Full-stack Quantum Hardware Design

Stefan Krastanov | MIT

Computing in the Real Universe

Roman Abacus
Roman Abacus
Inca Quipo
Roman Abacus
Inca Quipo
The Analytical Engine
The Analytical Engine, envisioned by Babbage and Lovelace as a programmable computer two centuries ago¹.

What do the laws of physics permit?

$\vec{x},\vec{p}$

$\frac{\mathrm{d}\vec{x}}{\mathrm{d}t}=\frac{\partial\mathcal{H}}{\partial\vec{p}}\ \dots$

Deterministic

P

$\vec{x},\vec{p}$

$\frac{\mathrm{d}\vec{x}}{\mathrm{d}t}=\frac{\partial\mathcal{H}}{\partial\vec{p}}\ \dots$

Deterministic

P

$\rho\scriptstyle\left(\vec{x},\vec{p}\right)$

$\frac{\partial \rho}{\partial t}=-\left\{\rho,\mathcal{H}\right\}$

Probabilistic

BPP

$\vec{x},\vec{p}$

$\frac{\mathrm{d}\vec{x}}{\mathrm{d}t}=\frac{\partial\mathcal{H}}{\partial\vec{p}}\ \dots$

Deterministic

P

$\rho\scriptstyle\left(\vec{x},\vec{p}\right)$

$\frac{\partial \rho}{\partial t}=-\left\{\rho,\mathcal{H}\right\}$

Probabilistic

BPP

$|\psi\rangle$

$i\hbar\frac{\mathrm{d}\ \ }{\mathrm{d} t}|\psi\rangle=\hat{H}|\psi\rangle$

Quantum

BQP

Why care about a quantum model of computation?

BQP seems bigger than P or BPP.

Useful problems become easy on a quantum device.

Going in the other direction: theoretical computer science can inform theoretical physics.

Where is the Quantum Advantage?

Computing a function on all possible inputs at the same time?

Consider searching for the zero $z$ of a function $\textrm{f}$
$\textrm{f}(z)=0$
$\textrm{f}(x)=1$ for $x\ne z$

$$ \begin{matrix} x_1 \\ x_2 \\ z \end{matrix} $$

possible inputs

$$ \begin{pmatrix} p_{x_1} \\ p_{x_2} \\ p_{z} \end{pmatrix} $$

initial state of the computer

$$ \hat{M} \begin{pmatrix} p_{x_1} \\ p_{x_2} \\ p_{z} \end{pmatrix} $$

executing the program

$$ \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} $$

desired final state

$$ \begin{matrix} x_1 \\ x_2 \\ z \end{matrix} $$

possible inputs

$$ \begin{pmatrix} p_{x_1} \\ p_{x_2} \\ p_{z} \end{pmatrix} $$

initial state of the computer

$$ \hat{M} \begin{pmatrix} p_{x_1} \\ p_{x_2} \\ p_{z} \end{pmatrix} $$

executing the program

$$ \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} $$

desired final state

$\hat{M}$ is "stochastic" in a probabilistic computer
$\hat{M}$ is "unitary" in a quantum computer

What about the bit?

$$ b \in \{0,1\} $$

classical bit

$$ \begin{pmatrix}p_0\\p_1\end{pmatrix} \in \mathbb{R}^2 $$ $$\scriptstyle p_0+p_1=1$$

classical probabilistic bit

$$ \begin{pmatrix}c_0\\c_1\end{pmatrix} \in \mathbb{C}^2$$ $$\scriptstyle |c_0|^2+|c_1|^2=1$$

quantum bit (qubit)

classical bit

classical probabilistic bit

quantum bit (qubit)

Where is the Quantum Advantage?

Interference!
Sometimes the wrong results can interfere destructively!

Why is it taking so long?

The Analytical Engine, envisioned by Babbage and Lovelace as a programmable computer two centuries ago¹.
The Analytical Engine¹.

The first design for error-corrected classical computation².
  2. von Neumann
    The Synthesis of Reliable Organisms […]
More than a hundred years between the conception of programmable machines and their realization.

  2. von Neumann
    The Synthesis of Reliable Organisms […]

The Quantum Technology Stack

Materials

Analog Control

Noisy Digital Circuits

Error Correction

Quantum Algorithms

Analog Quantum Hardware

Room-temp optical quantum computing¹
  1. Krastanov et al.
    Room-temperature photonic logical qubits via second-order nonlinearities
Room-temp optical quantum computing¹
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 et al. (me as last author)
    All-Photonic Artificial Neural Network Processor Via Non-linear Optics
Room-temp optical quantum computing¹
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 et al. (me as last author)
    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
Room-temp optical quantum computing¹
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 et al. (me as last author)
    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 [...]
Room-temp optical quantum computing¹
Near-term² photonic hardware and accelerators for classical computation³
Control⁴ and networking⁵ of microwave devices
Spin-mechanics interfaces⁶
Learning hardware parameters⁷⁸
  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 et al. (me as last author)
    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 [...]
  7. Krastanov et al.
    Stochastic estimation of dynamical variables
  8. Krastanov et al.
    Unboxing Quantum Black Box Models [...]

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.

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 et al. (me as last author)
    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 et al. (me as last author)
    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 et al. (me as last author)
    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 [...]

Digital Quantum Hardware

Optimized Entanglement Purification

Alice has a qubit
Alice has a qubit
Bob too
They can be entangled! \[\begin{aligned} A=|\phi_{+}\rangle=\frac{|00\rangle+|11\rangle}{\sqrt{2}}\\ B=|\psi_{-}\rangle=\frac{|01\rangle-|10\rangle}{\sqrt{2}}\\ C=|\psi_{+}\rangle=\frac{|01\rangle+|10\rangle}{\sqrt{2}}\\ D=|\phi_{-}\rangle=\frac{|00\rangle-|11\rangle}{\sqrt{2}} \end{aligned}\]
They can be entangled! \[\begin{aligned} A=|\phi_{+}\rangle=\frac{|00\rangle+|11\rangle}{\sqrt{2}}\\ B=|\psi_{-}\rangle=\frac{|01\rangle-|10\rangle}{\sqrt{2}}\\ C=|\psi_{+}\rangle=\frac{|01\rangle+|10\rangle}{\sqrt{2}}\\ D=|\phi_{-}\rangle=\frac{|00\rangle-|11\rangle}{\sqrt{2}} \end{aligned}\]
Hidden Variable theories¹
  1. Krastanov et al.
    Art installation on Non-contextual Hidden Variable theories

They can be noisy!

Desired:

\[\begin{aligned} A=\frac{|00\rangle+|11\rangle}{\sqrt{2}}\\ \end{aligned}\]

The hardware generated:

90% chance for \[\begin{aligned} A=\frac{|00\rangle+|11\rangle}{\sqrt{2}}\\ \end{aligned}\] 10% chance for a bit flip on Bob's qubit \[\begin{aligned} C=\frac{|01\rangle+|10\rangle}{\sqrt{2}}\\ \end{aligned}\]

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
\[\begin{aligned} A\propto|00\rangle+|11\rangle\\ B\propto|01\rangle-|10\rangle\\ C\propto|01\rangle+|10\rangle\\ D\propto|00\rangle-|11\rangle \end{aligned}\]
Purification as error propagation and detection
\[\begin{aligned} A\propto|00\rangle+|11\rangle\\ B\propto|01\rangle-|10\rangle\\ C\propto|01\rangle+|10\rangle\\ D\propto|00\rangle-|11\rangle \end{aligned}\]
Purification as reshuffling of probabilities
\[\begin{aligned} A\propto|00\rangle+|11\rangle\\ B\propto|01\rangle-|10\rangle\\ C\propto|01\rangle+|10\rangle\\ D\propto|00\rangle-|11\rangle \end{aligned}\]
Purification as reshuffling of probabilities
Possible coincidence measurements

... How are we going to find the "good" permutation?
What if we want multi-sacrifice circuit?

Discrete Optimization: Evolutionary Algorithm

Discrete Optimization: Evolutionary Algorithm

Mutations

Discrete Optimization: Evolutionary Algorithm

Mutations
Offspring circuits
(a) best previously known circuit (b) our optimized circuit¹
(c) resource usage for each
  1. Krastanov et al.
    Optimized Entanglement Purification
A collection of optimized circuits at qevo.krastanov.org¹
  1. Krastanov et al.
    Optimized Entanglement Purification
Optimized circuits for purification¹, better than any known circuits.
  1. Krastanov et al.
    Optimized Entanglement Purification

Continuing and Future Projects

Continuing and Future Projects

Purification of more general resource states¹²

Clifford simulators orders of magnitude better than alternatives²

Rigorous theory bounds on purification performance³

  1. Krastanov et al.
    Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices
  2. me and undergrads under my advisement
    QuantumClifford.jl software package
  3. recently started conversation with colleagues at Delft

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

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
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
Switching to noisy Clifford simulation for large scale circuits (preliminary results)
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.