, we implement a Toffoli gate, itself a univer-

sal gate for classical computation. We determine the energy

to operate these gates, both theoretically and experimentally,

with a special focus on the energy required to activate and con-

trol the logical gates, focusing on the power delivered to the

Quantum Processing Unit (QPU), as deﬁned later. We point

out possible improvements towards energy efﬁcient computa-

tion. Some works28 require realistic estimates for the energy

arXiv:2210.10470v2 [quant-ph] 4 Apr 2024

Utof (δ2n, φ2n)

πϕn

Utof (δ2n+1, φ2n+1)Uzz

πϕn

Uzz

=πϕ′

πϕnπ

0πϕnπ

3π/2

×NTOF ×NCNOT

FIG. 1. A Half-adder circuit using a Toffoli followed by a CNOT gate. We choose the central qubit as the target of the Toffoli gate to fullﬁl

the condition J12 =J23 from Equation (1). The Toffoli gate decomposes into a unitary UT OF (δn,φn)(generated from Hamiltonian (3) for

14.9ms/400) and single qubit π-pulses with some phase φ(πφ, implementing Dynamical Decoupling). The block is repeated NTOF =200

times with updated values of δn,ϕnand DD phases φnand φ′

n. The latter are chosen to implement a universal robust DD sequence on qubits 1

and 3 and a CPMGXY on qubit 2. The values (δ2n,δ2n+1)alternate between (δ,−δ)and (−δ,δ)for each π-pulse, while (ϕ2n,ϕ2n+1)alternates

between (0,π)and (π,0)for each ππ/2-pulse. The CNOT gate decomposes into a Uzz gate (implementing the zz coupling) and single qubit

π-pulses. The block is repeated NCNOT =120 times. The phases φnimplement a UR DD sequence on the control and target qubits.

consumed by quantum computers. Thus, our energetic analy-

sis, supported by experimental measurements, also ﬁlls a gap

in the literature, and establishes a baseline for additional re-

search towards understanding the energetic impact of quan-

tum technologies29.

A Half-Adder circuit is a fundamental component of arith-

metic circuits. It computes the logical AND (multiplication

modulo 2) and XOR (addition modulo 2) of two input bits. It

is a building block for the Full-Adder circuit, addition circuits

in their ripple-carry and carry-lookahead variants, multiplier

circuits and other tasks in contemporary computer processors.

The core operation behind our Half-Adder circuit is a quan-

tum Toffoli gate, followed by the application of a CNOT to the

two control qubits of the Toffoli (FIG. 1). A Toffoli gate, or a

controlled-controlled-NOT gate, is a universal three-bit oper-

ation, i.e., it is sufﬁcient to construct any classical reversible

circuit. Antonio et al. proposed a Toffoli gate suitable for

classical computation30, which can be realised on any three-

qubit physical system with constant nearest-neighbour Ising

couplings, via the Hamiltonian

HTOF =¯

2σz

1σz

2+σz

2σz

3+¯

hδ

2σz

2+¯

hΩ

2σx

2.(1)

Here, σi

jis the σiPauli operator acting on the j-th qubit, ap-

propriately tensored with the identity operators on the other

qubits. The real constants J,δand Ωdeﬁne interaction

strengths. We simulated numerically the time evolution under

the Hamiltonian (1) for a time of π/Ωand δ=2J. We found

that Ω≈1.1Jallows for a ≈99% classical Toffoli gate ﬁdelity

while minimising the gate time (see Supplemental Material).

Ions conﬁned in a linear Paul trap are natural candidates to

implement the Hamiltonian (1)30,31. We use 171Yb+ions con-

ﬁned in a linear Paul trap, with a superimposed static magnetic

ﬁeld gradient32. The qubit states |0⟩and |1⟩are the two hy-

perﬁne states of the electronic ground state 2S1/2with total

angular momentum quantum number and magnetic quantum

number |F,mF⟩=|0,0⟩and |1,1⟩, connected by a magnetic

dipole resonance near 2π×12.6GHz. The |1⟩state is sensi-

tive to the magnetic ﬁeld, which is position dependent, shift-

ing individually the ions’ resonances and, thus, allowing for

individual addressing by tuning the microwave ﬁeld driving

the qubit resonance33 For high ﬁdelity single qubit rotations,

the ion crystal is cooled close to its motional groundstate us-

ing a sympathetic side-band cooling34.

When irradiating the ions with a microwave ﬁeld with phase

φand frequency ωx, nearly resonant with the frequency ω2of

qubit 2, the ionic qubits are subject to the Hamiltonian

H(i)=∑

i̸=j

hJi j

2σz

iσz

| {z }

Hzz

+∑

hωjσz

2+¯

hΩcos(ωxt+φ)σx

2.(2)

Here, ωiis the resonance frequency of the ith ion. The two-

qubit couplings Ji j in a magnetic ﬁeld gradient are mediated

by the Coulomb interaction31,32. In the setup used here, the

magnetic ﬁeld gradient is 19.1 T/m at a secular axial trap

frequency of ωT=2π×128.4(1)kHz, and J12 =J23 =J≈

2π×31Hz, which implies a gate time of π/1.1J≈14.9 ms.

The additional J13σz

1σz

3coupling contributes with a complex

phase in the computational basis, which is irrelevant for clas-

sical computation, so we choose to omit it. Finally, Ωis deter-

mined by the amplitude of the incident microwave radiation.

Hzz is the Hamiltonian generating the required spin-spin in-

teraction via magnetic gradient induced coupling (MAGIC).

Cross-talk between qubits was neglected; its main source is

the non-resonant excitation of neighbouring qubits which has

been measured to be on the order 10−5 33. Choosing a detun-

ing δ, such that ωx=ω2−δ, and in an appropriate rotating

frame, HIreads as

H(i)

I≈Hzz +¯

hδ

2σz

2+¯

hΩ

2cos(φ)σx

2+sin(φ)σy

2,(3)

with an error of O(Ω/(2ω2−2δ))30. Choosing φ=0 recov-

ers the Hamiltonian (1).

Fluctuations in the magnetic ﬁeld dephase the qubits, which

are ﬁrst-order sensitive to them. Not using passive magnetic

shielding and active compensation, the coherence time in this

setup is ≈200µs35 – two orders of magnitude lower than our

gate times. We thus employ Dynamical Decoupling (DD) to

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ClassicalHalf-AdderusingTrapped-ionQuantumBits:TowardsEnergy-efficientComputationSagarSilvaPratapsi,1,2,a)PatrickH.Huber,3,a)PatrickBarthel,3SougatoBose,4ChristofWunderlich,3,a)andYasserOmar1,5,6,a)1)InstitutoSuperiorTécnico,UniversityofLisbon,Lisbon1049-001,Portugal.2)InstitutodeTelecomunicações,Li...

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