Zoe Holmes
@qzoeholmes.bsky.social
Quantum physicist. Assistant Prof at EPFL. Climber.
Among todays mad arxiv overflow is our preprint:
"When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits"
We introduce a path propagation classical simulation alg for bosonic circuits
And find a funky interplay between quantum resources and noise
🧵👇
"When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits"
We introduce a path propagation classical simulation alg for bosonic circuits
And find a funky interplay between quantum resources and noise
🧵👇
October 9, 2025 at 11:48 AM
Among todays mad arxiv overflow is our preprint:
"When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits"
We introduce a path propagation classical simulation alg for bosonic circuits
And find a funky interplay between quantum resources and noise
🧵👇
"When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits"
We introduce a path propagation classical simulation alg for bosonic circuits
And find a funky interplay between quantum resources and noise
🧵👇
And we have found one… we provide numerical evidence that our problem lives in the Goldilocks zone:
- trainable (no exponential concentration)
- not classically surrogatable (thanks to high entanglement + magic)
- trainable (no exponential concentration)
- not classically surrogatable (thanks to high entanglement + magic)
October 2, 2025 at 1:23 PM
And we have found one… we provide numerical evidence that our problem lives in the Goldilocks zone:
- trainable (no exponential concentration)
- not classically surrogatable (thanks to high entanglement + magic)
- trainable (no exponential concentration)
- not classically surrogatable (thanks to high entanglement + magic)
More concretely, we show that for a range of moderate entangling strengths the landscape is unimodal but non-separable landscapes.
Then numerics show adaptive hill-climbing converges efficiently
But non-adaptive approaches - blow up exponentially.
Then numerics show adaptive hill-climbing converges efficiently
But non-adaptive approaches - blow up exponentially.
October 2, 2025 at 1:23 PM
More concretely, we show that for a range of moderate entangling strengths the landscape is unimodal but non-separable landscapes.
Then numerics show adaptive hill-climbing converges efficiently
But non-adaptive approaches - blow up exponentially.
Then numerics show adaptive hill-climbing converges efficiently
But non-adaptive approaches - blow up exponentially.
We translate that logic into a quantum recompilation task
The hidden string = the placement of T-gates between layers of semi-random unitaries
Goal = uncover the T gates positions
As in LeadingOnes, identifying early T-gates helps you make progress, but you can’t optimize each gate independently
The hidden string = the placement of T-gates between layers of semi-random unitaries
Goal = uncover the T gates positions
As in LeadingOnes, identifying early T-gates helps you make progress, but you can’t optimize each gate independently
October 2, 2025 at 1:23 PM
We translate that logic into a quantum recompilation task
The hidden string = the placement of T-gates between layers of semi-random unitaries
Goal = uncover the T gates positions
As in LeadingOnes, identifying early T-gates helps you make progress, but you can’t optimize each gate independently
The hidden string = the placement of T-gates between layers of semi-random unitaries
Goal = uncover the T gates positions
As in LeadingOnes, identifying early T-gates helps you make progress, but you can’t optimize each gate independently
Our task is a quantum twist on the classic LeadingOnes-OneMax problem.
In this problem you're trying to learn a hidden bitstring.
Your score = how many leading bits match the target before the first mismatch.
So 1110… matches 1101 better than 1011… even if they have the same Hamming weight.
In this problem you're trying to learn a hidden bitstring.
Your score = how many leading bits match the target before the first mismatch.
So 1110… matches 1101 better than 1011… even if they have the same Hamming weight.
October 2, 2025 at 1:23 PM
Our task is a quantum twist on the classic LeadingOnes-OneMax problem.
In this problem you're trying to learn a hidden bitstring.
Your score = how many leading bits match the target before the first mismatch.
So 1110… matches 1101 better than 1011… even if they have the same Hamming weight.
In this problem you're trying to learn a hidden bitstring.
Your score = how many leading bits match the target before the first mismatch.
So 1110… matches 1101 better than 1011… even if they have the same Hamming weight.
We provide evidence of an exponential gap between adaptive & nonadaptive strategies for a quantum recompilation task
Key takeaways:
- Entanglement isn’t always a roadblock: its degree can aid training
- Discrete optimization may be key to finding sweet spots between concentration & surrogation
Key takeaways:
- Entanglement isn’t always a roadblock: its degree can aid training
- Discrete optimization may be key to finding sweet spots between concentration & surrogation
October 2, 2025 at 1:23 PM
We provide evidence of an exponential gap between adaptive & nonadaptive strategies for a quantum recompilation task
Key takeaways:
- Entanglement isn’t always a roadblock: its degree can aid training
- Discrete optimization may be key to finding sweet spots between concentration & surrogation
Key takeaways:
- Entanglement isn’t always a roadblock: its degree can aid training
- Discrete optimization may be key to finding sweet spots between concentration & surrogation
We thank the reviewer for bringing this citation to our attention...
July 22, 2025 at 2:57 PM
We thank the reviewer for bringing this citation to our attention...
Why should you care about any of this?
In all honesty, we partially just think these are cool observations.
But also we need more quantum algorithmic primitives but coming up with them is hard!
And we hope that maybe these thermodynamic/geometric insights could help with novel alg design?
In all honesty, we partially just think these are cool observations.
But also we need more quantum algorithmic primitives but coming up with them is hard!
And we hope that maybe these thermodynamic/geometric insights could help with novel alg design?
July 22, 2025 at 12:25 PM
Why should you care about any of this?
In all honesty, we partially just think these are cool observations.
But also we need more quantum algorithmic primitives but coming up with them is hard!
And we hope that maybe these thermodynamic/geometric insights could help with novel alg design?
In all honesty, we partially just think these are cool observations.
But also we need more quantum algorithmic primitives but coming up with them is hard!
And we hope that maybe these thermodynamic/geometric insights could help with novel alg design?
Finally, we show that quantum signal processing can be used to implement imaginary time evolution for unstructured search without post selection.
And this enables us to design a new `fixed-point' quantum search algorithm
i.e., a Grover type algorithm that never overshoots the solution
And this enables us to design a new `fixed-point' quantum search algorithm
i.e., a Grover type algorithm that never overshoots the solution
July 22, 2025 at 12:25 PM
Finally, we show that quantum signal processing can be used to implement imaginary time evolution for unstructured search without post selection.
And this enables us to design a new `fixed-point' quantum search algorithm
i.e., a Grover type algorithm that never overshoots the solution
And this enables us to design a new `fixed-point' quantum search algorithm
i.e., a Grover type algorithm that never overshoots the solution
We then take this perspective further and show that:
- The imaginary time dynamics trace the shortest path between the initial and the solution states in complex projective space
- The geodesic length of ITE determines the query complexity of Grover’s algorithm
- The imaginary time dynamics trace the shortest path between the initial and the solution states in complex projective space
- The geodesic length of ITE determines the query complexity of Grover’s algorithm
July 22, 2025 at 12:25 PM
We then take this perspective further and show that:
- The imaginary time dynamics trace the shortest path between the initial and the solution states in complex projective space
- The geodesic length of ITE determines the query complexity of Grover’s algorithm
- The imaginary time dynamics trace the shortest path between the initial and the solution states in complex projective space
- The geodesic length of ITE determines the query complexity of Grover’s algorithm
Then we notice that imaginary time evolution can be implemented via a Double Bracket Flow (essentially the exponential of a commutator between the input state and the target Hamiltonian)...
And this in turn can be approximated by a product formula...
And when you do out pops Grover's algorithm!
And this in turn can be approximated by a product formula...
And when you do out pops Grover's algorithm!
July 22, 2025 at 12:25 PM
Then we notice that imaginary time evolution can be implemented via a Double Bracket Flow (essentially the exponential of a commutator between the input state and the target Hamiltonian)...
And this in turn can be approximated by a product formula...
And when you do out pops Grover's algorithm!
And this in turn can be approximated by a product formula...
And when you do out pops Grover's algorithm!
The first step to seeing this is to note that unstructured search can be formulated as a ground state problem
And ground state problems can be solved (in the long time limit) by imaginary time evolution...
And ground state problems can be solved (in the long time limit) by imaginary time evolution...
July 22, 2025 at 12:25 PM
The first step to seeing this is to note that unstructured search can be formulated as a ground state problem
And ground state problems can be solved (in the long time limit) by imaginary time evolution...
And ground state problems can be solved (in the long time limit) by imaginary time evolution...
Here's a new perspective on why Grover’s algorithm algorithm works:
Unstructured search can be written as ground state problem.
Then Grover's is just a product formula approximation of imaginary-time evolution
or, equivalently, a Riemannian gradient flow on SU(d)
to find this ground state.
Unstructured search can be written as ground state problem.
Then Grover's is just a product formula approximation of imaginary-time evolution
or, equivalently, a Riemannian gradient flow on SU(d)
to find this ground state.
July 22, 2025 at 12:25 PM
Here's a new perspective on why Grover’s algorithm algorithm works:
Unstructured search can be written as ground state problem.
Then Grover's is just a product formula approximation of imaginary-time evolution
or, equivalently, a Riemannian gradient flow on SU(d)
to find this ground state.
Unstructured search can be written as ground state problem.
Then Grover's is just a product formula approximation of imaginary-time evolution
or, equivalently, a Riemannian gradient flow on SU(d)
to find this ground state.
To counterbalance the meme above, let me stress that while Pauli prop can compete with state of the art, it has weak spots
For example, it's a bad idea to use Pauli prop for EXACT simulations. Even at small sizes, exact Pauli prop can kill your memory- it is better used for quick rough estimates
For example, it's a bad idea to use Pauli prop for EXACT simulations. Even at small sizes, exact Pauli prop can kill your memory- it is better used for quick rough estimates
June 2, 2025 at 3:01 PM
To counterbalance the meme above, let me stress that while Pauli prop can compete with state of the art, it has weak spots
For example, it's a bad idea to use Pauli prop for EXACT simulations. Even at small sizes, exact Pauli prop can kill your memory- it is better used for quick rough estimates
For example, it's a bad idea to use Pauli prop for EXACT simulations. Even at small sizes, exact Pauli prop can kill your memory- it is better used for quick rough estimates
Retweeting this for the folks (myself included) that weren't online over the long weekend
PauliPropagation.jl is open source library that you can use to approximately simulate quantum circuits
We explain the nitty gritty of how these algorithms work in practise in our latest companion paper
🧵👇
PauliPropagation.jl is open source library that you can use to approximately simulate quantum circuits
We explain the nitty gritty of how these algorithms work in practise in our latest companion paper
🧵👇
June 2, 2025 at 3:01 PM
Retweeting this for the folks (myself included) that weren't online over the long weekend
PauliPropagation.jl is open source library that you can use to approximately simulate quantum circuits
We explain the nitty gritty of how these algorithms work in practise in our latest companion paper
🧵👇
PauliPropagation.jl is open source library that you can use to approximately simulate quantum circuits
We explain the nitty gritty of how these algorithms work in practise in our latest companion paper
🧵👇
Given these strengths (no post selection) / caveats (circuit depths scale super exponentially with polynomial order)
We see DB-QSP as most useful to deterministically implement low order polynomials in cases where the success probability of other methods is so small as to not be worth doing.
We see DB-QSP as most useful to deterministically implement low order polynomials in cases where the success probability of other methods is so small as to not be worth doing.
April 3, 2025 at 5:16 PM
Given these strengths (no post selection) / caveats (circuit depths scale super exponentially with polynomial order)
We see DB-QSP as most useful to deterministically implement low order polynomials in cases where the success probability of other methods is so small as to not be worth doing.
We see DB-QSP as most useful to deterministically implement low order polynomials in cases where the success probability of other methods is so small as to not be worth doing.
Today we posted a paper showing how a double-bracket quantum algorithm can implement quantum signal processing (DB-QSP), i.e., apply polynomial functions of operators to states.
Crucially our approach doesn't need any post-selection - but this comes at the expense of increased circuit depths.
Crucially our approach doesn't need any post-selection - but this comes at the expense of increased circuit depths.
April 3, 2025 at 5:16 PM
Today we posted a paper showing how a double-bracket quantum algorithm can implement quantum signal processing (DB-QSP), i.e., apply polynomial functions of operators to states.
Crucially our approach doesn't need any post-selection - but this comes at the expense of increased circuit depths.
Crucially our approach doesn't need any post-selection - but this comes at the expense of increased circuit depths.
We show how Majorana Propagation can be used with a variational algorithm (essentially a classical simulation of a Majorana version of adapt-VQE) to learn circuits to prepare approx ground states...
These could be used to initialize your favourite quantum alg for ground state energy estimates.
These could be used to initialize your favourite quantum alg for ground state energy estimates.
March 25, 2025 at 4:21 PM
We show how Majorana Propagation can be used with a variational algorithm (essentially a classical simulation of a Majorana version of adapt-VQE) to learn circuits to prepare approx ground states...
These could be used to initialize your favourite quantum alg for ground state energy estimates.
These could be used to initialize your favourite quantum alg for ground state energy estimates.
Under the raw scheme the number of terms blow up exponentially… but `coefficient' and `Majorana length’ truncations keep it efficient.
Intuitively, high-length monomials are unlikely to contribute to expectation values (and tend not to flow back in unstructured circuits) and so can be dropped.
Intuitively, high-length monomials are unlikely to contribute to expectation values (and tend not to flow back in unstructured circuits) and so can be dropped.
March 25, 2025 at 4:21 PM
Under the raw scheme the number of terms blow up exponentially… but `coefficient' and `Majorana length’ truncations keep it efficient.
Intuitively, high-length monomials are unlikely to contribute to expectation values (and tend not to flow back in unstructured circuits) and so can be dropped.
Intuitively, high-length monomials are unlikely to contribute to expectation values (and tend not to flow back in unstructured circuits) and so can be dropped.
The algorithm is inspired by Pauli Propagation but is tailored to Fermionic (rather than spin) systems.
Like Pauli propagation, the algorithm works in the Heisenberg picture but this time we back propagate Majorana monomials and then overlap them with an initial state.
Like Pauli propagation, the algorithm works in the Heisenberg picture but this time we back propagate Majorana monomials and then overlap them with an initial state.
March 25, 2025 at 4:21 PM
The algorithm is inspired by Pauli Propagation but is tailored to Fermionic (rather than spin) systems.
Like Pauli propagation, the algorithm works in the Heisenberg picture but this time we back propagate Majorana monomials and then overlap them with an initial state.
Like Pauli propagation, the algorithm works in the Heisenberg picture but this time we back propagate Majorana monomials and then overlap them with an initial state.
Hey! On the arXiv today we present `Majorana Propagation’ a new classical algorithm for simulating Fermionic circuits.
Depending on your mood... the algorithm can be viewed either as naturally suited to compete with, or collaboratively enhance, quantum hardware simulations.
Depending on your mood... the algorithm can be viewed either as naturally suited to compete with, or collaboratively enhance, quantum hardware simulations.
March 25, 2025 at 4:21 PM
Hey! On the arXiv today we present `Majorana Propagation’ a new classical algorithm for simulating Fermionic circuits.
Depending on your mood... the algorithm can be viewed either as naturally suited to compete with, or collaboratively enhance, quantum hardware simulations.
Depending on your mood... the algorithm can be viewed either as naturally suited to compete with, or collaboratively enhance, quantum hardware simulations.
We can prove that in a polynomially shrinking width region around a minima (and often around zero) there is no barren plateau
The proofs get long but the intuition is borderline trivial: as quantum losses are smooth, the region around a point with some curvature must have non-vanishing gradients
The proofs get long but the intuition is borderline trivial: as quantum losses are smooth, the region around a point with some curvature must have non-vanishing gradients
February 14, 2025 at 2:06 AM
We can prove that in a polynomially shrinking width region around a minima (and often around zero) there is no barren plateau
The proofs get long but the intuition is borderline trivial: as quantum losses are smooth, the region around a point with some curvature must have non-vanishing gradients
The proofs get long but the intuition is borderline trivial: as quantum losses are smooth, the region around a point with some curvature must have non-vanishing gradients
Here we take steps to understanding the potential of warm starts for VQAs
We provide a general variance lower bound for patches of loss landscapes:
- for both structured and unstructured circuits
- to provide small-angle-initialization 'guarantees'
- to study the scaling of regions of attraction
We provide a general variance lower bound for patches of loss landscapes:
- for both structured and unstructured circuits
- to provide small-angle-initialization 'guarantees'
- to study the scaling of regions of attraction
February 14, 2025 at 2:06 AM
Here we take steps to understanding the potential of warm starts for VQAs
We provide a general variance lower bound for patches of loss landscapes:
- for both structured and unstructured circuits
- to provide small-angle-initialization 'guarantees'
- to study the scaling of regions of attraction
We provide a general variance lower bound for patches of loss landscapes:
- for both structured and unstructured circuits
- to provide small-angle-initialization 'guarantees'
- to study the scaling of regions of attraction
@kunalq.bsky.social did at least also show us a sexy fridge
February 12, 2025 at 3:26 AM
@kunalq.bsky.social did at least also show us a sexy fridge
For the random circuit connoisseurs among you, I'd also like to highlight @aangrisani.bsky.social admirable efforts to reduce the randomness assumptions on the circuit - introducing a bunch of handy definitions/identities in the process.
Check out the early appendices if you're that way inclined.
Check out the early appendices if you're that way inclined.
January 28, 2025 at 8:37 PM
For the random circuit connoisseurs among you, I'd also like to highlight @aangrisani.bsky.social admirable efforts to reduce the randomness assumptions on the circuit - introducing a bunch of handy definitions/identities in the process.
Check out the early appendices if you're that way inclined.
Check out the early appendices if you're that way inclined.