Digital Twins for Quantum Hardware: Multi-formalism and Mixed-signal

Stefan Krastanov | MIT ⟶ UMass Amherst

The Quantum Technology Stack

Materials

Analog Control

Noisy Digital Circuits

Error Correction

Quantum Algorithms

Analog Quantum Hardware

Room-Temperature Optical Quantum Computing

Multimode cavity in a nonlinear optical medium¹
  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities
Multimode cavity¹
... and its spectrum
\[ \hat{H} = \hat{a}^\dagger \hat{b}\hat{b} + p(t)\hat{b}^\dagger\hat{c} + H.c. \]
  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities
\[ \hat{H} = \htmlClass{bc0}{\hat{a}^\dagger} \htmlClass{bc1}{\hat{b}\hat{b}} + \htmlClass{bc4}{p(t)} \htmlClass{bc1}{\hat{b}^\dagger} \htmlClass{bc2}{\hat{c}} + H.c. \]
  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities
\[ \hat{H} = \htmlClass{bc0}{\hat{a}^\dagger} \htmlClass{bc1}{\hat{b}\hat{b}} + \htmlClass{bc4}{p(t)} \htmlClass{bc1}{\hat{b}^\dagger} \htmlClass{bc2}{\hat{c}} + H.c. \]

A rather "poor" Hamiltonian...

  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities

Can be twisted into something useful:

Can be twisted into something useful:
Full error correction

\[\begin{aligned} |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{1}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{3}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{0}\rangle \\ \end{aligned}\]

Can be twisted into something useful:
Full error correction

\[\begin{aligned} |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{1}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{3}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{0}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{2}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{2}\htmlClass{bc2}{1}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{1}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{2}\htmlClass{bc2}{0}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{0}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{0}\htmlClass{bc2}{1}\rangle \\ \end{aligned}\]

Can be twisted into something useful:
Full error correction

\[\begin{aligned} |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{1}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{3}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{4}\htmlClass{bc2}{0}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{2}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{2}\htmlClass{bc2}{1}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{1}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{2}\htmlClass{bc2}{0}\rangle \\ |\htmlClass{bc0}{0}\htmlClass{bc1}{0}\htmlClass{bc2}{1}\rangle \rightarrow & |\htmlClass{bc0}{0}\htmlClass{bc1}{0}\htmlClass{bc2}{1}\rangle \\ \end{aligned}\]
Coherent feedback-free error correcting circuit for a \(\left\{|22\rangle,\frac{|40\rangle+|04\rangle}{\sqrt{2}}\right\}\) code.

Is this a realistic device?

\(\times 10^{10}\) of magnitude improvement in figures of merit in just 10 years...

Similar design work

Similar design work

Near-term² photonic hardware and accelerators for classical computation³
  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities
  2. Krastanov et al.
    Controlled-Phase Gate by Dynamic Coupling of Photons to a Two-Level Emitter
  3. Basani, …, Krastanov
    All-Photonic Artificial Neural Network Processor Via Non-linear Optics

Similar design work

Near-term² photonic hardware and accelerators for classical computation³
Control⁴ and networking⁵ of microwave devices
  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities
  2. Krastanov et al.
    Controlled-Phase Gate by Dynamic Coupling of Photons to a Two-Level Emitter
  3. Basani, …, Krastanov
    All-Photonic Artificial Neural Network Processor Via Non-linear Optics
  4. Krastanov et al.
    Universal control of an oscillator with dispersive coupling to a qubit
  5. Krastanov et al.
    Optically-Heralded Entanglement of Superconducting Systems in Quantum Networks

Similar design work

Near-term² photonic hardware and accelerators for classical computation³
Control⁴ and networking⁵ of microwave devices
Spin-mechanics interfaces⁶
  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities
  2. Krastanov et al.
    Controlled-Phase Gate by Dynamic Coupling of Photons to a Two-Level Emitter
  3. Basani, …, Krastanov
    All-Photonic Artificial Neural Network Processor Via Non-linear Optics
  4. Krastanov et al.
    Universal control of an oscillator with dispersive coupling to a qubit
  5. Krastanov et al.
    Optically-Heralded Entanglement of Superconducting Systems in Quantum Networks
  6. Raniwala*, Krastanov* et al.
    A spin-optomechanical quantum interface [...]

Better Tools for these Analog Control Problems

Take an Machine Learning view of control problems¹².
  1. Krastanov et al.
    Unboxing Quantum Black Box Models [...]
  2. Krastanov et al.
    Stochastic estimation of dynamical variables
Example with the Nakajima-Zwanzig master equation¹:
\(\frac{\mathrm{d}\rho}{\mathrm{d}t}= -i\left[H,\rho(t)\right]+\int_0^t\mathcal{K}(\tau)\mathcal{D}\left(L,\rho(t-\tau)\right)\mathrm{d}\tau\)
  1. Krastanov et al.
    Unboxing Quantum Black Box Models [...]

Less Pretentious Version of the Same Statement

Use automatic differentiation and stochastic gradient descent more, you will be surprised by the high quality of the results.

Digital Quantum Hardware

This either means "Clifford Circuits"
or "Quantum Supremacy"

Noisy Clifford Circuits

Purification of entanglement

\[\begin{aligned} A=|\phi_{+}\rangle=\frac{|00\rangle+|11\rangle}{\sqrt{2}}\\ B=|\psi_{-}\rangle=\frac{|01\rangle-|10\rangle}{\sqrt{2}}\\ C=|\psi_{+}\rangle=\frac{|01\rangle+|10\rangle}{\sqrt{2}}\\ D=|\phi_{-}\rangle=\frac{|00\rangle-|11\rangle}{\sqrt{2}} \end{aligned}\]
Simple entanglement purification circuit
Entanglement purification circuits can be quite complex.

Optimized circuits for purification¹, better than any known circuits.

  1. Krastanov et al.
    Optimized Entanglement Purification

Optimized circuits for purification¹, better than any known circuits.

Turns out they are also "the best" after exhaustive comparision².

  1. Krastanov et al.
    Optimized Entanglement Purification
  2. Jansen et al. @ Delft
    Enumerating all bilocal Clifford distillation protocols through symmetry reduction

Ongoing work

n-to-k purification circuits¹

Assymptotically faster simulations of purification circuits²

  1. Delft and MIT friends
  2. Ge, Krastanov
    Simulating Entangled States and Purification Circuits Faster than the Stabilizer Tableaux Formalism

Generating Good Error Correcting Codes

Fast evaluation of Clifford Circuits helps with the design of error correction codes¹

  1. Gullans et al.
    Quantum Coding with Low-Depth Random Circuits

Tools: Simulators for Noisy Clifford Circuits

QuantumClifford.jl

  • Tableau Algebra
  • Random Cliffords
  • Destabilizers
  • Symbolic
  • Fast

Tools: QuantumClifford.jl is fast


              julia> a = random_pauli(1_000_000_000);
              julia> b = random_pauli(1_000_000_000);
              julia> @benchmark QuantumClifford.mul_left!(a,b)
              Time  (median):     32.246 ms

Tools: QuantumClifford.jl lets you study symbolic structure

A noisy purification circuit


              g1 = sCNOT(1,3)
              g2 = sCNOT(2,4)
              m = BellMeasurement(...)
              v = VerifyOp(...)
              n = NoiseOpAll(epsilon)
              

              failure       = 4e*((1 - 3e)^3)
              false_success = 6e*((1 - 3e)^3)
              true_success  = (1 - 3e)^4 + ...

Tools: Ongoing work

GPU accelerated Clifford Circuits¹

Code libraries²

  1. El Dandachi, Krastanov
  2. Garcés, Krastanov

Full-Stack Design and Optimization Toolkit

Types of Dynamics

Types of Dynamics

Continuous:
Hamiltonians, Master Equations

Types of Dynamics

Continuous:
Hamiltonians, Master Equations
Discrete:
Gates, Circuits

Types of Dynamics

Continuous:
Hamiltonians, Master Equations
Discrete:
Gates, Circuits
Stochastic:
Weak Measurements, Feedback

State Representation

Kets and density matrices
Tableaux and graphs
Matrix product states and tensor network states
We need a tool to seamlessly mix these diverse formalisms.

Continuous evolution at one layer, followed by noisy Clifford circuit simulator...

... and discrete event simulators

... and support for symbolic algebra systems

... running on computational accelerators like GPUs

... support for other formalisms

... all of this, with auto-differentiation and reverse design

QuantumSavory.jl

QuantumSavory.jl

QuantumSavory.jl

QuantumSavory.jl

QuantumSavory.jl

QuantumSavory.jl: A tool for analog and digital quantum hardware design.

Automatic tracking of noise processes

Automatic conversion between representations


              Int * Float ⟶ Float
              Ket ⊗ Density Matrix ⟶ Density Matrix
              Ket ⊗ Tableau ⟶ Ket
              Ket ⊗ Tableau ⟶ Twirled Density Matrix ???

First-gen Quantum Repeater Example

Neighbor-entangler without a swapper.

              for (;src, dst) in edges(mgraph)
                  @process entangler(sim, mgraph, src, dst, ...)
              end
Full repeater sim with automatic instrumentation.

              for (;src, dst) in edges(mgraph)
                  @process entangler(sim, mgraph, src, dst, ...)
              end
              for node in vertices(mgraph)
                  @process swapper(sim, mgraph, node, ...)
              end
              for (;src, dst) in all_node_pairs(mgraph)
                  @process entangler(sim, mgraph, src, dst, ...)
              end
Simulating the Sandia/MIT/Mitre Quantum Moonshot architecture¹
  1. Dong et al.
    High-speed programmable photonic circuits in a cryogenically compatible, visible–near-infrared 200 mm CMOS architecture
Such tools would be crucial for the design of

low-level hardware control,

resource purification,

optimization of error-correcting codes,

quantum network protocols,

and generally co-design across the layers of the technology stack.

Try out QuantumClifford.jl - it is public and stable

Be an early tester for QuantumSavory.jl

Consider a postdoc at UMass Amherst:

Design of optical/mechanical/spin devices with Sandia, Mitre, and MIT.

Creating new tools for the entire community.