Algorithms · Quantum linear algebra
Hybrid HHL++ for portfolio optimization
Adapt the Harrow-Hassidim-Lloyd (HHL) quantum linear-systems algorithm, most of whose components current noisy quantum hardware cannot reach, into a form that near-term devices can actually execute, and demonstrate it on an application.
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- Record typeLiterature reference
- Reference implementationhybrid_hhl_for_portfolio_optimization
- Reported costNot stated by the sources read
- Papers1
A part this method uses, worked through
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— here is a concrete, runnable instance of it.
Phase estimation of P(3*pi/4)
3 counting qubits estimating the phase of P(3π/4), which is 2π·3/8 exactly: a phase 3-bit QPE can represent exactly.
Where it ends up
- 1011100%
The counting register reads 011 = 3 with probability 1: angle/(2π) = 3/8, recovered exactly.
One of its steps changes only phase: the outcome probabilities stay put while the state does not.
Open this part in StudioAdapt the Harrow-Hassidim-Lloyd (HHL) quantum linear-systems algorithm, most of whose components current noisy quantum hardware cannot reach, into a form that near-term devices can actually execute, and demonstrate it on an application. Yalovetzky, Minssen, Herman and Pistoia work on the gap between near-term-friendly proposals for the Harrow-Hassidim-Lloyd (HHL) algorithm — a quantum linear-algebra primitive whose components the abstract says are largely out of reach of noisy intermediate-scale quantum devices — and the circuits that can actually run on noisy hardware today. Building on the Hybrid HHL algorithm proposed by Lee and colleagues, the authors propose two modifications that together give their algorithm, Hybrid HHL++: a novel algorithm for choosing a scaling factor for the linear-system matrix that maximizes the use of the ancillary qubits allocated to HHL's phase-estimation component, and a heuristic for compressing the HHL circuit. They demonstrate the modified algorithm by running it on Quantinuum System Model H-series trapped-ion quantum computers, solving different instances of small-scale portfolio-optimization problems, which the abstract calls the largest experimental demonstrations of HHL for an application to date. The abstract frames this against the broader difficulty of application-oriented benchmarking of current quantum hardware, which it says the limited scale of most quantum-algorithmic demonstrations makes hard to perform.
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No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
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No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
Yalovetzky, Minssen, Herman and Pistoia work on the gap between near-term-friendly proposals for the Harrow-Hassidim-Lloyd (HHL) algorithm — a quantum linear-algebra primitive whose components the abstract says are largely out of reach of noisy intermediate-scale quantum devices — and the circuits that can actually run on noisy hardware today. Building on the Hybrid HHL algorithm proposed by Lee and colleagues, the authors propose two modifications that together give their algorithm, Hybrid HHL++: a novel algorithm for choosing a scaling factor for the linear-system matrix that maximizes the use of the ancillary qubits allocated to HHL's phase-estimation component, and a heuristic for compressing the HHL circuit. They demonstrate the modified algorithm by running it on Quantinuum System Model H-series trapped-ion quantum computers, solving different instances of small-scale portfolio-optimization problems, which the abstract calls the largest experimental demonstrations of HHL for an application to date. The abstract frames this against the broader difficulty of application-oriented benchmarking of current quantum hardware, which it says the limited scale of most quantum-algorithmic demonstrations makes hard to perform. The sources read state no complexity bound for this record (The abstract of arXiv:2110.15958, the only source read for this record, states no complexity bound: no big-O expression, no run time, no qubit or gate count, and no scaling with the size of the linear system, the condition number, or any error parameter. What it states is a design contribution — "we propose two modifications to the Hybrid HHL algorithm proposed by Lee etal. leading to our algorithm Hybrid HHL++" — namely "a novel algorithm for determining a scaling factor for the linear system matrix that maximizes the utility of the amount of ancillary qubits allocated to the phase estimation component of HHL" and "a heuristic for compressing the HHL circuit" — and a hardware claim: "We demonstrate the efficacy of our work by running our modified Hybrid HHL on Quantinuum System Model H-series trapped-ion quantum computers to solve different problem instances of small-scale portfolio optimization problems, leading to the largest experimental demonstrations of HHL for an application to date." The demonstration this record covers states no complexity bound of its own. The field is therefore left empty on purpose rather than filled with a bound written from memory.).
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
- Record type
- Literature reference
- Reference implementation
- hybrid_hhl_for_portfolio_optimization
- Reported cost
- Not stated by the sources read
- Complexity basis
- The abstract of arXiv:2110.15958, the only source read for this record, states no complexity bound: no big-O expression, no run time, no qubit or gate count, and no scaling with the size of the linear system, the condition number, or any error parameter. What it states is a design contribution — "we propose two modifications to the Hybrid HHL algorithm proposed by Lee etal. leading to our algorithm Hybrid HHL++" — namely "a novel algorithm for determining a scaling factor for the linear system matrix that maximizes the utility of the amount of ancillary qubits allocated to the phase estimation component of HHL" and "a heuristic for compressing the HHL circuit" — and a hardware claim: "We demonstrate the efficacy of our work by running our modified Hybrid HHL on Quantinuum System Model H-series trapped-ion quantum computers to solve different problem instances of small-scale portfolio optimization problems, leading to the largest experimental demonstrations of HHL for an application to date." The demonstration this record covers states no complexity bound of its own. The field is therefore left empty on purpose rather than filled with a bound written from memory.
- Circuit
- Not supplied
This record is not a concrete circuit.
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ALGORITHM: Hybrid HHL++ for portfolio optimization
PROBLEM: Adapt the Harrow-Hassidim-Lloyd (HHL) quantum linear-systems algorithm, most of whose components current noisy quantum hardware cannot reach, into a form that near-term devices can actually execute, and demonstrate it on an application.
IDEA: Yalovetzky, Minssen, Herman and Pistoia work on the gap between near-term-friendly proposals for the Harrow-Hassidim-Lloyd (HHL) algorithm — a quantum linear-algebra primitive whose components the abstract says are largely out of reach of noisy intermediate-scale quantum devices — and the circuits that can actually run on noisy hardware today. Building on the Hybrid HHL algorithm proposed by Lee and colleagues, the authors propose two modifications that together give their algorithm, Hybrid HHL++: a novel algorithm for choosing a scaling factor for the linear-system matrix that maximizes the use of the ancillary qubits allocated to HHL's phase-estimation component, and a heuristic for compressing the HHL circuit. They demonstrate the modified algorithm by running it on Quantinuum System Model H-series trapped-ion quantum computers, solving different instances of small-scale portfolio-optimization problems, which the abstract calls the largest experimental demonstrations of HHL for an application to date. The abstract frames this against the broader difficulty of application-oriented benchmarking of current quantum hardware, which it says the limited scale of most quantum-algorithmic demonstrations makes hard to perform.
REPORTED COST: Not stated by the sources read
BASIS: The abstract of arXiv:2110.15958, the only source read for this record, states no complexity bound: no big-O expression, no run time, no qubit or gate count, and no scaling with the size of the linear system, the condition number, or any error parameter. What it states is a design contribution — "we propose two modifications to the Hybrid HHL algorithm proposed by Lee etal. leading to our algorithm Hybrid HHL++" — namely "a novel algorithm for determining a scaling factor for the linear system matrix that maximizes the utility of the amount of ancillary qubits allocated to the phase estimation component of HHL" and "a heuristic for compressing the HHL circuit" — and a hardware claim: "We demonstrate the efficacy of our work by running our modified Hybrid HHL on Quantinuum System Model H-series trapped-ion quantum computers to solve different problem instances of small-scale portfolio optimization problems, leading to the largest experimental demonstrations of HHL for an application to date." The demonstration this record covers states no complexity bound of its own. The field is therefore left empty on purpose rather than filled with a bound written from memory.
PRIMARY SOURCE: Romina Yalovetzky, Pierre Minssen, Dylan Herman, Marco Pistoia (2021), Solving Linear Systems on Quantum Hardware with Hybrid HHL++ — https://arxiv.org/abs/2110.15958
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Where this sits
This record is named by the layer graph at:
- HHL: eigenvalue inversion by phase estimation Method
Takes An access model for — sparse row/column entry oracles, or a block-encoding; a unitary preparing ; a known upper bound on the condition number; the normalisation ; and a target state error . Returns A flagged state -close in to . It does not return , any entry of , or any classical functional of — those cost extra and are decided a layer above.
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- HHL linear-systems reference
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References
- Solving Linear Systems on Quantum Hardware with Hybrid HHL++
Romina Yalovetzky, Pierre Minssen, Dylan Herman, Marco Pistoia · 2021
Primary source: it proposes the two modifications, the scaling-factor algorithm and the circuit-compression heuristic, that define Hybrid HHL++ on top of the Hybrid HHL algorithm of Lee and colleagues, and it reports running the modified algorithm on Quantinuum System Model H-series trapped-ion hardware to solve small-scale portfolio-optimization instances, calling this the largest experimental demonstration of HHL for an application to date. Consult it for how the scaling-factor algorithm and the compression heuristic actually work, for the size and structure of the portfolio-optimization instances solved, and for any complexity or resource analysis, none of which the abstract states.